{ "entities": [ { "kind": "module", "id": "Semantics.AMMR", "name": "AMMR", "path": "Semantics/AMMR.lean", "namespace": "Semantics.AMMR", "doc": "inductive CarrierKind | cpu | fpga | pcie | quantumAccelerator | grid | shell deriving Repr, DecidableEq, BEq /-- Finite RGFlow verdict classes for the AMMR wrapper.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 9, "def_count": 22, "struct_count": 5, "inductive_count": 3, "line_count": 286 }, { "kind": "theorem", "id": "Semantics.AMMR.projectK_preservesInvariant", "name": "projectK_preservesInvariant", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.rgflowStrip_preservesInvariant", "name": "rgflowStrip_preservesInvariant", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.quaternionReductionUpdate_preservesInvariant", "name": "quaternionReductionUpdate_preservesInvariant", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.defaultCarrierHealthValid", "name": "defaultCarrierHealthValid", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.defaultAMMRStepLawful", "name": "defaultAMMRStepLawful", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.rejectIncrementsMathScar", "name": "rejectIncrementsMathScar", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.defaultStripRetainsAllChannels", "name": "defaultStripRetainsAllChannels", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.torsionalTileQuaternion_isMediator", "name": "torsionalTileQuaternion_isMediator", "module": "Semantics.AMMR" }, { "kind": "theorem", "id": "Semantics.AMMR.ammrStateFromTorsionalTile_usesTileInvariant", "name": "ammrStateFromTorsionalTile_usesTileInvariant", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.zeroFailureMemory", "name": "zeroFailureMemory", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.defaultWitnessRoot", "name": "defaultWitnessRoot", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.defaultStripPolicy", "name": "defaultStripPolicy", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.defaultState", "name": "defaultState", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.invariantOf", "name": "invariantOf", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.projectK", "name": "projectK", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.rgflowStrip", "name": "rgflowStrip", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.rgflowStripRetainedChannels", "name": "rgflowStripRetainedChannels", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.validCarrierHealth", "name": "validCarrierHealth", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.rgflowStripLawful", "name": "rgflowStripLawful", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.verdictAllowsRoute", "name": "verdictAllowsRoute", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.rotorInverse", "name": "rotorInverse", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.quaternionMotion", "name": "quaternionMotion", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.quaternionReductionUpdate", "name": "quaternionReductionUpdate", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.updateFailureMemory", "name": "updateFailureMemory", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.ammrSafe", "name": "ammrSafe", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.ammrStep", "name": "ammrStep", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.torsionalTileQuaternion", "name": "torsionalTileQuaternion", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.torsionalOISCStep", "name": "torsionalOISCStep", "module": "Semantics.AMMR" }, { "kind": "def", "id": "Semantics.AMMR.torsionalTileDelta", "name": "torsionalTileDelta", "module": "Semantics.AMMR" }, { "kind": "module", "id": "Semantics.ASCIIArtCompetition", "name": "ASCIIArtCompetition", "path": "Semantics/ASCIIArtCompetition.lean", "namespace": "Semantics.ASCIIArtCompetition", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ASCIIArtCompetition.lean \u2014 ASCII Art Competition Scoring Replaces infra/ascii_art_competition.py scoring logic with a formal Lean module. 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Authors: Research Stack Team ASCIIArtStore.lean \u2014 ASCII Art Layout Analysis Replaces infra/ascii_art_store.py layout/diff logic with a formal Lean module. Defines ASCII art layout analysis and style detection algorithms. Per AGEN", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 7, "struct_count": 5, "inductive_count": 1, "line_count": 175 }, { "kind": "theorem", "id": "Semantics.ASCIIArtStore.lineCountEqualsHeight", "name": "lineCountEqualsHeight", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.zero", "name": "zero", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.one", "name": "one", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.ofFrac", "name": "ofFrac", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.detectStyle", "name": "detectStyle", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.analyzeLayout", "name": "analyzeLayout", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.computeAspectRatio", "name": "computeAspectRatio", "module": "Semantics.ASCIIArtStore" }, { "kind": "def", "id": "Semantics.ASCIIArtStore.hasConsistentLines", "name": "hasConsistentLines", "module": "Semantics.ASCIIArtStore" }, { "kind": "module", "id": "Semantics.ASCIIGen", "name": "ASCIIGen", "path": "Semantics/ASCIIGen.lean", "namespace": "Semantics.ASCIIGen", "doc": "structure ASCIIArtEntry where id : String -- Unique identifier name : String -- Human-readable name art : String -- ASCII art content width : Nat height : Nat kotCost : UInt32 -- Cost in KOT tokens category : String -- Category (e.g., \"animals\", \"fractals\", \"text\") encodingHash : String -- Has", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 3, "inductive_count": 0, "line_count": 200 }, { "kind": "def", "id": "Semantics.ASCIIGen.asciiArtDatabase", "name": "asciiArtDatabase", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.lookupASCIIArt", "name": "lookupASCIIArt", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.lookupASCIIArtByCategory", "name": "lookupASCIIArtByCategory", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.getASCIICategories", "name": "getASCIICategories", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.purchaseASCIIArt", "name": "purchaseASCIIArt", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.analyzeASCIIEncoding", "name": "analyzeASCIIEncoding", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.emptyASCIIDataAccumulator", "name": "emptyASCIIDataAccumulator", "module": "Semantics.ASCIIGen" }, { "kind": "def", "id": "Semantics.ASCIIGen.updateASCIIDataAccumulator", "name": "updateASCIIDataAccumulator", "module": "Semantics.ASCIIGen" }, { "kind": "module", "id": "Semantics.ASICTopology", "name": "ASICTopology", "path": "Semantics/ASICTopology.lean", "namespace": "Semantics.ASICTopology", "doc": "**Core Inversion:** Normal view: ASIC = specific chip, fixed function, limited use TopoASIC view: ASIC = topology of constrained transformations, routing surface, operation manifold, interfaceable substrate **Principle:** An ASIC is a crystallized algorithm; TopoASIC treats the crystal as terrain. ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 5, "def_count": 21, "struct_count": 15, "inductive_count": 6, "line_count": 867 }, { "kind": "theorem", "id": "Semantics.ASICTopology.findNode_some_if_exists", "name": "findNode_some_if_exists", "module": "Semantics.ASICTopology" }, { "kind": "theorem", "id": "Semantics.ASICTopology.findNode_none_if_not_exists", "name": "findNode_none_if_not_exists", "module": "Semantics.ASICTopology" }, { "kind": "theorem", "id": "Semantics.ASICTopology.findEdgesFrom_sourceId_correct", "name": "findEdgesFrom_sourceId_correct", "module": "Semantics.ASICTopology" }, { "kind": "theorem", "id": "Semantics.ASICTopology.arbitraryCompute_never_admissible", "name": "arbitraryCompute_never_admissible", "module": "Semantics.ASICTopology" }, { "kind": "theorem", "id": "Semantics.ASICTopology.checkOperationAdmissibility_deterministic", "name": "checkOperationAdmissibility_deterministic", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.rtl8126Topology", "name": "rtl8126Topology", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.findNode", "name": "findNode", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.findEdgesFrom", "name": "findEdgesFrom", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.geodesicDistance", "name": "geodesicDistance", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.findOptimalPath", "name": "findOptimalPath", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.checkOperationAdmissibility", "name": "checkOperationAdmissibility", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.checkWorkloadAdmissibility", "name": "checkWorkloadAdmissibility", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.applyAngrySphinxGate", "name": "applyAngrySphinxGate", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.projectWorkloadToTopology", "name": "projectWorkloadToTopology", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.createASICToManifoldMapping", "name": "createASICToManifoldMapping", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.createManifoldToASICMapping", "name": "createManifoldToASICMapping", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.translateManifoldToASIC", "name": "translateManifoldToASIC", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.translateASICToManifold", "name": "translateASICToManifold", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicOptimizedAddressTranslation", "name": "asicOptimizedAddressTranslation", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicOptimizedChecksum", "name": "asicOptimizedChecksum", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.performASICOptimizedOperation", "name": "performASICOptimizedOperation", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicInputInvariant", "name": "asicInputInvariant", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicOutputInvariant", "name": "asicOutputInvariant", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicOperationCost", "name": "asicOperationCost", "module": "Semantics.ASICTopology" }, { "kind": "def", "id": "Semantics.ASICTopology.asicBind", "name": "asicBind", "module": "Semantics.ASICTopology" }, { "kind": "module", "id": "Semantics.AVM", "name": "AVM", "path": "Semantics/AVM.lean", "namespace": "Semantics.AVM", "doc": "inductive Value where | int : Int \u2192 Value | q16 : Q16_16 \u2192 Value | q0 : Q0_16 \u2192 Value | bool : Bool \u2192 Value | label : Nat \u2192 Value deriving Repr, BEq /-- AVM Instruction Set Extended with arithmetic, comparison, stack manipulation, memory access, and halt for the Erd\u0151s\u2013Tur\u00e1n AVM program.", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 2, "line_count": 157 }, { "kind": "def", "id": "Semantics.AVM.setMemory", "name": "setMemory", "module": "Semantics.AVM" }, { "kind": "def", "id": "Semantics.AVM.bindStep", "name": "bindStep", "module": "Semantics.AVM" }, { "kind": "def", "id": "Semantics.AVM.step", "name": "step", "module": "Semantics.AVM" }, { "kind": "def", "id": "Semantics.AVM.run", "name": "run", "module": "Semantics.AVM" }, { "kind": "def", "id": "Semantics.AVM.runTrace", "name": "runTrace", "module": "Semantics.AVM" }, { "kind": "module", "id": "Semantics.AVMIsa.Emit", "name": "Emit", "path": "Semantics/AVMIsa/Emit.lean", "namespace": "Semantics.AVMIsa.Emit", "doc": "AVM ISA v1 \u2014 Goal A: run a canary, construct an RRC record, emit JSON.", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 1, "inductive_count": 0, "line_count": 263 }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.progNot", "name": "progNot", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.progAnd", "name": "progAnd", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.progOr", "name": "progOr", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.initState", "name": "initState", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.checkTopBool", "name": "checkTopBool", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.canaryReceipt", "name": "canaryReceipt", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.canaryReceipts", "name": "canaryReceipts", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.canaryLogogramReceipt", "name": "canaryLogogramReceipt", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonBool", "name": "jsonBool", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonStr", "name": "jsonStr", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonReceiptKind", "name": "jsonReceiptKind", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonReceipt", "name": "jsonReceipt", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonRRCShape", "name": "jsonRRCShape", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": "Semantics.AVMIsa.Emit.jsonRegime", "name": "jsonRegime", "module": "Semantics.AVMIsa.Emit" }, { "kind": "def", "id": 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Split from AVMRProofs.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 1, "line_count": 28 }, { "kind": "def", "id": "Semantics.AVMRClassification.classifyEvent", "name": "classifyEvent", "module": "Semantics.AVMRClassification" }, { "kind": "mathlib", "id": "Mathlib", "name": "Mathlib" }, { "kind": "module", "id": "Semantics.AVMRCore", "name": "AVMRCore", "path": "Semantics/AVMRCore.lean", "namespace": "", "doc": "Shell decomposition foundation structures and functions. Split from AVMRProofs.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "avm", "sorry_count": 0, "theorem_count": 2, "def_count": 1, "struct_count": 2, "inductive_count": 0, "line_count": 52 }, { "kind": "theorem", "id": "Semantics.AVMRCore.squareShellIdentity", "name": "squareShellIdentity", "module": "Semantics.AVMRCore" }, { "kind": "theorem", "id": "Semantics.AVMRCore.complementaryIdentity", "name": "complementaryIdentity", "module": "Semantics.AVMRCore" }, { "kind": "def", "id": "Semantics.AVMRCore.shellState", "name": "shellState", "module": "Semantics.AVMRCore" }, { "kind": "module", "id": "Semantics.AVMRInformation", "name": "AVMRInformation", "path": "Semantics/AVMRInformation.lean", "namespace": "", "doc": "Information-theoretic consequences and genetic code connections. Split from AVMRProofs.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 3, "def_count": 2, "struct_count": 0, "inductive_count": 1, "line_count": 152 }, { "kind": "theorem", "id": "Semantics.AVMRInformation.shellEntropyBound", "name": "shellEntropyBound", "module": "Semantics.AVMRInformation" }, { "kind": "theorem", "id": "Semantics.AVMRInformation.totalCodons", "name": "totalCodons", "module": "Semantics.AVMRInformation" }, { "kind": "theorem", "id": "Semantics.AVMRInformation.avgDegeneracyCloseToE", "name": "avgDegeneracyCloseToE", "module": "Semantics.AVMRInformation" }, { "kind": "def", "id": "Semantics.AVMRInformation.shellEntropy", "name": "shellEntropy", "module": "Semantics.AVMRInformation" }, { "kind": "def", "id": "Semantics.AVMRInformation.degeneracy", "name": "degeneracy", "module": "Semantics.AVMRInformation" }, { "kind": "module", "id": "Semantics.AVMRProofs", "name": "AVMRProofs", "path": "Semantics/AVMRProofs.lean", "namespace": "", "doc": "AVMR (Algebraic Vector Mountain Range) - Proof Completion ======================================================== This module re-exports the three admitted AVMR theorems from split modules: 1. tipCoordinateMassResonance - Shell position determines mass resonance 2. fortyFiveLineFactorRevelation - T", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 34 }, { "kind": "module", "id": "Semantics.AVMRTheorems", "name": "AVMRTheorems", "path": "Semantics/AVMRTheorems.lean", "namespace": "", "doc": "The three main AVMR theorems: Tip Coordinate Mass Resonance, 45\u00b0 Line Factor Revelation, and Missing Link ODE. Split from AVMRProofs.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 10, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 333 }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.tipCoordinateMassResonance", "name": "tipCoordinateMassResonance", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.massMidpoint", "name": "massMidpoint", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.fortyFiveLineFactorRevelation", "name": "fortyFiveLineFactorRevelation", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.pronicFactorization", "name": "pronicFactorization", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.fortyFiveLineIsGC", "name": "fortyFiveLineIsGC", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.missingLinkODE", "name": "missingLinkODE", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.gradientFlowForm", "name": "gradientFlowForm", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.vectorField\u211d_lipschitz", "name": "vectorField\u211d_lipschitz", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.base_dynamics", "name": "base_dynamics", "module": "Semantics.AVMRTheorems" }, { "kind": "theorem", "id": "Semantics.AVMRTheorems.ode_existence", "name": "ode_existence", "module": "Semantics.AVMRTheorems" }, { "kind": "module", "id": "Semantics.AbelianSandpileRouting", "name": "AbelianSandpileRouting", "path": "Semantics/AbelianSandpileRouting.lean", "namespace": "Semantics.AbelianSandpileRouting", "doc": "# Abelian Sandpile Routing This module isolates the algebraic core of the proposed \"Millennium problem as routing\" framing. A neural sandpile state is represented as an integer-valued chip/load assignment over a finite neuron set. A firing/toppling at one neuron is a routing operator induced by a", "math_kind": "routing", "sorry_count": 0, "theorem_count": 10, "def_count": 17, "struct_count": 4, "inductive_count": 3, "line_count": 426 }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.refineModeWithForest_close_verified", "name": "refineModeWithForest_close_verified", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.chooseForestProfileRoute_address_range", "name": "chooseForestProfileRoute_address_range", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.selectMorphicMode_close", "name": "selectMorphicMode_close", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.selectMorphicMode_far", "name": "selectMorphicMode_far", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.chooseProfileRoute_close_action", "name": "chooseProfileRoute_close_action", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.allNeuronalProfiles_nonempty", "name": "allNeuronalProfiles_nonempty", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.totalLoad_topple", "name": "totalLoad_topple", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.topple_commute", "name": "topple_commute", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.runRoute_pair_swap", "name": "runRoute_pair_swap", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "theorem", "id": "Semantics.AbelianSandpileRouting.routingProof_sound", "name": "routingProof_sound", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.allNeuronalProfiles", "name": "allNeuronalProfiles", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.profilePattern", "name": "profilePattern", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.profileFamily", "name": "profileFamily", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.natAbsDiff", "name": "natAbsDiff", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.selectMorphicMode", "name": "selectMorphicMode", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.morphicModeToAction", "name": "morphicModeToAction", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.bin8OfNat", "name": "bin8OfNat", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.forestGenome", "name": "forestGenome", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.forestSignalsForProfile", "name": "forestSignalsForProfile", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.refineModeWithForest", "name": "refineModeWithForest", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.chooseProfileRoute", "name": "chooseProfileRoute", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.chooseForestProfileRoute", "name": "chooseForestProfileRoute", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.emittedLoad", "name": "emittedLoad", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.toppleDelta", "name": "toppleDelta", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.topple", "name": "topple", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.runRoute", "name": "runRoute", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "def", "id": "Semantics.AbelianSandpileRouting.totalLoad", "name": "totalLoad", "module": "Semantics.AbelianSandpileRouting" }, { "kind": "mathlib", "id": "Mathlib.Data.Fin.Basic", "name": "Mathlib.Data.Fin.Basic" }, { "kind": "module", "id": "Semantics.Adaptation", "name": "Adaptation", "path": "Semantics/Adaptation.lean", "namespace": "Semantics.Swarm", "doc": "Witnesses", "math_kind": "routing", "sorry_count": 0, "theorem_count": 2, "def_count": 15, "struct_count": 2, "inductive_count": 0, "line_count": 124 }, { "kind": "theorem", "id": "Semantics.Adaptation.flowAuditLoopFinalEqEventually", "name": "flowAuditLoopFinalEqEventually", "module": "Semantics.Adaptation" }, { "kind": "theorem", "id": "Semantics.Adaptation.finalLawfulEqEventuallyLawful", "name": "finalLawfulEqEventuallyLawful", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.Genome", "name": "Genome", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.isLawful", "name": "isLawful", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.betaStep", "name": "betaStep", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.isScaleCoherent", "name": "isScaleCoherent", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.flowAuditLoop", "name": "flowAuditLoop", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.flowAudit", "name": "flowAudit", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.witnessLowNe", "name": "witnessLowNe", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.witnessAttractor", "name": "witnessAttractor", "module": "Semantics.Adaptation" }, { "kind": "def", "id": "Semantics.Adaptation.witnessBoundary", "name": "witnessBoundary", "module": "Semantics.Adaptation" }, { "kind": "module", "id": "Semantics.Adapters.AlphaProofNexus.Bridge", "name": "Bridge", "path": "Semantics/Adapters/AlphaProofNexus/Bridge.lean", "namespace": "", "doc": "# AlphaProof Nexus Integration \u2014 Custom Approach Integrates the results from AlphaProof Nexus (Google DeepMind, May 2026) into the Semantics infrastructure using our Sidon/Diophantine framework. Key Result: Erd\u0151s #152 \u2014 Sidon isolated points theorem. Archived proofs in Adapters/AlphaProofNexus/.", "math_kind": "number_theory", "sorry_count": 1, "theorem_count": 1, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 46 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.Bridge.apn_bridge_reference", "name": "apn_bridge_reference", "module": "Semantics.Adapters.AlphaProofNexus.Bridge" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.Bridge.sumset", "name": "sumset", "module": "Semantics.Adapters.AlphaProofNexus.Bridge" }, { "kind": "mathlib", "id": "Mathlib.Data.Finset.Basic", "name": "Mathlib.Data.Finset.Basic" }, { "kind": "module", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction", "name": "bipartite_reconstruction", "path": "Semantics/Adapters/AlphaProofNexus/bipartite_reconstruction.lean", "namespace": "", "doc": "Copyright 2026 Google LLC Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 52, "def_count": 14, "struct_count": 1, "inductive_count": 0, "line_count": 1332 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.isBipartiteWith_deleteIncidenceSet", "name": "isBipartiteWith_deleteIncidenceSet", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degreeProfile_eq", "name": "degreeProfile_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.multiset_map_eq_implies_bij", "name": "multiset_map_eq_implies_bij", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.BipartiteIso_edgeCount", "name": "BipartiteIso_edgeCount", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.edgeCount_deleteIncidenceSet", "name": "edgeCount_deleteIncidenceSet", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.classEdgeCount_eq", "name": "classEdgeCount_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.bipartiteDeck_edgeCountDeck", "name": "bipartiteDeck_edgeCountDeck", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.sum_edgeCount_deleteIncidenceSet", "name": "sum_edgeCount_deleteIncidenceSet", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.sum_classEdgeCount_deck", "name": "sum_classEdgeCount_deck", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.multiset_sum_eq", "name": "multiset_sum_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.bipartiteDeck_determines_edgeCount", "name": "bipartiteDeck_determines_edgeCount", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.deck_edgeCounts_eq", "name": "deck_edgeCounts_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degreeMultiset_eq_map_edgeCount", "name": "degreeMultiset_eq_map_edgeCount", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.bipartiteDeck_determines_degreeMultiset", "name": "bipartiteDeck_determines_degreeMultiset", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degreeMultiset_eq_of_bipartiteIso", "name": "degreeMultiset_eq_of_bipartiteIso", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degree_deleteIncidenceSet", "name": "degree_deleteIncidenceSet", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.count_degreeMultiset", "name": "count_degreeMultiset", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.count_degreeMultiset_del", "name": "count_degreeMultiset_del", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.count_degreeProfile_eq", "name": "count_degreeProfile_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.sum_indicator_eq", "name": "sum_indicator_eq", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.count_degreeMultiset_deleteIncidenceSet_add", "name": "count_degreeMultiset_deleteIncidenceSet_add", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.eq_of_add_eq_add_succ", "name": "eq_of_add_eq_add_succ", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.count_degreeProfile_eq_zero", "name": "count_degreeProfile_eq_zero", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.profile_eq_of_iso", "name": "profile_eq_of_iso", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.unique_isolated_of_2_connected", "name": "unique_isolated_of_2_connected", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.iso_maps_isolated", "name": "iso_maps_isolated", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.f_preserves_partitions", "name": "f_preserves_partitions", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.connected_of_induce_connected", "name": "connected_of_induce_connected", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.unique_isolated_mapped", "name": "unique_isolated_mapped", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.deleteIncidenceSet_induce_connected", "name": "deleteIncidenceSet_induce_connected", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.bipartiteDeck", "name": "bipartiteDeck", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degreeProfile", "name": "degreeProfile", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.\u03c4", "name": "\u03c4", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.R", "name": "R", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.doubleDeck", "name": "doubleDeck", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.BipartiteIso_refl", "name": "BipartiteIso_refl", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.BipartiteIso_symm", "name": "BipartiteIso_symm", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.degreeMultiset", "name": "degreeMultiset", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.typeDrop", "name": "typeDrop", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.rightV_types", "name": "rightV_types", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.S_multiset", "name": "S_multiset", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.T_multiset", "name": "T_multiset", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction.typeProfile", "name": "typeProfile", "module": "Semantics.Adapters.AlphaProofNexus.bipartite_reconstruction" }, { "kind": "module", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i", "name": "i", "path": "Semantics/Adapters/AlphaProofNexus/erdos_12.parts.i.lean", "namespace": "Erdos12", "doc": "Copyright 2025 Google LLC Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 68, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 1238 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.exists_prime_bounded", "name": "exists_prime_bounded", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.q_prime", "name": "q_prime", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.q_gt", "name": "q_gt", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.q_ge_5", "name": "q_ge_5", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.K_pos", "name": "K_pos", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.P_pos", "name": "P_pos", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.M_succ", "name": "M_succ", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.pow_eight_le", "name": "pow_eight_le", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.M_increasing", "name": "M_increasing", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": 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"Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.mod_3_eq_1", "name": "mod_3_eq_1", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.prime_dvd_K", "name": "prime_dvd_K", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.K_q_coprime", "name": "K_q_coprime", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.K_ge_3", "name": "K_ge_3", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.P_dvd_M", "name": "P_dvd_M", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.K_dvd_P", "name": "K_dvd_P", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.q_dvd_P", "name": "q_dvd_P", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.K_dvd_M", "name": "K_dvd_M", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.q_dvd_M", "name": "q_dvd_M", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.pow_four_le", "name": "pow_four_le", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.i.x_val_lt_P", "name": "x_val_lt_P", "module": 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You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 28, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 795 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.not_infinite_iff_eventually", "name": "not_infinite_iff_eventually", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_case_same", "name": "sarkozy_case_same", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_case_diff2", "name": "sarkozy_case_diff2", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_case_diff1", "name": "sarkozy_case_diff1", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_implies_good", "name": "sarkozy_implies_good", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_seq_of_aux", "name": "sarkozy_seq_of_aux", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.sarkozy_primes", "name": "sarkozy_primes", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii.mod_eq_of_mod_mul", "name": "mod_eq_of_mod_mul", "module": "Semantics.Adapters.AlphaProofNexus.erdos_12.parts.ii" }, { "kind": "theorem", "id": 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You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 19, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 371 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.zero_in_A", "name": "zero_in_A", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.zero_in_B", "name": "zero_in_B", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.zero_in_A_plus_B", "name": "zero_in_A_plus_B", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.A_max_k", "name": "A_max_k", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.B_max_m", "name": "B_max_m", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.A_B_gap", "name": "A_B_gap", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density.A_decomp", "name": "A_decomp", "module": "Semantics.Adapters.AlphaProofNexus.erdos_125.variants.positive_lower_density" }, { "kind": "theorem", "id": 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You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 22, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 919 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference.ap_must_end", "name": "ap_must_end", "module": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference.extend_one_step", "name": "extend_one_step", "module": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference.has_mono_ap_ext", "name": "has_mono_ap_ext", "module": "Semantics.Adapters.AlphaProofNexus.erdos_138.variants.difference" }, { "kind": "theorem", "id": 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2025 Google LLC Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. 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compliance with the License. You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing,", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 107, "def_count": 7, "struct_count": 0, "inductive_count": 0, "line_count": 1505 }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i.split1_bound", "name": "split1_bound", "module": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i.split1_mod", "name": "split1_mod", "module": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i.B1_sum_mod", "name": "B1_sum_mod", "module": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.erdos_741.parts.i.split1_div", "name": "split1_div", "module": 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under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. 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may not use this file except in compliance with the License. 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"Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.witness_phi_in_base\u03a6", "name": "witness_phi_in_base\u03a6", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.sum_zmod3_eq_c", "name": "sum_zmod3_eq_c", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.functional_witness_phi_gt", "name": "functional_witness_phi_gt", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.base\u03a6_bddAbove", "name": "base\u03a6_bddAbove", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.supportFn_\u03a6_gt_5", "name": "supportFn_\u03a6_gt_5", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": 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"Eisen_toComplex_mul", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Eisen_toComplex_star", "name": "Eisen_toComplex_star", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.normSq_w_root_poly", "name": "normSq_w_root_poly", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Eisen_toComplex_normSq", "name": "Eisen_toComplex_normSq", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "theorem", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Eisen_toComplex_re_double", "name": "Eisen_toComplex_re_double", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.tripleKernel", "name": "tripleKernel", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.base\u03a6", "name": "base\u03a6", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.\u03a6", "name": "\u03a6", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.functional", "name": "functional", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.supportFn", "name": "supportFn", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.a_vec", "name": "a_vec", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.witness_f1", "name": "witness_f1", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.witness_f2", "name": "witness_f2", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.witness_f3", "name": "witness_f3", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.witness_phi", "name": "witness_phi", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.w_root", "name": "w_root", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Uhat", "name": "Uhat", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Vhat", "name": "Vhat", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.What", "name": "What", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "def", "id": "Semantics.Adapters.AlphaProofNexus.green_57.Eisen", "name": "Eisen", "module": "Semantics.Adapters.AlphaProofNexus.green_57" }, { "kind": "module", "id": "Semantics.Adapters.ErgodicAdditive", "name": "ErgodicAdditive", "path": "Semantics/Adapters/ErgodicAdditive.lean", "namespace": "", "doc": "# Ergodic\u2013Additive Adapter Bridge Connects the ergodic/dynamical kernel (Dim 2: Obscure Math) to the additive combinatorics kernel (Dim 1: Combinatorics) and the Diophantine kernel (Dim 0: Number Theory). ## Background The paper `math/0608105` \"Ergodic Methods in Additive Combinatorics\" and the a", "math_kind": "number_theory", "sorry_count": 1, "theorem_count": 3, "def_count": 1, "struct_count": 1, "inductive_count": 0, "line_count": 102 }, { "kind": "theorem", "id": "Semantics.Adapters.ErgodicAdditive.for", "name": "for", "module": "Semantics.Adapters.ErgodicAdditive" }, { "kind": "theorem", "id": "Semantics.Adapters.ErgodicAdditive.ergodic_additive_diophantine_triangle", "name": "ergodic_additive_diophantine_triangle", "module": "Semantics.Adapters.ErgodicAdditive" }, { "kind": "theorem", "id": "Semantics.Adapters.ErgodicAdditive.polynomial_method_adapter", "name": "polynomial_method_adapter", "module": "Semantics.Adapters.ErgodicAdditive" }, { "kind": "def", "id": "Semantics.Adapters.ErgodicAdditive.upperBanachDensity", "name": "upperBanachDensity", "module": "Semantics.Adapters.ErgodicAdditive" }, { "kind": "module", "id": "Semantics.Adapters.SidonMatroid", "name": "SidonMatroid", "path": "Semantics/Adapters/SidonMatroid.lean", "namespace": "", "doc": "# Sidon\u2013Matroid Adapter Bridge Connects the Sidon-set kernel (Dim 0: Diophantine/Number Theory) to the matroid kernel (Dim 1: Combinatorics).", "math_kind": "number_theory", "sorry_count": 1, "theorem_count": 5, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 108 }, { "kind": "theorem", "id": "Semantics.Adapters.SidonMatroid.sidonIndep_empty", "name": "sidonIndep_empty", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "theorem", "id": "Semantics.Adapters.SidonMatroid.sidonIndep_hereditary", "name": "sidonIndep_hereditary", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "theorem", "id": "Semantics.Adapters.SidonMatroid.sidonRank_eq_max_card", "name": "sidonRank_eq_max_card", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "theorem", "id": "Semantics.Adapters.SidonMatroid.sidon_matroid_bridge", "name": "sidon_matroid_bridge", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "theorem", "id": "Semantics.Adapters.SidonMatroid.sidon_set_size_bound", "name": "sidon_set_size_bound", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "def", "id": "Semantics.Adapters.SidonMatroid.sidonIndep", "name": "sidonIndep", "module": "Semantics.Adapters.SidonMatroid" }, { "kind": "module", "id": "Semantics.AdjugateMatrix", "name": "AdjugateMatrix", "path": "Semantics/AdjugateMatrix.lean", "namespace": "Semantics.AdjugateMatrix", "doc": "Semantics.AdjugateMatrix \u2014 Division-free matrix inversion via the adjugate method", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 20, "def_count": 27, "struct_count": 0, "inductive_count": 0, "line_count": 609 }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det_self_inverse_approx", "name": "det_self_inverse_approx", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.identity8_self_inverse", "name": "identity8_self_inverse", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.identity8_mul_self", "name": "identity8_mul_self", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det8_identity", "name": "det8_identity", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det_self_inverse_identity", "name": "det_self_inverse_identity", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cayley_transform_zero", "name": "cayley_transform_zero", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.adjugate_identity8", "name": "adjugate_identity8", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.adjugate_diag2m", "name": "adjugate_diag2m", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactorProductEntry_identity8_entry", "name": "cofactorProductEntry_identity8_entry", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactor_identity_diag2_entries", "name": "cofactor_identity_diag2_entries", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det8_diag2m_eq", "name": "det8_diag2m_eq", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det_self_inverse_exact_diag2_axiom", "name": "det_self_inverse_exact_diag2_axiom", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactorProductEntry_identity_clear", "name": "cofactorProductEntry_identity_clear", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactor_identity_identity_diag", "name": "cofactor_identity_identity_diag", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactor_identity_identity_offdiag", "name": "cofactor_identity_identity_offdiag", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactor_identity_diag2", "name": "cofactor_identity_diag2", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det_self_inverse_exact_diag2", "name": "det_self_inverse_exact_diag2", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.errorBound_from_energy", "name": "errorBound_from_energy", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.cofactor_identity_bound", "name": "cofactor_identity_bound", "module": "Semantics.AdjugateMatrix" }, { "kind": "theorem", "id": "Semantics.AdjugateMatrix.det_self_inverse_exact_from_cofactor", "name": "det_self_inverse_exact_from_cofactor", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.getEntry", "name": "getEntry", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.getEntryQ", "name": "getEntryQ", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.minorQ", "name": "minorQ", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.detQ", "name": "detQ", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det8", "name": "det8", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det7", "name": "det7", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det6", "name": "det6", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det5", "name": "det5", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det4", "name": "det4", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det3", "name": "det3", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.det2", "name": "det2", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.minor8", "name": "minor8", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.cofactor8", "name": "cofactor8", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.adjugate", "name": "adjugate", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.matrixMultiply", "name": "matrixMultiply", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.matrixInverse", "name": "matrixInverse", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.identity8", "name": "identity8", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.cayleyTransform", "name": "cayleyTransform", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.matrixApproxEq", "name": "matrixApproxEq", "module": "Semantics.AdjugateMatrix" }, { "kind": "def", "id": "Semantics.AdjugateMatrix.cofactorSign", "name": "cofactorSign", "module": "Semantics.AdjugateMatrix" }, { "kind": "module", "id": "Semantics.AffineMappingLTSF", "name": "AffineMappingLTSF", "path": "Semantics/AffineMappingLTSF.lean", "namespace": "Semantics.AffineMappingLTSF", "doc": "# Affine Mapping for Long-Term Time Series Forecasting This module formalizes the affine mapping equations for long-term time series forecasting (LTSF). The paper \"Revisiting long-term time series forecasting: an investigation on affine mapping\" demonstrates that simple linear layers (affine transf", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 11, "struct_count": 5, "inductive_count": 0, "line_count": 160 }, { "kind": "theorem", "id": "Semantics.AffineMappingLTSF.scaledPeriodic_zero_scaling_is_constant", "name": "scaledPeriodic_zero_scaling_is_constant", "module": "Semantics.AffineMappingLTSF" }, { "kind": "theorem", "id": "Semantics.AffineMappingLTSF.affineTransform_zero_input_zero_weights_zero_output", "name": "affineTransform_zero_input_zero_weights_zero_output", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.affineTransform", "name": "affineTransform", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.decomposeTimeSeries", "name": "decomposeTimeSeries", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.reconstructTimeSeries", "name": "reconstructTimeSeries", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.periodicConditionSatisfied", "name": "periodicConditionSatisfied", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.applyScaledPeriodic", "name": "applyScaledPeriodic", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.initAffineMappingState", "name": "initAffineMappingState", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.periodicConditionBind", "name": "periodicConditionBind", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.scaledPeriodicBind", "name": "scaledPeriodicBind", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.affineMappingBind", "name": "affineMappingBind", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.zeroLayer", "name": "zeroLayer", "module": "Semantics.AffineMappingLTSF" }, { "kind": "def", "id": "Semantics.AffineMappingLTSF.sampleAffineState", "name": "sampleAffineState", "module": "Semantics.AffineMappingLTSF" }, { "kind": "mathlib", "id": "Mathlib.Tactic", "name": "Mathlib.Tactic" }, { "kind": "module", "id": "Semantics.AgentSwarmTemplateAlignment", "name": "AgentSwarmTemplateAlignment", "path": "Semantics/AgentSwarmTemplateAlignment.lean", "namespace": "Semantics.AgentSwarmTemplateAlignment", "doc": "# Agent Swarm Template Alignment This module translates external agent/swarm template patterns into the local AGENTS.md contract: * finite node kinds instead of open prompt routing; * explicit evaluation and receipt gates; * fail-closed `HOLD` when evidence is missing; * invalid receipts force `BL", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 5, "def_count": 10, "struct_count": 1, "inductive_count": 3, "line_count": 200 }, { "kind": "theorem", "id": "Semantics.AgentSwarmTemplateAlignment.classifyTemplateNeverReviewed", "name": "classifyTemplateNeverReviewed", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "theorem", "id": "Semantics.AgentSwarmTemplateAlignment.noReceiptsHold", "name": "noReceiptsHold", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "theorem", "id": "Semantics.AgentSwarmTemplateAlignment.invalidReceiptBlocks", "name": "invalidReceiptBlocks", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "theorem", "id": "Semantics.AgentSwarmTemplateAlignment.codeReviewGraphCandidate", "name": "codeReviewGraphCandidate", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "theorem", "id": "Semantics.AgentSwarmTemplateAlignment.unsafeSupportGraphHeld", "name": "unsafeSupportGraphHeld", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.hasBoundary", "name": "hasBoundary", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.needsEvaluation", "name": "needsEvaluation", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.needsApproval", "name": "needsApproval", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.requiredReceiptKinds", "name": "requiredReceiptKinds", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.graphStructurallyLawful", "name": "graphStructurallyLawful", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.hasPromotionReceipts", "name": "hasPromotionReceipts", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.classifyTemplate", "name": "classifyTemplate", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.codeReviewGraph", "name": "codeReviewGraph", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.codeReviewReceipts", "name": "codeReviewReceipts", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "def", "id": "Semantics.AgentSwarmTemplateAlignment.unsafeSupportGraph", "name": "unsafeSupportGraph", "module": "Semantics.AgentSwarmTemplateAlignment" }, { "kind": "module", "id": "Semantics.AgenticCore", "name": "AgenticCore", "path": "Semantics/AgenticCore.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "Core agent types, states, and tasks for orchestration. Split from AgenticOrchestration.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 2, "line_count": 106 }, { "kind": "def", "id": "Semantics.AgenticCore.name", "name": "name", "module": "Semantics.AgenticCore" }, { "kind": "def", "id": "Semantics.AgenticCore.capabilities", "name": "capabilities", "module": "Semantics.AgenticCore" }, { "kind": "def", "id": "Semantics.AgenticCore.researchPipeline", "name": "researchPipeline", "module": "Semantics.AgenticCore" }, { "kind": "mathlib", "id": "Mathlib.Data.Nat.Basic", "name": "Mathlib.Data.Nat.Basic" }, { "kind": "module", "id": "Semantics.AgenticOrchestration", "name": "AgenticOrchestration", "path": "Semantics/AgenticOrchestration.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AgenticOrchestration.lean \u2014 Multi-Agent Coordination for Research Automation This module re-exports agentic orchestration components from split modules: Hardware-native agent structures (AgenticHardwar", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 20, "struct_count": 5, "inductive_count": 2, "line_count": 492 }, { "kind": "theorem", "id": "Semantics.AgenticOrchestration.researchPipelineIsAcyclic", "name": "researchPipelineIsAcyclic", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.create", "name": "create", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.send", "name": "send", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.receive", "name": "receive", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.deliver", "name": "deliver", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.flushOutbox", "name": "flushOutbox", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.inboxSize", "name": "inboxSize", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.empty", "name": "empty", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.registerMailbox", "name": "registerMailbox", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.findMailbox", "name": "findMailbox", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.updateMailbox", "name": "updateMailbox", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.deliveryCycle", "name": "deliveryCycle", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.totalPending", "name": "totalPending", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.agentTypeToDomain", "name": "agentTypeToDomain", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.domainToAgentType", "name": "domainToAgentType", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.agentStateToSpawnedSubagent", "name": "agentStateToSpawnedSubagent", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.agentStatesToSubagentSystem", "name": "agentStatesToSubagentSystem", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.allTasksCompleted", "name": "allTasksCompleted", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.hasCircularDependency", "name": "hasCircularDependency", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.DeadlockFreedom", "name": "DeadlockFreedom", "module": "Semantics.AgenticOrchestration" }, { "kind": "def", "id": "Semantics.AgenticOrchestration.StarvationFreedom", "name": "StarvationFreedom", "module": "Semantics.AgenticOrchestration" }, { "kind": "module", "id": "Semantics.AgenticOrchestrationField", "name": "AgenticOrchestrationField", "path": "Semantics/AgenticOrchestrationField.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "Orchestration field computation for agent coordination. Split from AgenticOrchestration.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 84 }, { "kind": "def", "id": "Semantics.AgenticOrchestrationField.agentField", "name": "agentField", "module": "Semantics.AgenticOrchestrationField" }, { "kind": "def", "id": "Semantics.AgenticOrchestrationField.coordinationField", "name": "coordinationField", "module": "Semantics.AgenticOrchestrationField" }, { "kind": "def", "id": "Semantics.AgenticOrchestrationField.teamOrchestrationField", "name": "teamOrchestrationField", "module": "Semantics.AgenticOrchestrationField" }, { "kind": "module", "id": "Semantics.AgenticTaskAssignment", "name": "AgenticTaskAssignment", "path": "Semantics/AgenticTaskAssignment.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "Task assignment and orchestration algorithm. Split from AgenticOrchestration.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 118 }, { "kind": "def", "id": "Semantics.AgenticTaskAssignment.assignTask", "name": "assignTask", "module": "Semantics.AgenticTaskAssignment" }, { "kind": "def", "id": "Semantics.AgenticTaskAssignment.dependenciesSatisfied", "name": "dependenciesSatisfied", "module": "Semantics.AgenticTaskAssignment" }, { "kind": "def", "id": "Semantics.AgenticTaskAssignment.readyTasks", "name": "readyTasks", "module": "Semantics.AgenticTaskAssignment" }, { "kind": "def", "id": "Semantics.AgenticTaskAssignment.orchestrationStep", "name": "orchestrationStep", "module": "Semantics.AgenticTaskAssignment" }, { "kind": "def", "id": "Semantics.AgenticTaskAssignment.runOrchestration", "name": "runOrchestration", "module": "Semantics.AgenticTaskAssignment" }, { "kind": "module", "id": "Semantics.AgenticTheorems", "name": "AgenticTheorems", "path": "Semantics/AgenticTheorems.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "lemma foldl_pred_mem {\u03b1 \u03b2 : Type} (p : \u03b1 \u2192 Prop) (q : \u03b2 \u2192 Prop) (f : \u03b1 \u2192 \u03b2 \u2192 \u03b1) (l : List \u03b2) (init : \u03b1) (h_list : \u2200 b \u2208 l, q b) (h_init : p init) (h_step : \u2200 a b, p a \u2192 q b \u2192 p (f a b)) : p (l.foldl f init) := by induction l generalizing init with | nil => exact h_init | cons head tail ih => simp [L", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 7, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 289 }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.foldl_pred_mem", "name": "foldl_pred_mem", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.assignmentRespectsCapabilities", "name": "assignmentRespectsCapabilities", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.dependenciesRespected", "name": "dependenciesRespected", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.orchestrationTermination", "name": "orchestrationTermination", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.synergyImprovesPerformance", "name": "synergyImprovesPerformance", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.agentFieldBounded", "name": "agentFieldBounded", "module": "Semantics.AgenticTheorems" }, { "kind": "theorem", "id": "Semantics.AgenticTheorems.loadPenaltyDecreasesField", "name": "loadPenaltyDecreasesField", "module": "Semantics.AgenticTheorems" }, { "kind": "module", "id": "Semantics.AnalysisFoundations", "name": "AnalysisFoundations", "path": "Semantics/AnalysisFoundations.lean", "namespace": "Semantics.AnalysisFoundations", "doc": "============================================================================", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 9, "def_count": 8, "struct_count": 0, "inductive_count": 1, "line_count": 214 }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.constant_continuous", "name": "constant_continuous", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.identity_continuous", "name": "identity_continuous", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.square_continuous", "name": "square_continuous", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.square_differentiable", "name": "square_differentiable", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.division_by_constant_differentiable", "name": "division_by_constant_differentiable", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.norm_squared_convex", "name": "norm_squared_convex", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.zero_lipschitz", "name": "zero_lipschitz", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.picard_lindelof", "name": "picard_lindelof", "module": "Semantics.AnalysisFoundations" }, { "kind": "theorem", "id": "Semantics.AnalysisFoundations.ode_uniqueness", "name": "ode_uniqueness", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.ContinuousAt", "name": "ContinuousAt", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.Continuous", "name": "Continuous", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.DifferentiableAt", "name": "DifferentiableAt", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.Differentiable", "name": "Differentiable", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.CInf", "name": "CInf", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.Convex", "name": "Convex", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.Lipschitz", "name": "Lipschitz", "module": "Semantics.AnalysisFoundations" }, { "kind": "def", "id": "Semantics.AnalysisFoundations.ODESolution", "name": "ODESolution", "module": "Semantics.AnalysisFoundations" }, { "kind": "module", "id": "Semantics.AngrySphinx", "name": "AngrySphinx", "path": "Semantics/AngrySphinx.lean", "namespace": "Semantics.AngrySphinx", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AngrySphinx.lean \u2014 Proof-of-Defense Primitive AngrySphinx is a lattice-based post-quantum protection system in which attack energy is exponentially transformed into solve-domain cost. Core theorem: E_", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 6, "inductive_count": 0, "line_count": 219 }, { "kind": "theorem", "id": "Semantics.AngrySphinx.solveEnergyExponential", "name": "solveEnergyExponential", "module": "Semantics.AngrySphinx" }, { "kind": "theorem", "id": "Semantics.AngrySphinx.nanBoundaryCorrect", "name": "nanBoundaryCorrect", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.frustrationUnderPressure", "name": "frustrationUnderPressure", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.landauerBitCost", "name": "landauerBitCost", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.defaultGearRatio", "name": "defaultGearRatio", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.gearProduct", "name": "gearProduct", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.gearProductQ", "name": "gearProductQ", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.solveEnergy", "name": "solveEnergy", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.solveDenominator", "name": "solveDenominator", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.initPod", "name": "initPod", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.accumulateWork", "name": "accumulateWork", "module": "Semantics.AngrySphinx" }, { "kind": "def", "id": "Semantics.AngrySphinx.verifyPod", "name": "verifyPod", "module": "Semantics.AngrySphinx" }, { "kind": "module", "id": "Semantics.AngrySphinxPolicy", "name": "AngrySphinxPolicy", "path": "Semantics/AngrySphinxPolicy.lean", "namespace": "Semantics", "doc": "structure AngrySphinxPolicy where scope : String allowedUse : List String forbiddenUse : List String domainBoundary : String consentRule : String receiptRule : String killSwitchRule : String reviewRequirement : String deriving Repr /-- Required policy gates for AngrySphinx compliance.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 1, "inductive_count": 1, "line_count": 73 }, { "kind": "def", "id": "Semantics.AngrySphinxPolicy.defaultAngrySphinxPolicy", "name": "defaultAngrySphinxPolicy", "module": "Semantics.AngrySphinxPolicy" }, { "kind": "def", "id": "Semantics.AngrySphinxPolicy.checkAngrySphinxCompliance", "name": "checkAngrySphinxCompliance", "module": "Semantics.AngrySphinxPolicy" }, { "kind": "def", "id": "Semantics.AngrySphinxPolicy.angrySphinxConstitutionalRule", "name": "angrySphinxConstitutionalRule", "module": "Semantics.AngrySphinxPolicy" }, { "kind": "def", "id": "Semantics.AngrySphinxPolicy.enforceAngrySphinxGate", "name": "enforceAngrySphinxGate", "module": "Semantics.AngrySphinxPolicy" }, { "kind": "def", "id": "Semantics.AngrySphinxPolicy.angrySphinxPolicyLayer", "name": "angrySphinxPolicyLayer", "module": "Semantics.AngrySphinxPolicy" }, { "kind": "module", "id": "Semantics.AnomalyDrift", "name": "AnomalyDrift", "path": "Semantics/AnomalyDrift.lean", "namespace": "Semantics.AnomalyDrift", "doc": "AnomalyDrift.lean \u2014 Modeling Physics Anomalies as Drift in Barrier Structures This module connects the observed anomalies (muon g-2, B\u2192K*\u03bc\u03bc, W mass) to the universal barrier-crossing framework. Key insight: Every anomaly is a \"drift\" \u2014 a deviation between the predicted barrier-crossing rate (SM) a", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 3, "inductive_count": 1, "line_count": 207 }, { "kind": "def", "id": "Semantics.AnomalyDrift.computeSigma", "name": "computeSigma", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.muon_g2_anomaly", "name": "muon_g2_anomaly", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.b_to_s_ll_anomaly", "name": "b_to_s_ll_anomaly", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.w_mass_anomaly", "name": "w_mass_anomaly", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.knownAnomalies", "name": "knownAnomalies", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.anomalyToDrift", "name": "anomalyToDrift", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.driftToScale", "name": "driftToScale", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.consistentWithCommonSource", "name": "consistentWithCommonSource", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.generateDriftReport", "name": "generateDriftReport", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.muon_drift", "name": "muon_drift", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.bphysics_drift", "name": "bphysics_drift", "module": "Semantics.AnomalyDrift" }, { "kind": "def", "id": "Semantics.AnomalyDrift.testReport", "name": "testReport", "module": "Semantics.AnomalyDrift" }, { "kind": "module", "id": "Semantics.AntiBraidStorm", "name": "AntiBraidStorm", "path": "Semantics/AntiBraidStorm.lean", "namespace": "Semantics.AntiBraidStorm", "doc": "AntiBraidStorm.lean \u2014 Adversarial Verification Layer for Braid Eigensolid Compressor This module implements the Anti-BraidStorm adversarial check, which validates: 1) Receipt invariant aliasing under topological equivalence 2) Yang-Baxter relation invariance under receipt encoding 3) Far-commutatio", "math_kind": "avm", "sorry_count": 0, "theorem_count": 9, "def_count": 7, "struct_count": 1, "inductive_count": 0, "line_count": 284 }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.braidState_ext", "name": "braidState_ext", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.step_count_invariant", "name": "step_count_invariant", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.sidon_slack_invariant", "name": "sidon_slack_invariant", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.crossing_matrix_admissible_invariant", "name": "crossing_matrix_admissible_invariant", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.scar_absent_invariant", "name": "scar_absent_invariant", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.execSwap_yang_baxter", "name": "execSwap_yang_baxter", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.execSwap_far_comm", "name": "execSwap_far_comm", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.yang_baxter_invariance", "name": "yang_baxter_invariance", "module": "Semantics.AntiBraidStorm" }, { "kind": "theorem", "id": "Semantics.AntiBraidStorm.far_commutation_invariance", "name": "far_commutation_invariance", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.detectAliasingViolation", "name": "detectAliasingViolation", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.execSwap", "name": "execSwap", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.execPath", "name": "execPath", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.yangBaxterTestCase", "name": "yangBaxterTestCase", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.farCommutationTestCase", "name": "farCommutationTestCase", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.ReceiptInvariant", "name": "ReceiptInvariant", "module": "Semantics.AntiBraidStorm" }, { "kind": "def", "id": "Semantics.AntiBraidStorm.runAdversarialTests", "name": "runAdversarialTests", "module": "Semantics.AntiBraidStorm" }, { "kind": "module", "id": "Semantics.AntiDiophantine", "name": "AntiDiophantine", "path": "Semantics/AntiDiophantine.lean", "namespace": "", "doc": "# Anti-Diophantine Constructions and the Sidon Intersection A **Diophantine** equation `P(x) = 0` has finitely many integer solutions (Baker). An **Anti-Diophantine** construction has infinitely many or dense solutions. Sidon sets `a\u1d62 + a\u2c7c = a\u2096 + a\u2097 \u21d2 {i,j} = {k,l}` live at the intersection: **Dio", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 10, "def_count": 6, "struct_count": 2, "inductive_count": 0, "line_count": 154 }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.sidonSlack_eq", "name": "sidonSlack_eq", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.canonicalSidonLabels_nonempty", "name": "canonicalSidonLabels_nonempty", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.canonicalSidonLabels_max", "name": "canonicalSidonLabels_max", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.canonical_labels_sidon", "name": "canonical_labels_sidon", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.canonical_sidon_slack", "name": "canonical_sidon_slack", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.sidon_agreement_upper", "name": "sidon_agreement_upper", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.sidon_agreement_lower", "name": "sidon_agreement_lower", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.sidon_agreement_theorem", "name": "sidon_agreement_theorem", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.slack_regime_transition", "name": "slack_regime_transition", "module": "Semantics.AntiDiophantine" }, { "kind": "theorem", "id": "Semantics.AntiDiophantine.diophantine_antiDiophantine_comparison", "name": "diophantine_antiDiophantine_comparison", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.IsDiophantineFamily", "name": "IsDiophantineFamily", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.IsAntiDiophantineFamily", "name": "IsAntiDiophantineFamily", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.sidonSlack", "name": "sidonSlack", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.isAntiDiophantineSlack", "name": "isAntiDiophantineSlack", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.isDiophantineSlack", "name": "isDiophantineSlack", "module": "Semantics.AntiDiophantine" }, { "kind": "def", "id": "Semantics.AntiDiophantine.canonicalSidonLabels", "name": "canonicalSidonLabels", "module": "Semantics.AntiDiophantine" }, { "kind": "mathlib", "id": "Mathlib.Data.Set.Basic", "name": "Mathlib.Data.Set.Basic" }, { "kind": "module", "id": "Semantics.AtomicResolution", "name": "AtomicResolution", "path": "Semantics/AtomicResolution.lean", "namespace": "Semantics.AtomicResolution", "doc": "Conservative witness for what atomic support remains distinguishable after compression. This does not identify chemistry; it only budgets distinguishable sites and bounded coordinate residual against an admissible environment witness.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 7, "struct_count": 1, "inductive_count": 0, "line_count": 127 }, { "kind": "theorem", "id": "Semantics.AtomicResolution.atomicallyAdmissibleOfBounds", "name": "atomicallyAdmissibleOfBounds", "module": "Semantics.AtomicResolution" }, { "kind": "theorem", "id": "Semantics.AtomicResolution.resolvedSitesLeBasisDim", "name": "resolvedSitesLeBasisDim", "module": "Semantics.AtomicResolution" }, { "kind": "theorem", "id": "Semantics.AtomicResolution.compressionContractsAtomicResolution", "name": "compressionContractsAtomicResolution", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.siteCovered", "name": "siteCovered", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.occupancyCovered", "name": "occupancyCovered", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.coordinateResidualBounded", "name": "coordinateResidualBounded", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.atomicallyAdmissible", "name": "atomicallyAdmissible", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.witnessOfEnvironment", "name": "witnessOfEnvironment", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.sampleAtomicEnvironment", "name": "sampleAtomicEnvironment", "module": "Semantics.AtomicResolution" }, { "kind": "def", "id": "Semantics.AtomicResolution.sampleAtomicResolutionWitness", "name": "sampleAtomicResolutionWitness", "module": "Semantics.AtomicResolution" }, { "kind": "module", "id": "Semantics.Atoms", "name": "Atoms", "path": "Semantics/Atoms.lean", "namespace": "Semantics", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 7, "inductive_count": 1, "line_count": 154 }, { "kind": "def", "id": "Semantics.Atoms.computeSemanticChristoffel", "name": "computeSemanticChristoffel", "module": "Semantics.Atoms" }, { "kind": "def", "id": "Semantics.Atoms.semanticCos", "name": "semanticCos", "module": "Semantics.Atoms" }, { "kind": "def", "id": "Semantics.Atoms.computeSemanticFrustration", "name": "computeSemanticFrustration", "module": "Semantics.Atoms" }, { "kind": "def", "id": "Semantics.Atoms.computeSemanticLockingEnergy", "name": "computeSemanticLockingEnergy", "module": "Semantics.Atoms" }, { "kind": "def", "id": "Semantics.Atoms.updateSemanticStateFromGeometry", "name": "updateSemanticStateFromGeometry", "module": "Semantics.Atoms" }, { "kind": "def", "id": "Semantics.Atoms.updateSemanticStateFromChristoffel", "name": "updateSemanticStateFromChristoffel", "module": "Semantics.Atoms" }, { "kind": "module", "id": "Semantics.Autobalance", "name": "Autobalance", "path": "Semantics/Autobalance.lean", "namespace": "Semantics.Autobalance", "doc": "NodeState: Represents the health of a research node.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 49 }, { "kind": "def", "id": "Semantics.Autobalance.isGrounded", "name": "isGrounded", "module": "Semantics.Autobalance" }, { "kind": "def", "id": "Semantics.Autobalance.balanceCost", "name": "balanceCost", "module": "Semantics.Autobalance" }, { "kind": "def", "id": "Semantics.Autobalance.balanceBind", "name": "balanceBind", "module": "Semantics.Autobalance" }, { "kind": "module", "id": "Semantics.BHOCS", "name": "BHOCS", "path": "Semantics/BHOCS.lean", "namespace": "Semantics.BHOCS", "doc": "TREE(3) is incomputable, but Kruskal's theorem proves it's finite We use a symbolic constant for the theoretical bound def maxDepth : Nat := 1000000000000 -- Symbolic placeholder for TREE(3) /-- Inner MMR with orthogonal projection", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 7, "struct_count": 6, "inductive_count": 0, "line_count": 109 }, { "kind": "theorem", "id": "Semantics.BHOCS.depth_bound", "name": "depth_bound", "module": "Semantics.BHOCS" }, { "kind": "theorem", "id": "Semantics.BHOCS.lookup_terminates", "name": "lookup_terminates", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.maxDepth", "name": "maxDepth", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.computeHash", "name": "computeHash", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.lookup", "name": "lookup", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.integrity_preserved", "name": "integrity_preserved", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.bhocsCost", "name": "bhocsCost", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.isLawful", "name": "isLawful", "module": "Semantics.BHOCS" }, { "kind": "def", "id": "Semantics.BHOCS.extractInvariant", "name": "extractInvariant", "module": "Semantics.BHOCS" }, { "kind": "module", "id": "Semantics.BaselineComparison", "name": "BaselineComparison", "path": "Semantics/BaselineComparison.lean", "namespace": "Semantics.BaselineComparison", "doc": "BaselineComparison.lean \u2014 BraidCore Predictions vs Standard Physics For every pre-registered prediction, this module states what standard, established physics predicts for the SAME observable, then classifies BraidCore's relationship to that baseline. Classification categories: `agrees` \u2014 B", "math_kind": "braid", "sorry_count": 0, "theorem_count": 15, "def_count": 24, "struct_count": 0, "inductive_count": 1, "line_count": 300 }, { "kind": "theorem", "id": "Semantics.BaselineComparison.for", "name": "for", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p01Relation_correct", "name": "p01Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p02Relation_correct", "name": "p02Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p03Relation_correct", "name": "p03Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p05Relation_correct", "name": "p05Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p07Relation_correct", "name": "p07Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p08Relation_correct", "name": "p08Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p10Relation_correct", "name": "p10Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p11Relation_correct", "name": "p11Relation_correct", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.p04Relation_withdrawn", "name": "p04Relation_withdrawn", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.countGoesBeyond", "name": "countGoesBeyond", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.countAgrees", "name": "countAgrees", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.countDisagrees", "name": "countDisagrees", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.countNoPrediction", "name": "countNoPrediction", "module": "Semantics.BaselineComparison" }, { "kind": "theorem", "id": "Semantics.BaselineComparison.totalClassified", "name": "totalClassified", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.BaselineRelation", "name": "BaselineRelation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p01StandardPhysics", "name": "p01StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p01Relation", "name": "p01Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p02StandardPhysics", "name": "p02StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p02Relation", "name": "p02Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p03StandardPhysics", "name": "p03StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p03Relation", "name": "p03Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p04StandardPhysics", "name": "p04StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p04Relation", "name": "p04Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p05StandardPhysics", "name": "p05StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p05Relation", "name": "p05Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p06StandardPhysics", "name": "p06StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p06Relation", "name": "p06Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p07StandardPhysics", "name": "p07StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p07Relation", "name": "p07Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p08StandardPhysics", "name": "p08StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p08Relation", "name": "p08Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p09StandardPhysics", "name": "p09StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p09Relation", "name": "p09Relation", "module": "Semantics.BaselineComparison" }, { "kind": "def", "id": "Semantics.BaselineComparison.p10StandardPhysics", "name": "p10StandardPhysics", "module": "Semantics.BaselineComparison" }, { "kind": "module", "id": "Semantics.Basic", "name": "Basic", "path": "Semantics/Basic.lean", "namespace": "Semantics.Basic", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 6, "inductive_count": 0, "line_count": 192 }, { "kind": "def", "id": "Semantics.Basic.computeBasicChristoffel", "name": "computeBasicChristoffel", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.basicCos", "name": "basicCos", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.computeBasicFrustration", "name": "computeBasicFrustration", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.computeBasicLockingEnergy", "name": "computeBasicLockingEnergy", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.updateBasicStateFromGeometry", "name": "updateBasicStateFromGeometry", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.updateBasicStateFromChristoffel", "name": "updateBasicStateFromChristoffel", "module": "Semantics.Basic" }, { "kind": "def", "id": "Semantics.Basic.hello", "name": "hello", "module": "Semantics.Basic" }, { "kind": "module", "id": "Semantics.BeaverMaskFreshness", "name": "BeaverMaskFreshness", "path": "Semantics/BeaverMaskFreshness.lean", "namespace": "Semantics.BeaverMaskFreshness", "doc": "is admissible for privacy-equivalent Beaver masking in this gate model.", "math_kind": "braid", "sorry_count": 0, "theorem_count": 6, "def_count": 10, "struct_count": 1, "inductive_count": 1, "line_count": 94 }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.freshUnusedAdmits", "name": "freshUnusedAdmits", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.distinctFreshSequenceAdmits", "name": "distinctFreshSequenceAdmits", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.reusedSourceRejected", "name": "reusedSourceRejected", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.reusedMaskIdRejected", "name": "reusedMaskIdRejected", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.topologyDerivedRejected", "name": "topologyDerivedRejected", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "theorem", "id": "Semantics.BeaverMaskFreshness.adversarialChosenRejected", "name": "adversarialChosenRejected", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.sourceFreshIndependent", "name": "sourceFreshIndependent", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.eventFreshIndependent", "name": "eventFreshIndependent", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.maskIdUsedBefore", "name": "maskIdUsedBefore", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.admissibleMaskEvent", "name": "admissibleMaskEvent", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.admitMaskEvent", "name": "admitMaskEvent", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.freshA", "name": "freshA", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.freshB", "name": "freshB", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.reusedA", "name": "reusedA", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.topologyA", "name": "topologyA", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "def", "id": "Semantics.BeaverMaskFreshness.adversarialA", "name": "adversarialA", "module": "Semantics.BeaverMaskFreshness" }, { "kind": "module", "id": "Semantics.Benchmarks.Grid17x17", "name": "Grid17x17", "path": "Semantics/Benchmarks/Grid17x17.lean", "namespace": "Semantics.Benchmarks.Grid17x17", "doc": "structure Grid where data : Fin 17 \u2192 Fin 17 \u2192 Fin 4 /-- A grid is Sabotaged if there exists a rectangle with monochrome corners. This is the informatic signature of \"Godzilla\" in the 17x17 space.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 66 }, { "kind": "theorem", "id": "Semantics.Benchmarks.Grid17x17.exists_lawful_grid", "name": "exists_lawful_grid", "module": "Semantics.Benchmarks.Grid17x17" }, { "kind": "def", "id": "Semantics.Benchmarks.Grid17x17.isSabotaged", "name": "isSabotaged", "module": "Semantics.Benchmarks.Grid17x17" }, { "kind": "def", "id": "Semantics.Benchmarks.Grid17x17.isLawful", "name": "isLawful", "module": "Semantics.Benchmarks.Grid17x17" }, { "kind": "def", "id": "Semantics.Benchmarks.Grid17x17.solutionGrid", "name": "solutionGrid", "module": "Semantics.Benchmarks.Grid17x17" }, { "kind": "module", "id": "Semantics.Benchmarks.HadwigerNelson", "name": "HadwigerNelson", "path": "Semantics/Benchmarks/HadwigerNelson.lean", "namespace": "", "doc": "The Moser spindle is known to be 4-chromatic; a computational proof would require exact coordinates and exhaustive search over 3^7 colorings. This is an external graph-theoretic fact.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 0, "line_count": 10 }, { "kind": "module", "id": "Semantics.BernoulliOccupancyShockbow", "name": "BernoulliOccupancyShockbow", "path": "Semantics/BernoulliOccupancyShockbow.lean", "namespace": "Semantics.BernoulliOccupancyShockbow", "doc": "Bernoulli occupancy and Shockbow gate for static decompressor replay. This module formalizes the small invariant surface from `BERNOULLI_OCCUPANCY_RECEIPT_MATH.md`. Claim boundary: this is integer receipt math for admission gates. It is not a compression-ratio claim and not a physical shockwave si", "math_kind": "avm", "sorry_count": 0, "theorem_count": 6, "def_count": 18, "struct_count": 2, "inductive_count": 1, "line_count": 189 }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.birthdayTripleAdmits", "name": "birthdayTripleAdmits", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.missingPriorHolds", "name": "missingPriorHolds", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.overCapacityQuarantines", "name": "overCapacityQuarantines", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.missingProofQuarantines", "name": "missingProofQuarantines", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.shockbowRejectQuarantines", "name": "shockbowRejectQuarantines", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "theorem", "id": "Semantics.BernoulliOccupancyShockbow.birthdayTripleInvariant", "name": "birthdayTripleInvariant", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.absDiff", "name": "absDiff", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.shockbowPass", "name": "shockbowPass", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.occupancyDenominator", "name": "occupancyDenominator", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.expectedExactNumerator", "name": "expectedExactNumerator", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.expectedAtLeastNumerator", "name": "expectedAtLeastNumerator", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.shapeValid", "name": "shapeValid", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.expectedFitsReplay", "name": "expectedFitsReplay", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.residualFits", "name": "residualFits", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.decideGate", "name": "decideGate", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.admittedInvariant", "name": "admittedInvariant", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.noShockbow", "name": "noShockbow", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.passingShockbow", "name": "passingShockbow", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.rejectingShockbow", "name": "rejectingShockbow", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.birthdayTripleFixture", "name": "birthdayTripleFixture", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.missingPriorFixture", "name": "missingPriorFixture", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.overCapacityFixture", "name": "overCapacityFixture", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.missingProofFixture", "name": "missingProofFixture", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "def", "id": "Semantics.BernoulliOccupancyShockbow.shockbowRejectFixture", "name": "shockbowRejectFixture", "module": "Semantics.BernoulliOccupancyShockbow" }, { "kind": "mathlib", "id": "Mathlib.Data.Nat.Choose.Basic", "name": "Mathlib.Data.Nat.Choose.Basic" }, { "kind": "module", "id": "Semantics.BigBangTemporalAnchor", "name": "BigBangTemporalAnchor", "path": "Semantics/BigBangTemporalAnchor.lean", "namespace": "Semantics.BigBangTemporalAnchor", "doc": "BigBangTemporalAnchor.lean -- Can the Big Bang Temporal Point Anchor P0? The user proposes: every cosmologist assigns a temporal point to the Big Bang (t = 0). This is a universally accepted origin. Can we derive P0 from this temporal point, making it physically motivated rather than fitted? 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A Metric measures the cost of lawful assemblage between two objects. All scalar fields use Q16.16 fixed-point for hardware-native execution. 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Authors: Research Stack Team QuaternionGenomic.lean \u2014 Quaternion-Based DNA Encoding for SLUG-3 Gates This module formalizes the PIST framework's SLUG-3 quaternion encoding: Each \"color\" = receipt-carrying fixed-point quaternion in", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 8, "def_count": 14, "struct_count": 1, "inductive_count": 0, "line_count": 275 }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.nucleotideQuaternionsCarryWitness", "name": "nucleotideQuaternionsCarryWitness", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.encodeSequenceCarriesWitness", "name": "encodeSequenceCarriesWitness", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.chiralIncompatibleBoolean", "name": "chiralIncompatibleBoolean", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.watsonCrickClassificationGate", "name": "watsonCrickClassificationGate", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.distanceMetricReceipt", "name": "distanceMetricReceipt", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.stochasticEvolutionPreservesUnitWitness", "name": "stochasticEvolutionPreservesUnitWitness", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.resonanceTunedRotationCarriesWitness", "name": "resonanceTunedRotationCarriesWitness", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "theorem", "id": "Semantics.Biology.QuaternionGenomic.stochasticQuaternionOptimizationPreservesUnitWitness", "name": "stochasticQuaternionOptimizationPreservesUnitWitness", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.nucleotideToQuaternion", "name": "nucleotideToQuaternion", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.quaternionToNucleotide", "name": "quaternionToNucleotide", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.slug3GenomicGate", "name": "slug3GenomicGate", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.genomicSlug3Threshold", "name": "genomicSlug3Threshold", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.isWatsonCrickPair", "name": "isWatsonCrickPair", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.encodeSequence", "name": "encodeSequence", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.sequenceDistanceCost", "name": "sequenceDistanceCost", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.quaternionCompressionRatio", "name": "quaternionCompressionRatio", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.parallelTransport", "name": "parallelTransport", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.torsionCurvature", "name": "torsionCurvature", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.primeIndexedQuaternion", "name": "primeIndexedQuaternion", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.stochasticEvolution", "name": "stochasticEvolution", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.resonanceTunedRotation", "name": "resonanceTunedRotation", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "def", "id": "Semantics.Biology.QuaternionGenomic.stochasticQuaternionOptimization", "name": "stochasticQuaternionOptimization", "module": "Semantics.Biology.QuaternionGenomic" }, { "kind": "module", "id": "Semantics.Biology.RGFlowBioinformatics", "name": "RGFlowBioinformatics", "path": "Semantics/Biology/RGFlowBioinformatics.lean", "namespace": "Semantics.RGFlowBioinformatics", "doc": "Genetic code mapping for codon to amino acid translation.", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 16, "struct_count": 4, "inductive_count": 0, "line_count": 374 }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.geneticCode", "name": "geneticCode", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.oncogenicCodons", "name": "oncogenicCodons", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.isKnownOncogenicCodon", "name": "isKnownOncogenicCodon", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.translateToAminoAcids", "name": "translateToAminoAcids", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.spectralDensity", "name": "spectralDensity", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.transitionRate", "name": "transitionRate", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.shannonEntropy", "name": "shannonEntropy", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.calculateSigma", "name": 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"evaluateLawfulness", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.analyzeSequenceWindow", "name": "analyzeSequenceWindow", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "def", "id": "Semantics.Biology.RGFlowBioinformatics.compareSequenceWindows", "name": "compareSequenceWindows", "module": "Semantics.Biology.RGFlowBioinformatics" }, { "kind": "module", "id": "Semantics.BitcoinRGFlow", "name": "BitcoinRGFlow", "path": "Semantics/BitcoinRGFlow.lean", "namespace": "Semantics", "doc": "RGFlow analysis for Bitcoin price data with proper sigma computation from local price dynamics and RGFlow invariant lawfulness checking. 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Authors: Research Stack Team BraidBitwiseODE.lean \u2014 Bitwise ODE integration for braid crossings Replaces continuous O(1) integration with XOR-based bitwise operations on Q16.16 fixed-point values. Pattern derived from PistBridge'", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 158 }, { "kind": "theorem", "id": "Semantics.BraidBitwiseODE.bitwise_ode_preserves_range", "name": "bitwise_ode_preserves_range", "module": "Semantics.BraidBitwiseODE" }, { "kind": "theorem", "id": "Semantics.BraidBitwiseODE.cross_step_preserves_slot", "name": "cross_step_preserves_slot", "module": "Semantics.BraidBitwiseODE" }, { "kind": "theorem", "id": "Semantics.BraidBitwiseODE.bitwise_ode_correct", "name": "bitwise_ode_correct", "module": "Semantics.BraidBitwiseODE" }, { "kind": "def", "id": "Semantics.BraidBitwiseODE.bitwiseCrossStep", "name": "bitwiseCrossStep", "module": "Semantics.BraidBitwiseODE" }, { "kind": "def", "id": "Semantics.BraidBitwiseODE.bitwiseODEIntegrate", "name": "bitwiseODEIntegrate", "module": "Semantics.BraidBitwiseODE" }, { "kind": "def", "id": "Semantics.BraidBitwiseODE.bitwiseODEIntegrateSeq", "name": "bitwiseODEIntegrateSeq", "module": "Semantics.BraidBitwiseODE" }, { "kind": "def", "id": "Semantics.BraidBitwiseODE.integrateStrand", "name": "integrateStrand", "module": "Semantics.BraidBitwiseODE" }, { "kind": "def", "id": "Semantics.BraidBitwiseODE.crossingODEStep", "name": "crossingODEStep", "module": "Semantics.BraidBitwiseODE" }, { "kind": "module", "id": "Semantics.BraidBracket", "name": "BraidBracket", "path": "Semantics/BraidBracket.lean", "namespace": "Semantics.BraidBracket", "doc": "BraidBracket.lean - Bracket Shell for Braid Strand Admissibility Brackets bound the flow. Each braid strand carries a bracket shell that encodes local admissibility geometry. Key rule: merge in linear space first, derive bracket afterward.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 16, "struct_count": 3, "inductive_count": 0, "line_count": 198 }, { "kind": "def", "id": "Semantics.BraidBracket.zero", "name": "zero", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.add", "name": "add", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.neg", "name": "neg", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.scale", "name": "scale", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.isZero", "name": "isZero", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.normApprox", "name": "normApprox", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.fromPhaseVec", "name": "fromPhaseVec", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.gapConserved", "name": "gapConserved", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.addComponentwise", "name": "addComponentwise", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.crossingResidual", "name": "crossingResidual", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.leafEntry", "name": "leafEntry", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.crossingEntry", "name": "crossingEntry", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.cosineSimilarity", "name": "cosineSimilarity", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.gradientAlignment", "name": "gradientAlignment", "module": "Semantics.BraidBracket" }, { "kind": "def", "id": "Semantics.BraidBracket.phaseAccumulation", "name": "phaseAccumulation", "module": "Semantics.BraidBracket" }, { "kind": "module", "id": "Semantics.BraidCross", "name": "BraidCross", "path": "Semantics/BraidCross.lean", "namespace": "Semantics.BraidCross", "doc": "BraidCross.lean - Braid Crossing and Strand Merge Operations Crossing topology: strands interact, merge, and generate residuals. The merge rule remains linear on phaseAcc; bracket is recomputed after. z\u1d62\u2c7c = z\u1d62 + z\u2c7c (linear merge) \u03bc\u1d62\u2c7c = X(\u03bc\u1d62, \u03bc\u2c7c) (crossing slot operator) B\u1d62\u2c7c = C(z\u1d62\u2c7c, \u03bc\u1d62\u2c7c) (brack", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 132 }, { "kind": "def", "id": "Semantics.BraidCross.crossSlot", "name": "crossSlot", "module": "Semantics.BraidCross" }, { "kind": "def", "id": "Semantics.BraidCross.braidCross", "name": "braidCross", "module": "Semantics.BraidCross" }, { "kind": "def", "id": "Semantics.BraidCross.parallelCross", "name": "parallelCross", "module": "Semantics.BraidCross" }, { "kind": "def", "id": "Semantics.BraidCross.crossingAdmissible", "name": "crossingAdmissible", "module": "Semantics.BraidCross" }, { "kind": "def", "id": "Semantics.BraidCross.crossingResidualNorm", "name": "crossingResidualNorm", "module": "Semantics.BraidCross" }, { "kind": "def", "id": "Semantics.BraidCross.fromCross", "name": "fromCross", "module": "Semantics.BraidCross" }, { "kind": "module", "id": "Semantics.BraidDiatCodec", "name": "BraidDiatCodec", "path": "Semantics/BraidDiatCodec.lean", "namespace": "Semantics.BraidDiatCodec", "doc": "BraidDiatCodec.lean \u2014 Chirality-DIAT Slot + Mountain Pack + Braid Residual Codec Codec for the mountains-on-mountain / braid / DIAT stack. Layer 1 \u2014 Chirality-DIAT Slot Address (64 bits) bits [1:0] Chirality flag (00=none, 01=left, 10=right, 11=achiral) bits [9:2] DIAT shell k (floor(sqr", "math_kind": "braid", "sorry_count": 0, "theorem_count": 13, "def_count": 19, "struct_count": 5, "inductive_count": 0, "line_count": 849 }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.add_sub_cancel_uint32", "name": "add_sub_cancel_uint32", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.encode_decode_roundtrip", "name": "encode_decode_roundtrip", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.decodeQ02_encodeQ02", "name": "decodeQ02_encodeQ02", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.decodeQ02_encodeQ02_id", "name": "decodeQ02_encodeQ02_id", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.bracket_roundtrip", "name": "bracket_roundtrip", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.fromQRState_reflectionData_length_test_2_2_1", "name": "fromQRState_reflectionData_length_test_2_2_1", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.fromQRState_rData_length_test_2_2_1", "name": "fromQRState_rData_length_test_2_2_1", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.foldl_append_size", "name": "foldl_append_size", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.fromQRState_reflectionData_length", "name": "fromQRState_reflectionData_length", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.fromQRState_rData_length", "name": "fromQRState_rData_length", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.decode_encode_roundtrip", "name": "decode_encode_roundtrip", "module": "Semantics.BraidDiatCodec" }, { "kind": "theorem", "id": "Semantics.BraidDiatCodec.qr_encode_decode_roundtrip", "name": "qr_encode_decode_roundtrip", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.maxOffset", "name": "maxOffset", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.encode", "name": "encode", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.decode", "name": "decode", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.fromMountain", "name": "fromMountain", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.toMountain", "name": "toMountain", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.encodeQ02", "name": "encodeQ02", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.decodeQ02", "name": "decodeQ02", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.fromBracket", "name": "fromBracket", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.toBracket", "name": "toBracket", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.isQ02Range", "name": "isQ02Range", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.fromQRState", "name": "fromQRState", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.fromQRNode", "name": "fromQRNode", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.empty", "name": "empty", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.testQR_2_2_1", "name": "testQR_2_2_1", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.testQR_2_2_2", "name": "testQR_2_2_2", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.isValid", "name": "isValid", "module": "Semantics.BraidDiatCodec" }, { "kind": "def", "id": "Semantics.BraidDiatCodec.estimatedBytes", "name": "estimatedBytes", "module": "Semantics.BraidDiatCodec" }, { "kind": "module", "id": "Semantics.BraidEigensolid", "name": "BraidEigensolid", "path": "Semantics/BraidEigensolid.lean", "namespace": "Semantics.BraidEigensolid", "doc": "BraidEigensolid.lean \u2014 Eigensolid Compressor Correctness Theorems This is the canonical compressor target mandated by AGENTS.md \u00a7\"Compression First Principles\". Every compressor requires exactly two theorems: 1. `eigensolid_convergence` \u2014 the braid crossing loop stabilizes 2. `receipt_invertible", "math_kind": "braid", "sorry_count": 0, "theorem_count": 16, "def_count": 19, "struct_count": 4, "inductive_count": 0, "line_count": 807 }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.eigensolid_convergence", "name": "eigensolid_convergence", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.encodeReceipt_residuals_length", "name": "encodeReceipt_residuals_length", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.encodeReceipt_step_count", "name": "encodeReceipt_step_count", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.encodeReceipt_residuals_def", "name": "encodeReceipt_residuals_def", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.encodeReceipt_residual_at", "name": "encodeReceipt_residual_at", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.encodeReceipt_crossing_matrix_eq", "name": "encodeReceipt_crossing_matrix_eq", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.receipt_invertible", "name": "receipt_invertible", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.IsTopologicallyTrivial_iff", "name": "IsTopologicallyTrivial_iff", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.add_eq_left_of_non_saturated", "name": "add_eq_left_of_non_saturated", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.crossPartner_involutive", "name": "crossPartner_involutive", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.eigensolid_trivial", "name": "eigensolid_trivial", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.inZeroGenusLayer_iff", "name": "inZeroGenusLayer_iff", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.jsrr_residue_fixed", "name": "jsrr_residue_fixed", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.jsrr_profile_fixed", "name": "jsrr_profile_fixed", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.kkt_block_bounded", "name": "kkt_block_bounded", "module": "Semantics.BraidEigensolid" }, { "kind": "theorem", "id": "Semantics.BraidEigensolid.zero_genus_kkt_bounded", "name": "zero_genus_kkt_bounded", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.goldenCentering", "name": "goldenCentering", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.crossStep", "name": "crossStep", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.encodeReceipt", "name": "encodeReceipt", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.IsEigensolid", "name": "IsEigensolid", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.zero", "name": "zero", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.add", "name": "add", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.stepA", "name": "stepA", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.stepB", "name": "stepB", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.torusCrossStep", "name": "torusCrossStep", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.spatialWinding", "name": "spatialWinding", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.phaseWinding", "name": "phaseWinding", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.IsTopologicallyTrivial", "name": "IsTopologicallyTrivial", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.IsTopologicallyTrivialBool", "name": "IsTopologicallyTrivialBool", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.IsNonSaturatedPhase", "name": "IsNonSaturatedPhase", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.IsNonSaturated", "name": "IsNonSaturated", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.crossPartner", "name": "crossPartner", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.ZeroGenusLayer", "name": "ZeroGenusLayer", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.inZeroGenusLayer", "name": "inZeroGenusLayer", "module": "Semantics.BraidEigensolid" }, { "kind": "def", "id": "Semantics.BraidEigensolid.strandResidue", "name": "strandResidue", "module": "Semantics.BraidEigensolid" }, { "kind": "module", "id": "Semantics.BraidField", "name": "BraidField", "path": "Semantics/BraidField.lean", "namespace": "Semantics.BraidField", "doc": "# BraidField.lean ## Spherion\u2013MMR Recursive Architecture with PIST Field Formalizes the recursive structure where: `Mountain` = a PyramidDAG = a single peak in a local MMR `MMR` = a Merkle Mountain Range of Mountains (self-similar) `betaStep` = discrete Wilsonian RG integration ", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 23, "struct_count": 5, "inductive_count": 2, "line_count": 485 }, { "kind": "def", "id": "Semantics.BraidField.IntNode", "name": "IntNode", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.BettiCycleSet", "name": "BettiCycleSet", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.merge", "name": "merge", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.size", "name": "size", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.peaks", "name": "peaks", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.latestPeak", "name": "latestPeak", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.mountainList", "name": "mountainList", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.append", "name": "append", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.isStable", "name": "isStable", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.burdenCost", "name": "burdenCost", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.geometryCost", "name": "geometryCost", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.adaptationCost", "name": "adaptationCost", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.protectionCost", "name": "protectionCost", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.computePIST", "name": "computePIST", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.SpherionState", "name": "SpherionState", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.voidUpdate", "name": "voidUpdate", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.betaStep", "name": "betaStep", "module": "Semantics.BraidField" }, { "kind": "def", "id": "Semantics.BraidField.rgFlow", "name": "rgFlow", "module": "Semantics.BraidField" }, { "kind": "mathlib", "id": "Mathlib.Data.List.Basic", "name": "Mathlib.Data.List.Basic" }, { "kind": "module", "id": "Semantics.BraidSerial", "name": "BraidSerial", "path": "Semantics/BraidSerial.lean", "namespace": "Semantics.BraidSerial", "doc": "BraidSerial.lean - Braid-Encoded Serial Communication This module keeps the serial-transport surface small enough to compile and extract. Bytes are carried explicitly at the strand boundary, while the braid phase/bracket fields provide the local receipt used by downstream transport checks. The phas", "math_kind": "braid", "sorry_count": 0, "theorem_count": 8, "def_count": 26, "struct_count": 6, "inductive_count": 1, "line_count": 292 }, { "kind": "theorem", "id": "Semantics.BraidSerial.witnessRoundtripHeader", "name": "witnessRoundtripHeader", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.witnessRoundtripPayload", "name": "witnessRoundtripPayload", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.invalidFrameRejected", "name": "invalidFrameRejected", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.directCodecRoundtripBytes", "name": "directCodecRoundtripBytes", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.headerBytes_length", "name": "headerBytes_length", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.packetBytes_length_bound", "name": "packetBytes_length_bound", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.PacketFitsOneFrame", "name": "PacketFitsOneFrame", "module": "Semantics.BraidSerial" }, { "kind": "theorem", "id": "Semantics.BraidSerial.oneFramePayloadPreserved", "name": "oneFramePayloadPreserved", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.empty", "name": "empty", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.fromBytes", "name": "fromBytes", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.length", "name": "length", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.maxWires", "name": "maxWires", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.validWireCount", "name": "validWireCount", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.byteOfNat", "name": "byteOfNat", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.byteToPhase", "name": "byteToPhase", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.phaseBucket", "name": "phaseBucket", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.slotScalar", "name": "slotScalar", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.bytePhaseVec", "name": "bytePhaseVec", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.headerBytes", "name": "headerBytes", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.packetBytes", "name": "packetBytes", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.laneBytes", "name": "laneBytes", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.byteAt", "name": "byteAt", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.decodeHeader", "name": "decodeHeader", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.decodePayload", "name": "decodePayload", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.encodeStrand", "name": "encodeStrand", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.encodeStrands", "name": "encodeStrands", "module": "Semantics.BraidSerial" }, { "kind": "def", "id": "Semantics.BraidSerial.encodePacket", "name": "encodePacket", "module": "Semantics.BraidSerial" }, { "kind": "module", "id": "Semantics.BraidSpherionBridge", "name": "BraidSpherionBridge", "path": "Semantics/BraidSpherionBridge.lean", "namespace": "Semantics.BraidSpherionBridge", "doc": "BraidSpherionBridge.lean \u2014 SpherionState \u2194 BraidState Equivalence Shows the correspondence between: SpherionState (MMR + Mountains + RG flow via betaStep) BraidState (8 strands + crossStep) Two formalisms, one coarse-graining step at different scales: braidCross on (i,j) \u2194 Mountain.merge for th", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 25, "def_count": 9, "struct_count": 0, "inductive_count": 1, "line_count": 523 }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.crossPair_0", "name": "crossPair_0", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.crossPair_1", "name": "crossPair_1", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.crossPair_2", "name": "crossPair_2", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.crossPair_3", "name": "crossPair_3", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.strandPair_distinct", "name": "strandPair_distinct", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.q16Clamp_add_clamp", "name": "q16Clamp_add_clamp", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.ofNat_add_eq", "name": "ofNat_add_eq", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.ofNat_toNat_add", "name": "ofNat_toNat_add", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.phaseVec_add_eq", "name": "phaseVec_add_eq", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.getD_nonneg", "name": "getD_nonneg", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.ofNat_zero_eq", "name": "ofNat_zero_eq", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.intNodeToPhaseVec_getD", "name": "intNodeToPhaseVec_getD", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.add_coords_getD", "name": "add_coords_getD", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.IntNodeToPhaseVec_add", "name": "IntNodeToPhaseVec_add", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.braidCross_phase_linear", "name": "braidCross_phase_linear", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.Mountain_merge_apex_add", "name": "Mountain_merge_apex_add", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.braidCross_merge_correspondence", "name": "braidCross_merge_correspondence", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.spike_step_correspondence", "name": "spike_step_correspondence", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.strandFlow_step_count", "name": "strandFlow_step_count", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.k_spike_step_count", "name": "k_spike_step_count", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.ofNat_val_nonneg", "name": "ofNat_val_nonneg", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.crossSlot_val_nonneg", "name": "crossSlot_val_nonneg", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.braidCross_bracket_admissible", "name": "braidCross_bracket_admissible", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.receipt_correspondence", "name": "receipt_correspondence", "module": "Semantics.BraidSpherionBridge" }, { "kind": "theorem", "id": "Semantics.BraidSpherionBridge.receipt_encode_stable", "name": "receipt_encode_stable", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.IntNodeToPhaseVec", "name": "IntNodeToPhaseVec", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.mountain", "name": "mountain", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.strandPair", "name": "strandPair", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.strandZero", "name": "strandZero", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.initStrandState", "name": "initStrandState", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.spikeToStrandUpdate", "name": "spikeToStrandUpdate", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.strandFlow", "name": "strandFlow", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.extractCrossingMatrix", "name": "extractCrossingMatrix", "module": "Semantics.BraidSpherionBridge" }, { "kind": "def", "id": "Semantics.BraidSpherionBridge.extractSidonSlack", "name": "extractSidonSlack", "module": "Semantics.BraidSpherionBridge" }, { "kind": "module", "id": "Semantics.BraidStrand", "name": "BraidStrand", "path": "Semantics/BraidStrand.lean", "namespace": "Semantics.BraidStrand", "doc": "BraidStrand.lean - Transport Topology with Bracket Shell Braids carry the flow. Each strand accumulates PhaseVec contributions linearly and carries a BraidBracket shell for local admissibility. Hierarchy: DIAT leaf \u2192 AMMR vector \u2192 braid strand \u2192 bracket shell", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 2, "inductive_count": 0, "line_count": 121 }, { "kind": "def", "id": "Semantics.BraidStrand.fromLeaf", "name": "fromLeaf", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.updateBracket", "name": "updateBracket", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.addContribution", "name": "addContribution", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.zero", "name": "zero", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.isAdmissible", "name": "isAdmissible", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.magnitude", "name": "magnitude", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.phaseAngle", "name": "phaseAngle", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.empty", "name": "empty", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.register", "name": "register", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.count", "name": "count", "module": "Semantics.BraidStrand" }, { "kind": "def", "id": "Semantics.BraidStrand.allAdmissible", "name": "allAdmissible", "module": "Semantics.BraidStrand" }, { "kind": "module", "id": "Semantics.BraidTreeDIATPIST", "name": "BraidTreeDIATPIST", "path": "Semantics/BraidTreeDIATPIST.lean", "namespace": "Semantics.BraidTreeDIATPIST", "doc": "BraidTreeDIATPIST.lean \u2014 TreeDIAT/PIST Arrays with Q0_2 Fixed-Point and FAMM Gate Problem: 8-strand braid compressor as TreeDIAT/PIST spectral arrays: Each strand carries a Q0_2 phase and bracket (fixed-point) Each step sums crossing residuals via Q0_2 arithmetic Strands are braided pairwise (Braid", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 9, "def_count": 11, "struct_count": 6, "inductive_count": 0, "line_count": 243 }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.raw_add_mono", "name": "raw_add_mono", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.raw_mul_mono", "name": "raw_mul_mono", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.raw_abs_nonneg", "name": "raw_abs_nonneg", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.raw_abs_triangle", "name": "raw_abs_triangle", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.raw_sum_nonneg", "name": "raw_sum_nonneg", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.eigensolid_convergence", "name": "eigensolid_convergence", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.receipt_invertible", "name": "receipt_invertible", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.q0_2_add_nonneg", "name": "q0_2_add_nonneg", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "theorem", "id": "Semantics.BraidTreeDIATPIST.q0_2_mul_nonneg", "name": "q0_2_mul_nonneg", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.q0_2_raw_add", "name": "q0_2_raw_add", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.q0_2_raw_mul", "name": "q0_2_raw_mul", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.q0_2_raw_abs", "name": "q0_2_raw_abs", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.q0_2_raw_sum", "name": "q0_2_raw_sum", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.isAdmissible", "name": "isAdmissible", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.allAdmissible", "name": "allAdmissible", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.fammGate", "name": "fammGate", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.crossStrands", "name": "crossStrands", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.crossStep", "name": "crossStep", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.IsEigensolid", "name": "IsEigensolid", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "def", "id": "Semantics.BraidTreeDIATPIST.encodeReceipt", "name": "encodeReceipt", "module": "Semantics.BraidTreeDIATPIST" }, { "kind": "module", "id": "Semantics.BraidVCNBridge", "name": "BraidVCNBridge", "path": "Semantics/BraidVCNBridge.lean", "namespace": "Semantics.BraidVCNBridge", "doc": "# BraidVCNBridge \u2014 Map braid operations to VCN frame encoding. Bridges the braid algebra (BraidStrand, BraidBracket) to the VCN video encode substrate for GPU-accelerated computation. Convergence, invertibility, mountain merge, and PISTField frame encoding are delegated to the canonical proven mod", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 125 }, { "kind": "theorem", "id": "Semantics.BraidVCNBridge.covers", "name": "covers", "module": "Semantics.BraidVCNBridge" }, { "kind": "theorem", "id": "Semantics.BraidVCNBridge.eigensolid_convergence", "name": "eigensolid_convergence", "module": "Semantics.BraidVCNBridge" }, { "kind": "theorem", "id": "Semantics.BraidVCNBridge.receipt_invertible", "name": "receipt_invertible", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.encodeBraidStrand", "name": "encodeBraidStrand", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.encodeBraidCrossing", "name": "encodeBraidCrossing", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.encodeMountain", "name": "encodeMountain", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.decodeMountain", "name": "decodeMountain", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.encodeFrame", "name": "encodeFrame", "module": "Semantics.BraidVCNBridge" }, { "kind": "def", "id": "Semantics.BraidVCNBridge.decodeFrame", "name": "decodeFrame", "module": "Semantics.BraidVCNBridge" }, { "kind": "module", "id": "Semantics.BraidedField", "name": "BraidedField", "path": "Semantics/BraidedField.lean", "namespace": "Semantics.BraidedField", "doc": "BraidedField.lean Finite executable scaffold for a polaron-polariton braid-field candidate. This file intentionally uses integer phase ticks and discrete energy witnesses. It is a compileable semantics harness, not a proof that a physical material is topologically protected.", "math_kind": "braid", "sorry_count": 0, "theorem_count": 4, "def_count": 20, "struct_count": 8, "inductive_count": 1, "line_count": 232 }, { "kind": "theorem", "id": "Semantics.BraidedField.sample_braiding_history_len", "name": "sample_braiding_history_len", "module": "Semantics.BraidedField" }, { "kind": "theorem", "id": "Semantics.BraidedField.sample_invariant_tick", "name": "sample_invariant_tick", "module": "Semantics.BraidedField" }, { "kind": "theorem", "id": "Semantics.BraidedField.sample_candidate_protected", "name": "sample_candidate_protected", "module": "Semantics.BraidedField" }, { "kind": "theorem", "id": "Semantics.BraidedField.gap_collapse_not_candidate", "name": "gap_collapse_not_candidate", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.defaultQuasiparticle", "name": "defaultQuasiparticle", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.total", "name": "total", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.validIndex", "name": "validIndex", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.validBraiding", "name": "validBraiding", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.applyBraiding", "name": "applyBraiding", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.topologicalInvariant", "name": "topologicalInvariant", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sameInvariant", "name": "sameInvariant", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.braidPhase", "name": "braidPhase", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.wavefunctionTick", "name": "wavefunctionTick", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.intAbs", "name": "intAbs", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.effectiveMassMilli", "name": "effectiveMassMilli", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.braid", "name": "braid", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.totalPhase", "name": "totalPhase", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.isProtectionCandidate", "name": "isProtectionCandidate", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sampleHamiltonian", "name": "sampleHamiltonian", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sampleField", "name": "sampleField", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sampleBraids", "name": "sampleBraids", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sampleBraidedField", "name": "sampleBraidedField", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.sampleTopologicalField", "name": "sampleTopologicalField", "module": "Semantics.BraidedField" }, { "kind": "def", "id": "Semantics.BraidedField.gapCollapseField", "name": "gapCollapseField", "module": "Semantics.BraidedField" }, { "kind": "module", "id": "Semantics.BraidedFieldPaths", "name": "BraidedFieldPaths", "path": "Semantics/BraidedFieldPaths.lean", "namespace": "Semantics.BraidedField", "doc": "# Braided Field Sets & Virtual Information Paths This module formalizes the topology of virtual information paths created by braiding polaron-polariton quasiparticles (anyons). Instead of tracking particle locations in Cartesian space, information is stored in the topological equivalence class of t", "math_kind": "braid", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 1, "inductive_count": 1, "line_count": 109 }, { "kind": "theorem", "id": "Semantics.BraidedFieldPaths.path_integrity_preserved", "name": "path_integrity_preserved", "module": "Semantics.BraidedFieldPaths" }, { "kind": "theorem", "id": "Semantics.BraidedFieldPaths.far_commute_example", "name": "far_commute_example", "module": "Semantics.BraidedFieldPaths" }, { "kind": "theorem", "id": "Semantics.BraidedFieldPaths.yang_baxter_example", "name": "yang_baxter_example", "module": "Semantics.BraidedFieldPaths" }, { "kind": "theorem", "id": "Semantics.BraidedFieldPaths.far_commute_symmetric", "name": "far_commute_symmetric", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.s0", "name": "s0", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.s1", "name": "s1", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.s2", "name": "s2", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.farLeft", "name": "farLeft", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.farRight", "name": "farRight", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.yangBaxterLeft", "name": "yangBaxterLeft", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.yangBaxterRight", "name": "yangBaxterRight", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.pathLength", "name": "pathLength", "module": "Semantics.BraidedFieldPaths" }, { "kind": "def", "id": "Semantics.BraidedFieldPaths.generatorIndexSum", "name": "generatorIndexSum", "module": "Semantics.BraidedFieldPaths" }, { "kind": "module", "id": "Semantics.BrainBoxDescriptor", "name": "BrainBoxDescriptor", "path": "Semantics/BrainBoxDescriptor.lean", "namespace": "Semantics.BrainBoxDescriptor", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BrainBoxDescriptor.lean \u2014 BBD: Brain Box Descriptor An information-conservative processing unit with fixed-point bounds.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 7, "struct_count": 1, "inductive_count": 0, "line_count": 109 }, { "kind": "theorem", "id": "Semantics.BrainBoxDescriptor.composeAssoc", "name": "composeAssoc", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "theorem", "id": "Semantics.BrainBoxDescriptor.identityLeft", "name": "identityLeft", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "theorem", "id": "Semantics.BrainBoxDescriptor.identityRight", "name": "identityRight", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "theorem", "id": "Semantics.BrainBoxDescriptor.pipelineCompressionAchievesTarget", "name": "pipelineCompressionAchievesTarget", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "theorem", "id": "Semantics.BrainBoxDescriptor.pipelineErrorBelowOnePercent", "name": "pipelineErrorBelowOnePercent", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.bbdKernelDeltaExtraction", "name": "bbdKernelDeltaExtraction", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.bbdGeneticCodon", "name": "bbdGeneticCodon", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.bbdDeltaGCL", "name": "bbdDeltaGCL", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.bbdSwarmComposition", "name": "bbdSwarmComposition", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.compose", "name": "compose", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.identityBBD", "name": "identityBBD", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "def", "id": "Semantics.BrainBoxDescriptor.humanNeuralPipeline", "name": "humanNeuralPipeline", "module": "Semantics.BrainBoxDescriptor" }, { "kind": "module", "id": "Semantics.Burgers2DPDE", "name": "Burgers2DPDE", "path": "Semantics/Burgers2DPDE.lean", "namespace": "Semantics.Burgers2DPDE", "doc": "Burgers2DPDE.lean \u2014 2D Coupled Burgers Equation System in Q16_16 u_t + u\u00b7u_x + v\u00b7u_y = \u03bd\u00b7(u_xx + u_yy) v_t + u\u00b7v_x + v\u00b7v_y = \u03bd\u00b7(v_xx + v_yy) Coupled velocity components (u,v) on a 2D lattice with shared kinematic viscosity \u03bd. Reference: Gao 2017 (10.1016/j.apm.2016.12.010) \u2014 2D Burgers system", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 17, "struct_count": 1, "inductive_count": 0, "line_count": 270 }, { "kind": "theorem", "id": "Semantics.Burgers2DPDE.energy_correspondence_2d", "name": "energy_correspondence_2d", "module": "Semantics.Burgers2DPDE" }, { "kind": "theorem", "id": "Semantics.Burgers2DPDE.mass_correspondence_2d", "name": "mass_correspondence_2d", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.get2D", "name": "get2D", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.centralDiffX", "name": "centralDiffX", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.centralDiffY", "name": "centralDiffY", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.secondDiffX", "name": "secondDiffX", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.secondDiffY", "name": "secondDiffY", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgersU_RHS", "name": "burgersU_RHS", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgersV_RHS", "name": "burgersV_RHS", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.stepEuler", "name": "stepEuler", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.runSteps", "name": "runSteps", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.kineticEnergy", "name": "kineticEnergy", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.totalMass", "name": "totalMass", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.maxVelocity", "name": "maxVelocity", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgers2DInvariant", "name": "burgers2DInvariant", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.test2DState", "name": "test2DState", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgers2DToBraidDef", "name": "burgers2DToBraidDef", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgers2DToBraid", "name": "burgers2DToBraid", "module": "Semantics.Burgers2DPDE" }, { "kind": "def", "id": "Semantics.Burgers2DPDE.burgers2DTheoremReceipt", "name": "burgers2DTheoremReceipt", "module": "Semantics.Burgers2DPDE" }, { "kind": "module", "id": "Semantics.Burgers3DPDE", "name": "Burgers3DPDE", "path": "Semantics/Burgers3DPDE.lean", "namespace": "Semantics.Burgers3DPDE", "doc": "Burgers3DPDE.lean \u2014 3D Coupled Burgers Equation System in Q16_16 u_t + u\u00b7u_x + v\u00b7u_y + w\u00b7u_z = \u03bd\u00b7(u_xx + u_yy + u_zz) v_t + u\u00b7v_x + v\u00b7v_y + w\u00b7v_z = \u03bd\u00b7(v_xx + v_yy + v_zz) w_t + u\u00b7w_x + v\u00b7w_y + w\u00b7w_z = \u03bd\u00b7(w_xx + w_yy + w_zz)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 18, "struct_count": 1, "inductive_count": 0, "line_count": 163 }, { "kind": "theorem", "id": "Semantics.Burgers3DPDE.energy_correspondence_3d", "name": "energy_correspondence_3d", "module": "Semantics.Burgers3DPDE" }, { "kind": "theorem", "id": "Semantics.Burgers3DPDE.mass_correspondence_3d", "name": "mass_correspondence_3d", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.get3D", "name": "get3D", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.centralDiffX", "name": "centralDiffX", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.centralDiffY", "name": "centralDiffY", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.centralDiffZ", "name": "centralDiffZ", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.secondDiffX", "name": "secondDiffX", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.secondDiffY", "name": "secondDiffY", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.secondDiffZ", "name": "secondDiffZ", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgersU_RHS", "name": "burgersU_RHS", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgersV_RHS", "name": "burgersV_RHS", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgersW_RHS", "name": "burgersW_RHS", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.stepEuler", "name": "stepEuler", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.runSteps", "name": "runSteps", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.kineticEnergy", "name": "kineticEnergy", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgers3DInvariant", "name": "burgers3DInvariant", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.test3DState", "name": "test3DState", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgers3DToBraidDef", "name": "burgers3DToBraidDef", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgers3DToBraid", "name": "burgers3DToBraid", "module": "Semantics.Burgers3DPDE" }, { "kind": "def", "id": "Semantics.Burgers3DPDE.burgers3DTheoremReceipt", "name": "burgers3DTheoremReceipt", "module": "Semantics.Burgers3DPDE" }, { "kind": "module", "id": "Semantics.BurgersHilbertPDE", "name": "BurgersHilbertPDE", "path": "Semantics/BurgersHilbertPDE.lean", "namespace": "Semantics.BurgersHilbertPDE", "doc": "BurgersHilbertPDE.lean \u2014 Burgers-Hilbert Equation in Q16_16 u_t + u \u00b7 u_x = \u03b7 \u00b7 H[u_xx] Combines Burgers nonlinear advection with Hilbert transform dispersion. The Hilbert transform H is a singular integral operator that introduces nonlocal dispersion, leading to shock stability transitions. Refe", "math_kind": "routing", "sorry_count": 0, "theorem_count": 2, "def_count": 12, "struct_count": 1, "inductive_count": 0, "line_count": 193 }, { "kind": "theorem", "id": "Semantics.BurgersHilbertPDE.energy_correspondence_bh", "name": "energy_correspondence_bh", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "theorem", "id": "Semantics.BurgersHilbertPDE.threshold_stability_test_witness", "name": "threshold_stability_test_witness", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.discreteHilbert", "name": "discreteHilbert", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.burgersHilbertRHS", "name": "burgersHilbertRHS", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.stepEuler", "name": "stepEuler", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.runSteps", "name": "runSteps", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.kineticEnergy", "name": "kineticEnergy", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.totalMass", "name": "totalMass", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.burgersHilbertInvariant", "name": "burgersHilbertInvariant", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.testBHState", "name": "testBHState", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.burgersHilbertToBraidDef", "name": "burgersHilbertToBraidDef", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.etaCritical", "name": "etaCritical", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.threshold_instability_conjecture", "name": "threshold_instability_conjecture", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "def", "id": "Semantics.BurgersHilbertPDE.burgersHilbertTheoremReceipt", "name": "burgersHilbertTheoremReceipt", "module": "Semantics.BurgersHilbertPDE" }, { "kind": "module", "id": "Semantics.BurgersNKConsistency", "name": "BurgersNKConsistency", "path": "Semantics/BurgersNKConsistency.lean", "namespace": "Semantics.BurgersNKConsistency", "doc": "BurgersNKConsistency.lean \u2014 Burgers Consistency Proof for NK-Hodge-FAMM Axiom Shows that the 4 Burgers theorems (energy dissipation, CFL stability, mass conservation, complexity regularization) collectively imply the NK-Hodge-FAMM regularity axiom's conclusion for the Burgers PDE case. The key ins", "math_kind": "routing", "sorry_count": 0, "theorem_count": 7, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 167 }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.energy_dissipation_satisfies_scar_evolution", "name": "energy_dissipation_satisfies_scar_evolution", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.unconditional_cfl_stability", "name": "unconditional_cfl_stability", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.applyViscosity_one", "name": "applyViscosity_one", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.mass_conservation_inviscid_limit", "name": "mass_conservation_inviscid_limit", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.complexity_regularization", "name": "complexity_regularization", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.burgers_satisfies_nk_hodge_famm", "name": "burgers_satisfies_nk_hodge_famm", "module": "Semantics.BurgersNKConsistency" }, { "kind": "theorem", "id": "Semantics.BurgersNKConsistency.burgers_satisfies_nk_hodge_famm_betti", "name": "burgers_satisfies_nk_hodge_famm_betti", "module": "Semantics.BurgersNKConsistency" }, { "kind": "module", "id": "Semantics.BurgersPDE", "name": "BurgersPDE", "path": "Semantics/BurgersPDE.lean", "namespace": "Semantics.BurgersPDE", "doc": "Models the 1D and n-dimensional Burgers equation: u_t + u \u00b7 u_x = \u03bd \u00b7 u_xx Ported from academic literature via MATH_MODEL_MAP.tsv entries 2622-2634. Uses saturating Q16_16 fixed-point arithmetic throughout. References: Bertini 1994 (10.1007/BF02099769) \u2014 Stochastic Burgers Serre 2020 (10.1007/s002", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 20, "def_count": 29, "struct_count": 2, "inductive_count": 0, "line_count": 707 }, { "kind": "theorem", "id": "Semantics.BurgersPDE.energyChangeRateTestState", "name": "energyChangeRateTestState", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.quatModulusSq_nonneg", "name": "quatModulusSq_nonneg", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.dualQuatEnergy_nonneg", "name": "dualQuatEnergy_nonneg", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.Q16_16", "name": "Q16_16", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.applyViscosity_energy_le", "name": "applyViscosity_energy_le", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.energy_correspondence_testState", "name": "energy_correspondence_testState", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.step_correspondence_bounded", "name": "step_correspondence_bounded", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.energy_dissipation_testDQ", "name": "energy_dissipation_testDQ", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.energy_dissipation_testDQ2", "name": "energy_dissipation_testDQ2", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.energy_strictly_dissipates_testDQ", "name": "energy_strictly_dissipates_testDQ", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.viscosity_stable_testDQ_fine", "name": "viscosity_stable_testDQ_fine", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.viscosity_stable_testDQ_half", "name": "viscosity_stable_testDQ_half", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.viscosity_stable_testDQ_zero", "name": "viscosity_stable_testDQ_zero", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.viscosity_stable_testDQ_unit", "name": "viscosity_stable_testDQ_unit", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.viscosity_stable_testDQ2_half", "name": "viscosity_stable_testDQ2_half", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.mass_conservation_identity", "name": "mass_conservation_identity", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.mass_conservation_identity_dq2", "name": "mass_conservation_identity_dq2", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.mass_decreases_with_viscosity", "name": "mass_decreases_with_viscosity", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.complexityRegularizationTestState", "name": "complexityRegularizationTestState", "module": "Semantics.BurgersPDE" }, { "kind": "theorem", "id": "Semantics.BurgersPDE.braid_complexity_bounded", "name": "braid_complexity_bounded", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.forwardDiff", "name": "forwardDiff", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.centralDiff", "name": "centralDiff", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.secondDiff", "name": "secondDiff", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.burgersRHS", "name": "burgersRHS", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.stepEuler", "name": "stepEuler", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.runSteps", "name": "runSteps", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.kineticEnergy", "name": "kineticEnergy", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.maxVelocity", "name": "maxVelocity", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.burgersInvariant", "name": "burgersInvariant", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testState", "name": "testState", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.energyChangeRate", "name": "energyChangeRate", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.quatModulusSq", "name": "quatModulusSq", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.dualQuatEnergy", "name": "dualQuatEnergy", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.applyViscosity", "name": "applyViscosity", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.burgersToBraidDef", "name": "burgersToBraidDef", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testDQ_from_Burgers", "name": "testDQ_from_Burgers", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testDQ", "name": "testDQ", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testNuDecay", "name": "testNuDecay", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testDQ2", "name": "testDQ2", "module": "Semantics.BurgersPDE" }, { "kind": "def", "id": "Semantics.BurgersPDE.testNuHalf", "name": "testNuHalf", "module": "Semantics.BurgersPDE" }, { "kind": "module", "id": "Semantics.CERNEigensolidData", "name": "CERNEigensolidData", "path": "Semantics/CERNEigensolidData.lean", "namespace": "Semantics.CERNEigensolidData", "doc": "========================================================================", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 13, "def_count": 14, "struct_count": 1, "inductive_count": 0, "line_count": 194 }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.pseudorapidity_conservation", "name": "pseudorapidity_conservation", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.charge_parity_symmetry", "name": "charge_parity_symmetry", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.charge_parity_symmetry_perturbative", "name": "charge_parity_symmetry_perturbative", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.cross_section_conservation", "name": "cross_section_conservation", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.cross_section_unitarity", "name": "cross_section_unitarity", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.momentum_conservation", "name": "momentum_conservation", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.flavor_conservation_top_higgs", "name": "flavor_conservation_top_higgs", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.flavor_conservation_higgs_z", "name": "flavor_conservation_higgs_z", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.CP_violation_detected", "name": "CP_violation_detected", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.CPT_violation_detected", "name": "CPT_violation_detected", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.Lorentz_violation_detected", "name": "Lorentz_violation_detected", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.eigensolid_convergence_cern", "name": "eigensolid_convergence_cern", "module": "Semantics.CERNEigensolidData" }, { "kind": "theorem", "id": "Semantics.CERNEigensolidData.eigensolid_convergence_bounded", "name": "eigensolid_convergence_bounded", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pde_coupling_alpha_s", "name": "pde_coupling_alpha_s", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pde_fermi_constant", "name": "pde_fermi_constant", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pde_z_mass", "name": "pde_z_mass", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pde_top_mass", "name": "pde_top_mass", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pde_higgs_mass", "name": "pde_higgs_mass", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.desi_rederived_eigenvalue", "name": "desi_rederived_eigenvalue", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.desi_rederived_explained_mass", "name": "desi_rederived_explained_mass", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.desi_old_vs_new_diff_pct", "name": "desi_old_vs_new_diff_pct", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.pseudorapidityCheck", "name": "pseudorapidityCheck", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.crossSectionCheck", "name": "crossSectionCheck", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.momentumCheck", "name": "momentumCheck", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.flavorCheckTopHiggs", "name": "flavorCheckTopHiggs", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.flavorCheckHiggsZ", "name": "flavorCheckHiggsZ", "module": "Semantics.CERNEigensolidData" }, { "kind": "def", "id": "Semantics.CERNEigensolidData.receipt", "name": "receipt", "module": "Semantics.CERNEigensolidData" }, { "kind": "module", "id": "Semantics.CGAVersorAddress", "name": "CGAVersorAddress", "path": "Semantics/CGAVersorAddress.lean", "namespace": "Semantics.CGAVersorAddress", "doc": "Conformal Geometric Algebra (CGA) in \u211d\u2074\u00b7\u00b9: 3 Euclidean dimensions + 2 conformal dimensions (e\u208a, e\u208b). A versor encodes position in this 5D space. Access cost between two cells is the CGA distance derived from the inner product of their point representations. Key insight: the arbitrary `maxDelay` bou", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 13, "struct_count": 2, "inductive_count": 0, "line_count": 189 }, { "kind": "def", "id": "Semantics.CGAVersorAddress.cgaInner", "name": "cgaInner", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.e0", "name": "e0", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.einf", "name": "einf", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.isNull", "name": "isNull", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.cgaPoint", "name": "cgaPoint", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.squaredDiff", "name": "squaredDiff", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.cgaDistSq", "name": "cgaDistSq", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.accessCost", "name": "accessCost", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.delayFromDist", "name": "delayFromDist", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.cellFromAddress", "name": "cellFromAddress", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.originAddress", "name": "originAddress", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.unitXAddress", "name": "unitXAddress", "module": "Semantics.CGAVersorAddress" }, { "kind": "def", "id": "Semantics.CGAVersorAddress.point234Address", "name": "point234Address", "module": "Semantics.CGAVersorAddress" }, { "kind": "module", "id": "Semantics.CacheSieve", "name": "CacheSieve", "path": "Semantics/CacheSieve.lean", "namespace": "Semantics.CacheSieve", "doc": "CacheSieve.lean - L0 Local Sorter Cache Verification Migrates legacy f64 penalty evaluations and raw limits.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 1, "inductive_count": 1, "line_count": 88 }, { "kind": "def", "id": "Semantics.CacheSieve.edgeBand", "name": "edgeBand", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.isEdgeBand", "name": "isEdgeBand", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.stateToUInt8", "name": "stateToUInt8", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.advanceNode", "name": "advanceNode", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.triageSurvivorValue", "name": "triageSurvivorValue", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.sieveCost", "name": "sieveCost", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.sieveInvariant", "name": "sieveInvariant", "module": "Semantics.CacheSieve" }, { "kind": "def", "id": "Semantics.CacheSieve.sieveBind", "name": "sieveBind", "module": "Semantics.CacheSieve" }, { "kind": "module", "id": "Semantics.CalibratedKernel", "name": "CalibratedKernel", "path": "Semantics/CalibratedKernel.lean", "namespace": "Semantics.CalibratedKernel", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CalibratedKernel.lean \u2014 Hutter-Calibrated Trajectory Kernel Extends the domain-agnostic trajectory engine with: \u2022 Corpus-aware calibration (Hutter Prize inspired) \u2022 Runtime performance tracking \u2022 Base ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 1, "def_count": 32, "struct_count": 8, "inductive_count": 0, "line_count": 458 }, { "kind": "theorem", "id": "Semantics.CalibratedKernel.calibratedRejectionStructure", "name": "calibratedRejectionStructure", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.defaultKnobs", "name": "defaultKnobs", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.calibrate", "name": "calibrate", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.sigOfPayload", "name": "sigOfPayload", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.rescaleCoupling", "name": "rescaleCoupling", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.scaledCoupling", "name": "scaledCoupling", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.finalScoreCalibrated", "name": "finalScoreCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.bettiSwooshApprox", "name": "bettiSwooshApprox", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.stableDrivenScoreCalibrated", "name": "stableDrivenScoreCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.routeStableCalibrated", "name": "routeStableCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.allowTunnelCalibrated", "name": "allowTunnelCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.shouldPromoteCalibrated", "name": "shouldPromoteCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.budgetCalibratedStep", "name": "budgetCalibratedStep", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.budgetCalibrated", "name": "budgetCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.stabilizePayloadsCalibrated", "name": "stabilizePayloadsCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.chooseBestCalibrated", "name": "chooseBestCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.stepKernelCalibrated", "name": "stepKernelCalibrated", "module": "Semantics.CalibratedKernel" }, { "kind": "def", "id": "Semantics.CalibratedKernel.CalibratedTrace", "name": "CalibratedTrace", "module": "Semantics.CalibratedKernel" }, { "kind": "module", "id": "Semantics.CandidateDictionary", "name": "CandidateDictionary", "path": "Semantics/CandidateDictionary.lean", "namespace": "Semantics.CandidateDictionary", "doc": "# Candidate Dictionary Commit Surface This module formalizes the vectorless, external-store dictionary used by the logogram sidecar path. The dictionary is a committed token table: sidecar references may select ranges from it, but promotion still requires GCCL-Rep verification and replay evidence. ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 14, "def_count": 20, "struct_count": 4, "inductive_count": 0, "line_count": 304 }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.example_entry_declared", "name": "example_entry_declared", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.empty_payload_entry_not_declared", "name": "empty_payload_entry_not_declared", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.example_dictionary_entries_declared", "name": "example_dictionary_entries_declared", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.select_gamma_replays_single_entry", "name": "select_gamma_replays_single_entry", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.select_pair_replays_two_entries", "name": "select_pair_replays_two_entries", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.out_of_bounds_select_replays_none", "name": "out_of_bounds_select_replays_none", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.literal_token_is_not_dictionary_select", "name": "literal_token_is_not_dictionary_select", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.example_commit_verified", "name": "example_commit_verified", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.bad_count_commit_not_verified", "name": "bad_count_commit_not_verified", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.bad_entry_commit_not_verified", "name": "bad_entry_commit_not_verified", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.verified_commit_implies_verified_gccl_rep", "name": "verified_commit_implies_verified_gccl_rep", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.replay_some_implies_candidate_ref_admissible", "name": "replay_some_implies_candidate_ref_admissible", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.candidate_ref_promotion_implies_commit_verified", "name": "candidate_ref_promotion_implies_commit_verified", "module": "Semantics.CandidateDictionary" }, { "kind": "theorem", "id": "Semantics.CandidateDictionary.candidate_ref_promotion_implies_lawful_transition", "name": "candidate_ref_promotion_implies_lawful_transition", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateEntryDeclared", "name": "candidateEntryDeclared", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateDictEntriesDeclared", "name": "candidateDictEntriesDeclared", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateDictSize", "name": "candidateDictSize", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateRangeInBounds", "name": "candidateRangeInBounds", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateRefAdmissible", "name": "candidateRefAdmissible", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.replayCandidateRef", "name": "replayCandidateRef", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateDictCommitVerified", "name": "candidateDictCommitVerified", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.toGcclRepEvent", "name": "toGcclRepEvent", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.candidateRefPromotable", "name": "candidateRefPromotable", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.gammaEntry", "name": "gammaEntry", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.betaEntry", "name": "betaEntry", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.emptyPayloadEntry", "name": "emptyPayloadEntry", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.exampleDict", "name": "exampleDict", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.exampleSelectGamma", "name": "exampleSelectGamma", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.exampleSelectPair", "name": "exampleSelectPair", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.outOfBoundsSelect", "name": "outOfBoundsSelect", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.literalNotDictionarySelect", "name": "literalNotDictionarySelect", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.exampleCommit", "name": "exampleCommit", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.badCountCommit", "name": "badCountCommit", "module": "Semantics.CandidateDictionary" }, { "kind": "def", "id": "Semantics.CandidateDictionary.badEntryCommit", "name": "badEntryCommit", "module": "Semantics.CandidateDictionary" }, { "kind": "module", "id": "Semantics.Canon", "name": "Canon", "path": "Semantics/Canon.lean", "namespace": "Semantics", "doc": "Ported from `infra/access_control/core/canonical_state.py`. Unified state representation for the control system. All scalar fields use Q16_16 fixed-point per Commandment IV. Fixed-point usage justification (Section 13.3): Q16_16 used for all control state fields to preserve integer precision for co", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 11, "struct_count": 4, "inductive_count": 1, "line_count": 238 }, { "kind": "theorem", "id": "Semantics.Canon.defaultIsStable", "name": "defaultIsStable", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.default", "name": "default", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.computeConfidence", "name": "computeConfidence", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.mk", "name": "mk", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.toPbacsProjections", "name": "toPbacsProjections", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.toPbacsProjectionsList", "name": "toPbacsProjectionsList", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.toRegimeTrackerObservables", "name": "toRegimeTrackerObservables", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.toGeometryFeatures", "name": "toGeometryFeatures", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.fromPbacsProjections", "name": "fromPbacsProjections", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.fromGeometryFeatures", "name": "fromGeometryFeatures", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.isStable", "name": "isStable", "module": "Semantics.Canon" }, { "kind": "def", "id": "Semantics.Canon.isCritical", "name": "isCritical", "module": "Semantics.Canon" }, { "kind": "module", "id": "Semantics.CanonAdapters", "name": "CanonAdapters", "path": "Semantics/CanonAdapters.lean", "namespace": "Semantics", "doc": "Normalization modes, dimensions, vectors, and attractors for canonical state processing. Split from Canon.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 4, "struct_count": 5, "inductive_count": 2, "line_count": 133 }, { "kind": "theorem", "id": "Semantics.CanonAdapters.emptyCanonicalVectorWidth", "name": "emptyCanonicalVectorWidth", "module": "Semantics.CanonAdapters" }, { "kind": "theorem", "id": "Semantics.CanonAdapters.defaultCanonicalPackLength", "name": "defaultCanonicalPackLength", "module": "Semantics.CanonAdapters" }, { "kind": "theorem", "id": "Semantics.CanonAdapters.minmaxNormalizationHitsZero", "name": "minmaxNormalizationHitsZero", "module": "Semantics.CanonAdapters" }, { "kind": "def", "id": "Semantics.CanonAdapters.CanonicalDimension", "name": "CanonicalDimension", "module": "Semantics.CanonAdapters" }, { "kind": "def", "id": "Semantics.CanonAdapters.CanonicalVectorSpec", "name": "CanonicalVectorSpec", "module": "Semantics.CanonAdapters" }, { "kind": "def", "id": "Semantics.CanonAdapters.clampQ16", "name": "clampQ16", "module": "Semantics.CanonAdapters" }, { "kind": "def", "id": "Semantics.CanonAdapters.normalizeFeatureValue", "name": "normalizeFeatureValue", "module": "Semantics.CanonAdapters" }, { "kind": "module", "id": "Semantics.CanonSerialization", "name": "CanonSerialization", "path": "Semantics/CanonSerialization.lean", "namespace": "Semantics.ENE", "doc": "Binary serialization, encoding, and filtering for canonical forms. Split from Canon.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 19, "struct_count": 9, "inductive_count": 7, "line_count": 327 }, { "kind": "theorem", "id": "Semantics.CanonSerialization.q16_16_field_kind_core_safe", "name": "q16_16_field_kind_core_safe", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.canonicalEndian", "name": "canonicalEndian", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.canonicalBitOrder", "name": "canonicalBitOrder", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.pushByte", "name": "pushByte", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.encodeU16BE", "name": "encodeU16BE", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.encodeU32BE", "name": "encodeU32BE", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.encodeU64BE", "name": "encodeU64BE", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.encodeNatBE", "name": "encodeNatBE", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.encodeText", "name": "encodeText", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.fieldKindTag", "name": "fieldKindTag", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.intFitsSigned", "name": "intFitsSigned", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.serializeCanonicalValue", "name": "serializeCanonicalValue", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.serializeCanonicalField", "name": "serializeCanonicalField", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.serializeCanonicalBinaryForm", "name": "serializeCanonicalBinaryForm", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.fieldKindCoreSafe", "name": "fieldKindCoreSafe", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.uniqueFieldNames", "name": "uniqueFieldNames", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.RecordSchema", "name": "RecordSchema", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.SameIdentity", "name": "SameIdentity", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.IsCanonical", "name": "IsCanonical", "module": "Semantics.CanonSerialization" }, { "kind": "def", "id": "Semantics.CanonSerialization.applyFilters", "name": "applyFilters", "module": "Semantics.CanonSerialization" }, { "kind": "module", "id": "Semantics.CanonicalInterval", "name": "CanonicalInterval", "path": "Semantics/CanonicalInterval.lean", "namespace": "Semantics.CanonicalInterval", "doc": "CanonicalInterval.lean - Fixed-Point Canonical Interval Arithmetic", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 1, "inductive_count": 0, "line_count": 25 }, { "kind": "def", "id": "Semantics.CanonicalInterval.canonicalIntervalInvariant", "name": "canonicalIntervalInvariant", "module": "Semantics.CanonicalInterval" }, { "kind": "module", "id": "Semantics.CausalGeometry", "name": "CausalGeometry", "path": "Semantics/CausalGeometry.lean", "namespace": "Semantics.CausalGeometry", "doc": "", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 6, "inductive_count": 2, "line_count": 117 }, { "kind": "def", 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"theorem_count": 3, "def_count": 7, "struct_count": 1, "inductive_count": 2, "line_count": 102 }, { "kind": "theorem", "id": "Semantics.CellSnowballConstraint.snowballGrowthRespectsDiffusionLimit", "name": "snowballGrowthRespectsDiffusionLimit", "module": "Semantics.CellSnowballConstraint" }, { "kind": "theorem", "id": "Semantics.CellSnowballConstraint.ecmSupportExtendsSafeWindow", "name": "ecmSupportExtendsSafeWindow", "module": "Semantics.CellSnowballConstraint" }, { "kind": "theorem", "id": "Semantics.CellSnowballConstraint.snowballPreservesManifoldConnectivity", "name": "snowballPreservesManifoldConnectivity", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.diffusionLimitRadius", "name": "diffusionLimitRadius", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.vascularizationThreshold", "name": "vascularizationThreshold", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.ecmFormationTime", "name": "ecmFormationTime", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.snowballGrowthRate", "name": "snowballGrowthRate", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.safeCompressionWindowSeconds", "name": "safeCompressionWindowSeconds", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.snowballPhaseDuration", "name": "snowballPhaseDuration", "module": "Semantics.CellSnowballConstraint" }, { "kind": "def", "id": "Semantics.CellSnowballConstraint.computeAdaptationVerdict", "name": "computeAdaptationVerdict", "module": "Semantics.CellSnowballConstraint" }, { "kind": "module", "id": "Semantics.ChatLogConversion", "name": "ChatLogConversion", "path": "Semantics/ChatLogConversion.lean", "namespace": "ChatLogConversion", "doc": "structure 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"Semantics.ChatLogConversion" }, { "kind": "def", "id": "Semantics.ChatLogConversion.classifyTopics", "name": "classifyTopics", "module": "Semantics.ChatLogConversion" }, { "kind": "def", "id": "Semantics.ChatLogConversion.generateArchiveId", "name": "generateArchiveId", "module": "Semantics.ChatLogConversion" }, { "kind": "def", "id": "Semantics.ChatLogConversion.chatLogConversionBind", "name": "chatLogConversionBind", "module": "Semantics.ChatLogConversion" }, { "kind": "module", "id": "Semantics.ChentsovBridge", "name": "ChentsovBridge", "path": "Semantics/ChentsovBridge.lean", "namespace": "Semantics.ChentsovBridge", "doc": "ChentsovBridge.lean (2 sorries in \u00a72, 1 axiom in \u00a76) Formal bridge connecting the SIM transport metric (TransportTheory) to Chentsov's theorem: the Fisher-Rao metric is the unique monotone Riemannian metric on the discrete simplex. ARCHITECTURE: \u00a71 \u2014 Discrete simplex and probability vectors \u00a72 \u2014 M", "math_kind": "fixedpoint", "sorry_count": 3, "theorem_count": 4, "def_count": 8, "struct_count": 2, "inductive_count": 0, "line_count": 305 }, { "kind": "theorem", "id": "Semantics.ChentsovBridge.fisher_quadratic_form_eq", "name": "fisher_quadratic_form_eq", "module": "Semantics.ChentsovBridge" }, { "kind": "theorem", "id": "Semantics.ChentsovBridge.sim_metric_field_is_monotone", "name": "sim_metric_field_is_monotone", "module": "Semantics.ChentsovBridge" }, { "kind": "theorem", "id": "Semantics.ChentsovBridge.sim_metric_equals_fisher_when_torsion_free", "name": "sim_metric_equals_fisher_when_torsion_free", "module": "Semantics.ChentsovBridge" }, { "kind": "theorem", "id": "Semantics.ChentsovBridge.canonical_normalization", "name": "canonical_normalization", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.quadraticForm", "name": "quadraticForm", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.fisherQuadraticForm", "name": "fisherQuadraticForm", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.applyMarkov", "name": "applyMarkov", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.mergeTwo", "name": "mergeTwo", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.fisherMetricField", "name": "fisherMetricField", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.simMetricField", "name": "simMetricField", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.simQuadraticForm", "name": "simQuadraticForm", "module": "Semantics.ChentsovBridge" }, { "kind": "def", "id": "Semantics.ChentsovBridge.isTorsionFree", "name": "isTorsionFree", "module": "Semantics.ChentsovBridge" }, { "kind": "module", "id": "Semantics.ClassicalEuclideanGeometry", "name": "ClassicalEuclideanGeometry", "path": "Semantics/ClassicalEuclideanGeometry.lean", "namespace": "ClassicalEuclideanGeometry", "doc": "ClassicalEuclideanGeometry.lean Helper module for classical Euclidean geometry theorems that support S3C geometry and other geometric constructions in the codebase. 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This file connects: codon-level efficiency \u03a6_codon translation into amino-acid labels peptide-level efficiency \u03a6_peptide through a sequence-level aggregate score.", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 8, "def_count": 5, "struct_count": 2, "inductive_count": 0, "line_count": 372 }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.gateWeight_zero_folding", "name": "gateWeight_zero_folding", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.gateWeight_zero_bias", "name": "gateWeight_zero_bias", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.phiCDS_zero_peptide_weight", "name": "phiCDS_zero_peptide_weight", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.phiCDS_zero_codon_weight", "name": "phiCDS_zero_codon_weight", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.cotranslationalWindow_is_prefix", "name": "cotranslationalWindow_is_prefix", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.cotranslationalWindow_empty", "name": "cotranslationalWindow_empty", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.cotranslationalWindow_full", "name": "cotranslationalWindow_full", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "theorem", "id": "Semantics.CodonPeptideConsistency.phiCDS_bounded", "name": "phiCDS_bounded", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "def", "id": "Semantics.CodonPeptideConsistency.aaToPeptideClass", "name": "aaToPeptideClass", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "def", "id": "Semantics.CodonPeptideConsistency.synonymous", "name": "synonymous", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "def", "id": "Semantics.CodonPeptideConsistency.pointMutate", "name": "pointMutate", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "def", "id": "Semantics.CodonPeptideConsistency.beneficialAtCodon", "name": "beneficialAtCodon", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "def", "id": "Semantics.CodonPeptideConsistency.beneficialAtCDS", "name": "beneficialAtCDS", "module": "Semantics.CodonPeptideConsistency" }, { "kind": "module", "id": "Semantics.CognitiveLoad", "name": "CognitiveLoad", "path": "Semantics/CognitiveLoad.lean", "namespace": "Semantics.CognitiveLoad", "doc": "CognitiveLoad.lean - Formal Cognitive Load Theory (CLT) Bindings Ports rows 2-11 from MATH_MODEL_MAP.tsv (Python \u2192 Lean). All values are Q16.16 fixed-point. 1.0 = 0x00010000 = 65536. \u03b5 = 1 (smallest nonzero Q16.16 unit) to prevent division by zero.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 14, "struct_count": 1, "inductive_count": 0, "line_count": 94 }, { "kind": "def", "id": "Semantics.CognitiveLoad.epsilon", "name": "epsilon", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.intrinsicLoad", "name": "intrinsicLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.extraneousLoad", "name": "extraneousLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.germaneLoad", "name": "germaneLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.routingLoad", "name": "routingLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.memoryLoad", "name": "memoryLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.totalLoad", "name": "totalLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.cognitiveEfficiency", "name": "cognitiveEfficiency", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.regretAdjustedLoad", "name": "regretAdjustedLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.basinConditionalLoad", "name": "basinConditionalLoad", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.moePredictorDistribution", "name": "moePredictorDistribution", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.loadInvariant", "name": "loadInvariant", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.loadDeltaCost", "name": "loadDeltaCost", "module": "Semantics.CognitiveLoad" }, { "kind": "def", "id": "Semantics.CognitiveLoad.cognitiveLoadBind", "name": "cognitiveLoadBind", "module": "Semantics.CognitiveLoad" }, { "kind": "module", "id": "Semantics.CognitiveLoadInvariantEnhanced", "name": "CognitiveLoadInvariantEnhanced", "path": "Semantics/CognitiveLoadInvariantEnhanced.lean", "namespace": "Semantics.CognitiveLoadInvariantEnhanced", "doc": "CognitiveLoadInvariantEnhanced.lean \u2014 Invariant-Enhanced Cognitive Load Theory Extends CognitiveLoad.lean with invariant preservation, trajectory quality, and convergence inhibition as fundamental load dimensions. Per AGENTS.md \u00a71.4: All values are Q16_16 fixed-point. 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References: Cole 1", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 153 }, { "kind": "def", "id": "Semantics.ColeHopfTransform.forwardDiff", "name": "forwardDiff", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.centralDiff", "name": "centralDiff", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.secondDiff", "name": "secondDiff", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.heatRHS", "name": "heatRHS", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.stepHeatEuler", "name": "stepHeatEuler", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.coleHopfForward", "name": "coleHopfForward", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.toBurgersState", "name": "toBurgersState", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.expApprox", "name": "expApprox", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.cumulativeIntegral", "name": "cumulativeIntegral", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.inverseColeHopf", "name": "inverseColeHopf", "module": "Semantics.ColeHopfTransform" }, { "kind": "def", "id": "Semantics.ColeHopfTransform.testHeatState", "name": "testHeatState", "module": "Semantics.ColeHopfTransform" }, { "kind": "module", "id": "Semantics.CollectiveManifoldInterface", "name": "CollectiveManifoldInterface", "path": "Semantics/CollectiveManifoldInterface.lean", "namespace": "Semantics.CollectiveManifold", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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Authors: Research Stack Team CompileBridge.lean \u2014 GPU-Accelerated Compilation Bridge Formal Specification This module formalizes the interface between the Lean 4 build system (lake) and GPU-accelerated theorem verification. 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Authors: Research Stack Team CompressionLossComparison.lean \u2014 Unified Field Formulation of Learning Objectives THESIS STATEMENT: \"We define a unified field \u03a6(x) that incorporates accuracy, dynamics, geometry, entropy, and conserva", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 10, "def_count": 14, "struct_count": 5, "inductive_count": 0, "line_count": 632 }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.standard_is_degenerate_field", "name": "standard_is_degenerate_field", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.self_compression_has_curvature", "name": "self_compression_has_curvature", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.field_based_strictly_generalizes_standard", "name": "field_based_strictly_generalizes_standard", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.field_based_strictly_generalizes_self_compression", "name": "field_based_strictly_generalizes_self_compression", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.fixedPointStationary", "name": "fixedPointStationary", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.lyapunovStability", "name": "lyapunovStability", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.convergenceToAttractor", "name": "convergenceToAttractor", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.field_based_generalizes_standard_wf", "name": "field_based_generalizes_standard_wf", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.field_based_generalizes_self_compression_wf", "name": "field_based_generalizes_self_compression_wf", "module": "Semantics.CompressionLossComparison" }, { "kind": "theorem", "id": "Semantics.CompressionLossComparison.expressivity_hierarchy_completed", "name": "expressivity_hierarchy_completed", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.denominator", "name": "denominator", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.numerator", "name": "numerator", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.phi", "name": "phi", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.loss", "name": "loss", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.StandardTrainingLoss", "name": "StandardTrainingLoss", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.standardToUnified", "name": "standardToUnified", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.SelfCompressionLoss", "name": "SelfCompressionLoss", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.selfCompressionToUnified", "name": "selfCompressionToUnified", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.FieldBasedLoss", "name": "FieldBasedLoss", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.gradientStep", "name": "gradientStep", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.isFixedPoint", "name": "isFixedPoint", "module": "Semantics.CompressionLossComparison" }, { "kind": "def", "id": "Semantics.CompressionLossComparison.lyapunovV", "name": "lyapunovV", "module": "Semantics.CompressionLossComparison" }, { "kind": "module", "id": "Semantics.CompressionMaximization", "name": "CompressionMaximization", "path": "Semantics/CompressionMaximization.lean", "namespace": "Semantics.CompressionMaximization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CompressionMaximization.lean \u2014 Compression Maximization Results and Theoretical Limits Documents the WGSL parallel hypothesis generation results for Hutter Prize compression, including the winning equa", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 21, "struct_count": 0, "inductive_count": 0, "line_count": 186 }, { "kind": "theorem", "id": "Semantics.CompressionMaximization.theoreticalLimitNegative", "name": "theoreticalLimitNegative", "module": "Semantics.CompressionMaximization" }, { "kind": "theorem", "id": "Semantics.CompressionMaximization.speedImprovementSignificant", "name": "speedImprovementSignificant", "module": "Semantics.CompressionMaximization" }, { "kind": "theorem", "id": "Semantics.CompressionMaximization.memoryImprovementSignificant", "name": "memoryImprovementSignificant", "module": "Semantics.CompressionMaximization" }, { "kind": "theorem", "id": "Semantics.CompressionMaximization.theoreticalLimitViolatesPhysicalConstraint", "name": "theoreticalLimitViolatesPhysicalConstraint", "module": "Semantics.CompressionMaximization" }, { "kind": "theorem", "id": "Semantics.CompressionMaximization.limitReached", "name": "limitReached", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.maxIterations", "name": "maxIterations", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.numTemplates", "name": "numTemplates", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.totalHypotheses", "name": "totalHypotheses", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.hutterRecordRatio", "name": "hutterRecordRatio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.hutterTargetRatio", "name": "hutterTargetRatio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.winningEquation", "name": "winningEquation", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.winningEquationDescription", "name": "winningEquationDescription", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.winningEquationDomains", "name": "winningEquationDomains", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.iteration0Ratio", "name": "iteration0Ratio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.iteration50Ratio", "name": "iteration50Ratio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.iteration100Ratio", "name": "iteration100Ratio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.iteration500Ratio", "name": "iteration500Ratio", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.theoreticalLimit", "name": "theoreticalLimit", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.speedImprovement", "name": "speedImprovement", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.memoryImprovement", "name": "memoryImprovement", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.compressionRatioPhysicalConstraint", "name": "compressionRatioPhysicalConstraint", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.theoreticalLimitReached", "name": "theoreticalLimitReached", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.insight1", "name": "insight1", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.insight2", "name": "insight2", "module": "Semantics.CompressionMaximization" }, { "kind": "def", "id": "Semantics.CompressionMaximization.insight3", "name": "insight3", "module": "Semantics.CompressionMaximization" }, { "kind": "module", "id": "Semantics.CompressionMechanics", "name": "CompressionMechanics", "path": "Semantics/CompressionMechanics.lean", "namespace": "Semantics.CompressionMechanics", "doc": "Mechanical-level witness over a compression trace and an admissible atomic resolution witness. This budgets only contact order, actuation budget, and work budget; it does not claim geometry, force fields, or chemistry.", "math_kind": "fixedpoint", "sorry_count": 1, "theorem_count": 3, "def_count": 13, "struct_count": 2, "inductive_count": 0, "line_count": 242 }, { "kind": "theorem", "id": "Semantics.CompressionMechanics.mechanicallyAdmissibleOfBounds", "name": "mechanicallyAdmissibleOfBounds", "module": "Semantics.CompressionMechanics" }, { "kind": "theorem", "id": "Semantics.CompressionMechanics.positiveWorkOfIrreversibleCompression", "name": "positiveWorkOfIrreversibleCompression", "module": "Semantics.CompressionMechanics" }, { "kind": "theorem", "id": "Semantics.CompressionMechanics.compressionContractsMechanicalOrder", "name": "compressionContractsMechanicalOrder", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.summaryAligned", "name": "summaryAligned", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.contactOrderCovered", "name": "contactOrderCovered", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.actuationBudgeted", "name": "actuationBudgeted", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.workBudgeted", "name": "workBudgeted", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.allBudgetsCovered", "name": "allBudgetsCovered", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.mechanicallyAdmissible", "name": "mechanicallyAdmissible", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.witnessOfCompression", "name": "witnessOfCompression", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.sampleMechanicalCompressionWitness", "name": "sampleMechanicalCompressionWitness", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.timePenalty", "name": "timePenalty", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.gaFitnessFunction", "name": "gaFitnessFunction", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.compressionRatio", "name": "compressionRatio", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.defaultGAFitnessParams", "name": "defaultGAFitnessParams", "module": "Semantics.CompressionMechanics" }, { "kind": "def", "id": "Semantics.CompressionMechanics.adaptiveCompressionFitness", "name": "adaptiveCompressionFitness", "module": "Semantics.CompressionMechanics" }, { "kind": "module", "id": "Semantics.CompressionMechanicsBridge", "name": "CompressionMechanicsBridge", "path": "Semantics/CompressionMechanicsBridge.lean", "namespace": "Semantics.CompressionMechanicsBridge", "doc": "Minimal substrate witness for realizing a compression trace physically. This budgets only dissipation capacity, defect tolerance, and retained support.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 121 }, { "kind": "theorem", "id": "Semantics.CompressionMechanicsBridge.substrateAdmissibleOfBounds", "name": "substrateAdmissibleOfBounds", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "theorem", "id": "Semantics.CompressionMechanicsBridge.resolvedSitesLeSupportBudget", "name": "resolvedSitesLeSupportBudget", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "theorem", "id": "Semantics.CompressionMechanicsBridge.landauerCoveredBySubstrate", "name": "landauerCoveredBySubstrate", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "theorem", "id": "Semantics.CompressionMechanicsBridge.compressionTracePhysicallyAdmissible", "name": "compressionTracePhysicallyAdmissible", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.dissipationCovered", "name": "dissipationCovered", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.supportCovered", "name": "supportCovered", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.defectToleranceCovered", "name": "defectToleranceCovered", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.substrateAdmissible", "name": "substrateAdmissible", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.witnessOfDefect", "name": "witnessOfDefect", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "def", "id": "Semantics.CompressionMechanicsBridge.sampleSubstrateWitness", "name": "sampleSubstrateWitness", "module": "Semantics.CompressionMechanicsBridge" }, { "kind": "module", "id": "Semantics.CompressionYield", "name": "CompressionYield", "path": "Semantics/CompressionYield.lean", "namespace": "Semantics.CompressionYield", "doc": "CompressionYield.lean \u2014 Holographic compression yield theorem. Traditional compression minimizes bits per symbol along coordinate axes. Holographic compression packs N structures per coordinate by separating them in lambda-space. The total compression multiplier is the product of three independent", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 15, "def_count": 9, "struct_count": 1, "inductive_count": 0, "line_count": 199 }, { "kind": "theorem", "id": "Semantics.CompressionYield.max_bands_bounded_by_value_count", "name": "max_bands_bounded_by_value_count", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.dish_total_is_60000", "name": "dish_total_is_60000", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.baseline_total_is_20000", "name": "baseline_total_is_20000", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.full_lambda_total_is_60000000", "name": "full_lambda_total_is_60000000", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.full_lambda_dominates_baseline", "name": "full_lambda_dominates_baseline", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.full_lambda_dominates_dish", "name": "full_lambda_dominates_dish", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.holographic_advantage_over_baseline_dish", "name": "holographic_advantage_over_baseline_dish", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.three_rotation_advantage", "name": "three_rotation_advantage", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.logogram_holographic_advantage", "name": "logogram_holographic_advantage", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.logogram_holographic_is_3000x", "name": "logogram_holographic_is_3000x", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.multipliers_are_multiplicative", "name": "multipliers_are_multiplicative", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.delta_zero_gives_all_bands", "name": "delta_zero_gives_all_bands", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.delta_one_gives_one_band", "name": "delta_one_gives_one_band", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.delta_half_gives_two_bands", "name": "delta_half_gives_two_bands", "module": "Semantics.CompressionYield" }, { "kind": "theorem", "id": "Semantics.CompressionYield.delta_small_gives_many_bands", "name": "delta_small_gives_many_bands", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.totalMultiplier", "name": "totalMultiplier", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.q0_16_valueCount", "name": "q0_16_valueCount", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.maxLambdaBands", "name": "maxLambdaBands", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.dishHolographicYield", "name": "dishHolographicYield", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.fullLambdaYield", "name": "fullLambdaYield", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.baselineYield", "name": "baselineYield", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.threeRotationYield", "name": "threeRotationYield", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.logogramBaselineYield", "name": "logogramBaselineYield", "module": "Semantics.CompressionYield" }, { "kind": "def", "id": "Semantics.CompressionYield.logogramHolographicYield", "name": "logogramHolographicYield", "module": "Semantics.CompressionYield" }, { "kind": "module", "id": "Semantics.ComputationProfile", "name": "ComputationProfile", "path": "Semantics/ComputationProfile.lean", "namespace": "Semantics.ComputationProfile", "doc": "ComputationProfile.lean - Minimal stub", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 0, "line_count": 23 }, { "kind": "module", "id": "Semantics.ConflictResolution", "name": "ConflictResolution", "path": "Semantics/ConflictResolution.lean", "namespace": "Semantics.ConflictResolution", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ConflictResolution.lean \u2014 Conflict Resolution for Tile Flip Operations Defines conflict resolution mechanisms for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10). Handles simultaneous tile flips,", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 12, "struct_count": 2, "inductive_count": 2, "line_count": 240 }, { "kind": "theorem", "id": "Semantics.ConflictResolution.resolveByTimestampPriorityReturnsProposal", "name": "resolveByTimestampPriorityReturnsProposal", "module": "Semantics.ConflictResolution" }, { "kind": "theorem", "id": "Semantics.ConflictResolution.resolveByHashDeterministicReturnsProposal", "name": "resolveByHashDeterministicReturnsProposal", "module": "Semantics.ConflictResolution" }, { "kind": "theorem", "id": "Semantics.ConflictResolution.detectNetworkPartitionReturnsOption", "name": "detectNetworkPartitionReturnsOption", "module": "Semantics.ConflictResolution" }, { "kind": "theorem", "id": "Semantics.ConflictResolution.applyResolutionStrategyReturnsOption", "name": "applyResolutionStrategyReturnsOption", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.zero", "name": "zero", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.one", "name": "one", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.ofFrac", "name": "ofFrac", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.detectSimultaneousFlips", "name": "detectSimultaneousFlips", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.detectConflictingPatterns", "name": "detectConflictingPatterns", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.detectNetworkPartition", "name": "detectNetworkPartition", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.resolveByTimestampPriority", "name": "resolveByTimestampPriority", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.computeProposalHash", "name": "computeProposalHash", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.resolveByHashDeterministic", "name": "resolveByHashDeterministic", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.resolveByMajorityPartition", "name": "resolveByMajorityPartition", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.applyResolutionStrategy", "name": "applyResolutionStrategy", "module": "Semantics.ConflictResolution" }, { "kind": "def", "id": "Semantics.ConflictResolution.createTestProposal", "name": "createTestProposal", "module": "Semantics.ConflictResolution" }, { "kind": "module", "id": "Semantics.Connectors", "name": "Connectors", "path": "Semantics/Connectors.lean", "namespace": "Semantics.Connectors", "doc": "Semantics/Connectors.lean - Global Theory Connectors This module formalizes the \"Connectors\" identified in the April 2026 Research Stack. It bridges the Distant Semantic Maths: 1. Generalized Geometry (Aldi et al. 2026) \u2194 MMR Gossip 2. Stable Looped Scaling (Parcae 2026) \u2194 Cognitive Bandwidth (OMT)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 1, "inductive_count": 0, "line_count": 156 }, { "kind": "theorem", "id": "Semantics.Connectors.linearAccumulationIntegrable", "name": "linearAccumulationIntegrable", "module": "Semantics.Connectors" }, { "kind": "theorem", "id": "Semantics.Connectors.zeroIsVoid", "name": "zeroIsVoid", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.aldiTorsion", "name": "aldiTorsion", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.isIntegrable", "name": "isIntegrable", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.isStable", "name": "isStable", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.omegaMax", "name": "omegaMax", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.existsSOC", "name": "existsSOC", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.isVoidConcept", "name": "isVoidConcept", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.isLocked", "name": "isLocked", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.stressLawful", "name": "stressLawful", "module": "Semantics.Connectors" }, { "kind": "def", "id": "Semantics.Connectors.dualityLawful", "name": "dualityLawful", "module": "Semantics.Connectors" }, { "kind": "module", "id": "Semantics.Constitution", "name": "Constitution", "path": "Semantics/Constitution.lean", "namespace": "Semantics.ENE", "doc": "Constitution", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 11, "def_count": 3, "struct_count": 3, "inductive_count": 1, "line_count": 268 }, { "kind": "theorem", "id": "Semantics.Constitution.no_object_without_semantic_grounding", "name": "no_object_without_semantic_grounding", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.no_motion_without_lawful_path", "name": "no_motion_without_lawful_path", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.no_complexity_without_load_map", "name": "no_complexity_without_load_map", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.no_universality_loss_under_constitution", "name": "no_universality_loss_under_constitution", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.canonical_form_required", "name": "canonical_form_required", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.evolution_audit_required", "name": "evolution_audit_required", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.scalar_certification_required", "name": "scalar_certification_required", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.scalar_collapse_must_be_admissible", "name": "scalar_collapse_must_be_admissible", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.silencer_blocks_admissibility", "name": "silencer_blocks_admissibility", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.unacknowledged_flag_blocks_admissibility", "name": "unacknowledged_flag_blocks_admissibility", "module": "Semantics.Constitution" }, { "kind": "theorem", "id": "Semantics.Constitution.fully_translated_iff_empty", "name": "fully_translated_iff_empty", "module": "Semantics.Constitution" }, { "kind": "def", "id": "Semantics.Constitution.FullyAdmissible", "name": "FullyAdmissible", "module": "Semantics.Constitution" }, { "kind": "def", "id": "Semantics.Constitution.TranslationAdmissible", "name": "TranslationAdmissible", "module": "Semantics.Constitution" }, { "kind": "def", "id": "Semantics.Constitution.constitutionSelfContract", "name": "constitutionSelfContract", "module": "Semantics.Constitution" }, { "kind": "module", "id": "Semantics.Containment", "name": "Containment", "path": "Semantics/Containment.lean", "namespace": "Semantics.Containment", "doc": "Containment: Formal deterrence and safety protocol. Ensures that radioactive adversarial warding can ONLY be activated with a verified out-of-band Human Witness signature.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 1, "line_count": 46 }, { "kind": "def", "id": "Semantics.Containment.isContained", "name": "isContained", "module": "Semantics.Containment" }, { "kind": "def", "id": "Semantics.Containment.canEscalate", "name": "canEscalate", "module": "Semantics.Containment" }, { "kind": "module", "id": "Semantics.ContinuedFractionCompression", "name": "ContinuedFractionCompression", "path": "Semantics/ContinuedFractionCompression.lean", "namespace": "Semantics.ContinuedFractionCompression", "doc": "# Continued Fraction Compression Surface This module tests whether existing ratio-heavy Research Stack math can be adapted into a vectorless continued-fraction codec. The target is not real-number theorem proving. The target is exact, integer replay: a finite partial-quotient stream reconstructs a", "math_kind": "avm", "sorry_count": 0, "theorem_count": 10, "def_count": 12, "struct_count": 2, "inductive_count": 1, "line_count": 193 }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.phi_five_reconstructs", "name": "phi_five_reconstructs", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.phi_squared_reconstructs", "name": "phi_squared_reconstructs", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.ten_point_five_reconstructs", "name": "ten_point_five_reconstructs", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.phi_packet_promotable", "name": "phi_packet_promotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.phi_squared_packet_promotable", "name": "phi_squared_packet_promotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.ten_point_five_packet_promotable", "name": "ten_point_five_packet_promotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.large_quotient_not_promotable", "name": "large_quotient_not_promotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.aesthetic_cf_packet_not_promotable", "name": "aesthetic_cf_packet_not_promotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.promotable_cf_reconstructs", "name": "promotable_cf_reconstructs", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "theorem", "id": "Semantics.ContinuedFractionCompression.promotable_cf_satisfies_byte_law", "name": "promotable_cf_satisfies_byte_law", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.evalCf", "name": "evalCf", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.partialQuotientsAdmissible", "name": "partialQuotientsAdmissible", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.partialQuotientsByteSized", "name": "partialQuotientsByteSized", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.cfPayloadBytes", "name": "cfPayloadBytes", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.cfReconstructs", "name": "cfReconstructs", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.cfByteLawHolds", "name": "cfByteLawHolds", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.cfCompressionPromotable", "name": "cfCompressionPromotable", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.phiFivePacket", "name": "phiFivePacket", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.phiSquaredPacket", "name": "phiSquaredPacket", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.tenPointFivePacket", "name": "tenPointFivePacket", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.largeQuotientPacket", "name": "largeQuotientPacket", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "def", "id": "Semantics.ContinuedFractionCompression.aestheticCfPacket", "name": "aestheticCfPacket", "module": "Semantics.ContinuedFractionCompression" }, { "kind": "module", "id": "Semantics.CooperativeLUT", "name": "CooperativeLUT", "path": "Semantics/CooperativeLUT.lean", "namespace": "Semantics.CooperativeLUT", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CooperativeLUT.lean \u2014 Parallel LUT-based computation via 1D cooperative scalars. This module formalizes a substrate-limited compute model where: 1. The address space width is arbitrary (N-bit), bounded", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 28, "struct_count": 14, "inductive_count": 0, "line_count": 902 }, { "kind": "theorem", "id": "Semantics.CooperativeLUT.genomeToAddressBound", "name": "genomeToAddressBound", "module": "Semantics.CooperativeLUT" }, { "kind": "theorem", "id": "Semantics.CooperativeLUT.btbSizeInvariant", "name": "btbSizeInvariant", "module": "Semantics.CooperativeLUT" }, { "kind": "theorem", "id": "Semantics.CooperativeLUT.streakThresholdPos", "name": "streakThresholdPos", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.addressZero", "name": "addressZero", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.addressInc", "name": "addressInc", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.addressCompat", "name": "addressCompat", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.cellMask", "name": "cellMask", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.cellSet", "name": "cellSet", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.manifold2D", "name": "manifold2D", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.manifold3D", "name": "manifold3D", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.lutEmpty", "name": "lutEmpty", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.activeCount", "name": "activeCount", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.genomeToAddress", "name": "genomeToAddress", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.addressToGenome", "name": "addressToGenome", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.drakeConstant", "name": "drakeConstant", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.driftBarrierConstant", "name": "driftBarrierConstant", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.computeConstraintEntry", "name": "computeConstraintEntry", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.biophysicalLUT", "name": "biophysicalLUT", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.counterIncrement", "name": "counterIncrement", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.counterDecrement", "name": "counterDecrement", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.counterPredictsTaken", "name": "counterPredictsTaken", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.btbEmpty", "name": "btbEmpty", "module": "Semantics.CooperativeLUT" }, { "kind": "def", "id": "Semantics.CooperativeLUT.btbLookup", "name": "btbLookup", "module": "Semantics.CooperativeLUT" }, { "kind": "module", "id": "Semantics.CopyIfTactic", "name": "CopyIfTactic", "path": "Semantics/CopyIfTactic.lean", "namespace": "Semantics.CopyIfTactic", "doc": "CopyIfTactic.lean \u2014 Pre-filter tactic for Lean 4 Implements the copy-if pattern as a native Lean tactic: 1. Check if goal is trivially closable (zero delta) \u2192 close immediately 2. If non-trivial (non-zero delta) \u2192 delegate to solver Usage: theorem foo : 1 = 1 := by copy_if theorem bar : x + 0 = x ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 60 }, { "kind": "theorem", "id": "Semantics.CopyIfTactic.foo", "name": "foo", "module": "Semantics.CopyIfTactic" }, { "kind": "theorem", "id": "Semantics.CopyIfTactic.bar", "name": "bar", "module": "Semantics.CopyIfTactic" }, { "kind": "theorem", "id": "Semantics.CopyIfTactic.baz", "name": "baz", "module": "Semantics.CopyIfTactic" }, { "kind": "module", "id": "Semantics.Core.FoldedPointManifold", "name": "FoldedPointManifold", "path": "Semantics/Core/FoldedPointManifold.lean", "namespace": "Semantics.FoldedPointManifold", "doc": "FoldedPointManifold.lean \u2014 apparent 0D footprint with higher-dimensional interior This module makes explicit the frame distinction: observer-resolved dimension = 0 internal/folded dimension may be > 0 That prevents the model from treating \"0D\" as automatically empty. A point may be an observer-", "math_kind": "avm", "sorry_count": 0, "theorem_count": 21, "def_count": 28, "struct_count": 4, "inductive_count": 5, "line_count": 409 }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.improvedFixture_yields_improved", "name": "improvedFixture_yields_improved", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.decreasedFixture_yields_decreased", "name": "decreasedFixture_yields_decreased", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.rejectedFixture_yields_reject", "name": "rejectedFixture_yields_reject", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.heldFixture_yields_hold", "name": "heldFixture_yields_hold", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.gateCompose_reject_dominates_left", "name": "gateCompose_reject_dominates_left", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.gateCompose_reject_dominates_right", "name": "gateCompose_reject_dominates_right", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.gateCompose_hold_blocks_admit", "name": "gateCompose_hold_blocks_admit", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.gateCompose_admit_neutral", "name": "gateCompose_admit_neutral", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.deltaResolution_positive_fixture", "name": "deltaResolution_positive_fixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.deltaResolution_negative_fixture", "name": "deltaResolution_negative_fixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.deltaResolution_zero_fixture", "name": "deltaResolution_zero_fixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.folded16Fixture_admits", "name": "folded16Fixture_admits", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.missingReplayFixture_holds", "name": "missingReplayFixture_holds", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.overCapFixture_holds", "name": "overCapFixture_holds", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.ordinaryPointFixture_rejects", "name": "ordinaryPointFixture_rejects", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.folded16Fixture_loopsBack", "name": "folded16Fixture_loopsBack", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.noPermeabilityFixture_holdsLoopback", "name": "noPermeabilityFixture_holdsLoopback", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.ordinaryPointFixture_holdsLoopback", "name": "ordinaryPointFixture_holdsLoopback", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.mengerConservedFixture_conserved", "name": "mengerConservedFixture_conserved", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.brokenConservationFixture_rejects", "name": "brokenConservationFixture_rejects", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "theorem", "id": "Semantics.Core.FoldedPointManifold.missingMengerSeedFixture_holds", "name": "missingMengerSeedFixture_holds", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.isFoldedPoint", "name": "isFoldedPoint", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.withinDeclaredDimensionalCap", "name": "withinDeclaredDimensionalCap", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.hasTorsionPotential", "name": "hasTorsionPotential", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.resolutionLost", "name": "resolutionLost", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.decideFoldedPoint", "name": "decideFoldedPoint", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.decideLoopback", "name": "decideLoopback", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.conservedAcrossLevels", "name": "conservedAcrossLevels", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.decideConservation", "name": "decideConservation", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.folded16Fixture", "name": "folded16Fixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.missingReplayFixture", "name": "missingReplayFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.overCapFixture", "name": "overCapFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.ordinaryPointFixture", "name": "ordinaryPointFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.noPermeabilityFixture", "name": "noPermeabilityFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.mengerConservedFixture", "name": "mengerConservedFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.brokenConservationFixture", "name": "brokenConservationFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.missingMengerSeedFixture", "name": "missingMengerSeedFixture", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.gateCompose", "name": "gateCompose", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.gateComposeList", "name": "gateComposeList", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.deltaResolution", "name": "deltaResolution", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "def", "id": "Semantics.Core.FoldedPointManifold.interact", "name": "interact", "module": "Semantics.Core.FoldedPointManifold" }, { "kind": "module", "id": "Semantics.Core.MassNumber", "name": "MassNumber", "path": "Semantics/Core/MassNumber.lean", "namespace": "Semantics", "doc": "MassNumber.lean \u2014 Formal Mass Number as Admissibility Gate Defines the Mass Number as a theorem object with three layers: 1. Admissible reduction packet (A) 2. Residual risk receipt (R) 3. Routing/compression boundary marker (\u03b5 guard) Core rule (comparison form, no division): MassLe m thre", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 15, "struct_count": 4, "inductive_count": 0, "line_count": 204 }, { "kind": "theorem", "id": "Semantics.Core.MassNumber.MassLe_eq_Prop", "name": "MassLe_eq_Prop", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.MassLe", "name": "MassLe", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.MassLeProp", "name": "MassLeProp", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.MassLeDefault", "name": "MassLeDefault", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.mkMassNumber", "name": "mkMassNumber", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.mkMassNumberNat", "name": "mkMassNumberNat", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.gcclSwapGate", "name": "gcclSwapGate", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.fammRouteGate", "name": "fammRouteGate", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.braidTransferGate", "name": "braidTransferGate", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.tsmTransitionGate", "name": "tsmTransitionGate", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.hutterCompressionGate", "name": "hutterCompressionGate", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.depthPolicyOk", "name": "depthPolicyOk", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.promotionReady", "name": "promotionReady", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.underverseRule", "name": "underverseRule", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.exampleNotAdmissible", "name": "exampleNotAdmissible", "module": "Semantics.Core.MassNumber" }, { "kind": "def", "id": "Semantics.Core.MassNumber.exampleAdmissible", "name": "exampleAdmissible", "module": "Semantics.Core.MassNumber" }, { "kind": "module", "id": "Semantics.Core.PathEpigeneticManifold", "name": "PathEpigeneticManifold", "path": "Semantics/Core/PathEpigeneticManifold.lean", "namespace": "Semantics.PathEpigeneticManifold", "doc": "PathEpigeneticManifold.lean \u2014 1D regulatory path over a 16D manifold This module models the \"circuit path as epigenetic control strand\" idea: the 1D path is stable carrier geometry, while finite regulatory marks on that path determine which dimensions of a 16D manifold are expressed, damped, receip", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 7, "def_count": 21, "struct_count": 4, "inductive_count": 3, "line_count": 282 }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.admittedPathActivatesTorsion", "name": "admittedPathActivatesTorsion", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.admittedPathClosesWitness", "name": "admittedPathClosesWitness", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.admittedPathDecision", "name": "admittedPathDecision", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.holdPathLeavesTorsionUnchanged", "name": "holdPathLeavesTorsionUnchanged", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.holdPathDecision", "name": "holdPathDecision", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.quarantinePathRoutesResidual", "name": "quarantinePathRoutesResidual", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "theorem", "id": "Semantics.Core.PathEpigeneticManifold.quarantinePathDecision", "name": "quarantinePathDecision", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.zero", "name": "zero", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.get", "name": "get", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.set", "name": "set", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.markerAdmissible", "name": "markerAdmissible", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.applyMarker", "name": "applyMarker", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.applyPath", "name": "applyPath", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.anyLayoutViolation", "name": "anyLayoutViolation", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.anyMissingReceipt", "name": "anyMissingReceipt", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.anyQuarantineMarker", "name": "anyQuarantineMarker", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.decidePath", "name": "decidePath", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.runPath", "name": "runPath", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.qSmall", "name": "qSmall", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.qMedium", "name": "qMedium", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.torsionSite", "name": "torsionSite", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.dampResidualSite", "name": "dampResidualSite", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.witnessSite", "name": "witnessSite", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.missingReceiptSite", "name": "missingReceiptSite", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.layoutViolationSite", "name": "layoutViolationSite", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.admittedPath", "name": "admittedPath", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "def", "id": "Semantics.Core.PathEpigeneticManifold.holdPath", "name": "holdPath", "module": "Semantics.Core.PathEpigeneticManifold" }, { "kind": "module", "id": "Semantics.Core.QuantumFoamBoundary", "name": "QuantumFoamBoundary", "path": "Semantics/Core/QuantumFoamBoundary.lean", "namespace": "Semantics.QuantumFoamBoundary", "doc": "QuantumFoamBoundary.lean \u2014 bounded fluctuation guard around U0 Quantum foam is modeled here as an accounting boundary around the zero layer, not as a promotion rule. Exact neutral closure still belongs to U0. Foam only classifies sub-resolution, unreceipted, or stochastic jitter as HOLD.", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 3, "def_count": 5, "struct_count": 1, "inductive_count": 2, "line_count": 92 }, { "kind": "theorem", "id": "Semantics.Core.QuantumFoamBoundary.exactZeroFixture_closes", "name": "exactZeroFixture_closes", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "theorem", "id": "Semantics.Core.QuantumFoamBoundary.foamJitterFixture_holds", "name": "foamJitterFixture_holds", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "theorem", "id": "Semantics.Core.QuantumFoamBoundary.outOfBandFixture_rejects", "name": "outOfBandFixture_rejects", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "def", "id": "Semantics.Core.QuantumFoamBoundary.withinJitter", "name": "withinJitter", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "def", "id": "Semantics.Core.QuantumFoamBoundary.decideFoamBoundary", "name": "decideFoamBoundary", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "def", "id": "Semantics.Core.QuantumFoamBoundary.exactZeroFixture", "name": "exactZeroFixture", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "def", "id": "Semantics.Core.QuantumFoamBoundary.foamJitterFixture", "name": "foamJitterFixture", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "def", "id": "Semantics.Core.QuantumFoamBoundary.outOfBandFixture", "name": "outOfBandFixture", "module": "Semantics.Core.QuantumFoamBoundary" }, { "kind": "module", "id": "Semantics.Core.S3CProjectedGeodesicResolution", "name": "S3CProjectedGeodesicResolution", "path": "Semantics/Core/S3CProjectedGeodesicResolution.lean", "namespace": "Semantics.S3CProjectedGeodesicResolution", "doc": "S3CProjectedGeodesicResolution.lean \u2014 folded-throat resolution gate This module compares the old S3C projected-geodesic score against the refined folded-point theory: baseline S3C score = manifold distance minus shell/projection error folded-throat score = baseline distance plus throat shortcut g", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 10, "def_count": 15, "struct_count": 1, "inductive_count": 2, "line_count": 245 }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.improvedFixtureImproves", "name": "improvedFixtureImproves", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.decreasedFixtureDecreases", "name": "decreasedFixtureDecreases", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.holdFixtureHolds", "name": "holdFixtureHolds", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.rejectFixtureRejects", "name": "rejectFixtureRejects", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.unchangedFixtureUnchanged", "name": "unchangedFixtureUnchanged", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.improvedFixtureBaselineScore", "name": "improvedFixtureBaselineScore", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.improvedFixtureRefinedScore", "name": "improvedFixtureRefinedScore", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.improvedFixtureReason", "name": "improvedFixtureReason", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.decreasedFixtureReason", "name": "decreasedFixtureReason", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "theorem", "id": "Semantics.Core.S3CProjectedGeodesicResolution.unchangedFixtureReason", "name": "unchangedFixtureReason", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.baselineScore", "name": "baselineScore", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.shortcutGain", "name": "shortcutGain", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.genus3Aligned", "name": "genus3Aligned", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.foldedThroatAdmissible", "name": "foldedThroatAdmissible", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.refinedScore", "name": "refinedScore", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.resolutionBudget", "name": "resolutionBudget", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.resolutionDelta", "name": "resolutionDelta", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.compareScores", "name": "compareScores", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.decideResolution", "name": "decideResolution", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.explainResolution", "name": "explainResolution", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.improvedFixture", "name": "improvedFixture", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.decreasedFixture", "name": "decreasedFixture", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.holdFixture", "name": "holdFixture", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.rejectFixture", "name": "rejectFixture", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "def", "id": "Semantics.Core.S3CProjectedGeodesicResolution.unchangedFixture", "name": "unchangedFixture", "module": "Semantics.Core.S3CProjectedGeodesicResolution" }, { "kind": "module", "id": "Semantics.Core.UnderversePacket", "name": "UnderversePacket", "path": "Semantics/Core/UnderversePacket.lean", "namespace": "Semantics.Underverse", "doc": "UnderversePacket.lean \u2014 Finite Typed Auditable Shadow-Space Implements the Equation Underverse Doctrine as a fixed-point packet: \"The Underverse is the finite, typed, auditable shadow-space of the Equation Forest: for every positive equation, it records the residual, complement, forbidden route, fa", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 5, "struct_count": 1, "inductive_count": 3, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.Core.UnderversePacket.mass_conservation_structural", "name": "mass_conservation_structural", "module": "Semantics.Core.UnderversePacket" }, { "kind": "def", "id": "Semantics.Core.UnderversePacket.AbsenceClass", "name": "AbsenceClass", "module": "Semantics.Core.UnderversePacket" }, { "kind": "def", "id": "Semantics.Core.UnderversePacket.minimalReceipt", "name": "minimalReceipt", "module": "Semantics.Core.UnderversePacket" }, { "kind": "def", "id": "Semantics.Core.UnderversePacket.failedBinding", "name": "failedBinding", "module": "Semantics.Core.UnderversePacket" }, { "kind": "def", "id": "Semantics.Core.UnderversePacket.isFixedPoint", "name": "isFixedPoint", "module": "Semantics.Core.UnderversePacket" }, { "kind": "def", "id": "Semantics.Core.UnderversePacket.isWardenActionable", "name": "isWardenActionable", "module": "Semantics.Core.UnderversePacket" }, { "kind": "module", "id": "Semantics.Core.UnderverseZeroLayer", "name": "UnderverseZeroLayer", "path": "Semantics/Core/UnderverseZeroLayer.lean", "namespace": "Semantics.UnderverseZeroLayer", "doc": "UnderverseZeroLayer.lean \u2014 explicit neutral closure accounting The zero layer is the receipt boundary between observable accounting and Underverse/complement accounting. It prevents \"missing\" or \"opposite\" terms from becoming free variables: a neutral event is admitted only when the net charge clos", "math_kind": "avm", "sorry_count": 0, "theorem_count": 3, "def_count": 7, "struct_count": 1, "inductive_count": 2, "line_count": 101 }, { "kind": "theorem", "id": "Semantics.Core.UnderverseZeroLayer.genus3BalancedFixture_closes", "name": "genus3BalancedFixture_closes", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "theorem", "id": "Semantics.Core.UnderverseZeroLayer.missingReplayFixture_holds", "name": "missingReplayFixture_holds", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "theorem", "id": "Semantics.Core.UnderverseZeroLayer.nonzeroChargeFixture_rejects", "name": "nonzeroChargeFixture_rejects", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.netCharge", "name": "netCharge", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.closesNeutral", "name": "closesNeutral", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.genus3ZeroChargeEvent", "name": "genus3ZeroChargeEvent", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.decideZeroLayer", "name": "decideZeroLayer", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.genus3BalancedFixture", "name": "genus3BalancedFixture", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.missingReplayFixture", "name": "missingReplayFixture", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "def", "id": "Semantics.Core.UnderverseZeroLayer.nonzeroChargeFixture", "name": "nonzeroChargeFixture", "module": "Semantics.Core.UnderverseZeroLayer" }, { "kind": "module", "id": "Semantics.CosmicStructure", "name": "CosmicStructure", "path": "Semantics/CosmicStructure.lean", "namespace": "Semantics.CosmicStructure", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 5, "inductive_count": 3, "line_count": 185 }, { "kind": "def", "id": "Semantics.CosmicStructure.zoneBoundaryFluidity", "name": "zoneBoundaryFluidity", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.zoneDensityContrast", "name": "zoneDensityContrast", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.zoneEmissionStrength", "name": "zoneEmissionStrength", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.cosmicSignatureOf", "name": "cosmicSignatureOf", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.classifyCosmicStability", "name": "classifyCosmicStability", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.processCosmicTransition", "name": "processCosmicTransition", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.defaultHaloZone", "name": "defaultHaloZone", "module": "Semantics.CosmicStructure" }, { "kind": "def", "id": "Semantics.CosmicStructure.defaultCosmicStructure", "name": "defaultCosmicStructure", "module": "Semantics.CosmicStructure" }, { "kind": "module", "id": "Semantics.CostEffectiveVerification", "name": "CostEffectiveVerification", "path": "Semantics/CostEffectiveVerification.lean", "namespace": "Semantics.CostEffectiveVerification", "doc": "CostEffectiveVerification.lean \u2014 Cost-Effective Verification Target Theorem This module formalizes the cost-effective verification target: prove that the manifold can group ontologically different systems together when they share the same behavioral operator, rather than trying to prove the full gr", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 4, "struct_count": 7, "inductive_count": 0, "line_count": 144 }, { "kind": "theorem", "id": "Semantics.CostEffectiveVerification.manifoldGroupsOntologicallyDifferentSystems", "name": "manifoldGroupsOntologicallyDifferentSystems", "module": "Semantics.CostEffectiveVerification" }, { "kind": "theorem", "id": "Semantics.CostEffectiveVerification.cheapestVerificationTarget", "name": "cheapestVerificationTarget", "module": "Semantics.CostEffectiveVerification" }, { "kind": "def", "id": "Semantics.CostEffectiveVerification.shareSameOperator", "name": "shareSameOperator", "module": "Semantics.CostEffectiveVerification" }, { "kind": "def", "id": "Semantics.CostEffectiveVerification.ontologicallyDifferent", "name": "ontologicallyDifferent", "module": "Semantics.CostEffectiveVerification" }, { "kind": "def", "id": "Semantics.CostEffectiveVerification.groupByOperator", "name": "groupByOperator", "module": "Semantics.CostEffectiveVerification" }, { "kind": "def", "id": "Semantics.CostEffectiveVerification.testHypothesis", "name": "testHypothesis", "module": "Semantics.CostEffectiveVerification" }, { "kind": "module", "id": "Semantics.CouchFilterNormalization", "name": "CouchFilterNormalization", "path": "Semantics/CouchFilterNormalization.lean", "namespace": "Semantics.CouchFilterNormalization", "doc": "# Couch Filter Normalization Witness This module records the finite, proof-checkable part of `data/couch_filter_normalization.json` and `data/couch_equation_forest_analysis.json`. The floating trajectory data remains an external empirical artifact. The Genome18 position, PIST admissibility flag, ", "math_kind": "routing", "sorry_count": 0, "theorem_count": 28, "def_count": 18, "struct_count": 3, "inductive_count": 1, "line_count": 380 }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchGenomeAddress_eq", "name": "couchGenomeAddress_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchGenomeAddress_range", "name": "couchGenomeAddress_range", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchPISTWitness_admissible", "name": "couchPISTWitness_admissible", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_kappa050_eq", "name": "couchFNumber_kappa050_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_kappa250_eq", "name": "couchFNumber_kappa250_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_fullSweep_eq", "name": "couchFNumber_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_increases_kappa050_to_kappa250", "name": "couchFNumber_increases_kappa050_to_kappa250", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_strictlyRisesAcrossSweep", "name": "couchFNumber_strictlyRisesAcrossSweep", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_kappa250_high", "name": "couchFNumber_kappa250_high", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_kappa050_not_high", "name": "couchFNumber_kappa050_not_high", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchFNumber_highClassification_fullSweep", "name": "couchFNumber_highClassification_fullSweep", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchURotated_kappa050_eq", "name": "couchURotated_kappa050_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchURotated_kappa250_eq", "name": "couchURotated_kappa250_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchURotated_fullSweep_eq", "name": "couchURotated_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchURotated_increases_kappa050_to_kappa250", "name": "couchURotated_increases_kappa050_to_kappa250", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchURotated_strictlyRisesAcrossSweep", "name": "couchURotated_strictlyRisesAcrossSweep", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchYAxisContainer_kappa050_eq", "name": "couchYAxisContainer_kappa050_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchYAxisContainer_kappa250_eq", "name": "couchYAxisContainer_kappa250_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchYAxisContainer_fullSweep_eq", "name": "couchYAxisContainer_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchYAxisContainer_r_constant", "name": "couchYAxisContainer_r_constant", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchRoutePressure_fullSweep_eq", "name": "couchRoutePressure_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchRoutingMode_fullSweep_eq", "name": "couchRoutingMode_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchRoutingAction_fullSweep_eq", "name": "couchRoutingAction_fullSweep_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchForestGenome_eq", "name": "couchForestGenome_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchNormalizedRouteMode_eq", "name": "couchNormalizedRouteMode_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchNormalizedRouteAction_eq", "name": "couchNormalizedRouteAction_eq", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchCouplingSummary_sensitive", "name": "couchCouplingSummary_sensitive", "module": "Semantics.CouchFilterNormalization" }, { "kind": "theorem", "id": "Semantics.CouchFilterNormalization.couchAvgCurvature_kappa050_lt_kappa250", "name": "couchAvgCurvature_kappa050_lt_kappa250", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchCurvatureSummary", "name": "couchCurvatureSummary", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchGenome", "name": "couchGenome", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchGenomeAddress", "name": "couchGenomeAddress", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchPISTWitness", "name": "couchPISTWitness", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchFNumberMilli", "name": "couchFNumberMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchHighFThresholdMilli", "name": "couchHighFThresholdMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.isHighFNumberCouch", "name": "isHighFNumberCouch", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchKappaMilli", "name": "couchKappaMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchURotatedMilli", "name": "couchURotatedMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchRValueConstantMilli", "name": "couchRValueConstantMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchYAxisContainer", "name": "couchYAxisContainer", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchRoutePressureMilli", "name": "couchRoutePressureMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchAtlasThresholdMilli", "name": "couchAtlasThresholdMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchRejectThresholdMilli", "name": "couchRejectThresholdMilli", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", "id": "Semantics.CouchFilterNormalization.couchRoutingMode", "name": "couchRoutingMode", "module": "Semantics.CouchFilterNormalization" }, { "kind": "def", 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"def", "id": "Semantics.CriticalityDynamics.remainingAfterTopple", "name": "remainingAfterTopple", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.classifyAvalancheClass", "name": "classifyAvalancheClass", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.toppleStepOf", "name": "toppleStepOf", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.applyToppleToSite", "name": "applyToppleToSite", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.receiveLoad", "name": "receiveLoad", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.edgeContribution", "name": "edgeContribution", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.findSite", "name": "findSite", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.rewriteSite", "name": "rewriteSite", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.applyIncomingForEdge", "name": "applyIncomingForEdge", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.distributeFromSite", "name": "distributeFromSite", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.firstUnstableSite", "name": "firstUnstableSite", "module": "Semantics.CriticalityDynamics" }, { "kind": "def", "id": "Semantics.CriticalityDynamics.temporalPotentialBias", "name": "temporalPotentialBias", "module": "Semantics.CriticalityDynamics" }, { "kind": "module", "id": "Semantics.CrossDimensionalFilter", "name": "CrossDimensionalFilter", "path": "Semantics/CrossDimensionalFilter.lean", "namespace": "Semantics.CrossDimensionalFilter", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CrossDimensionalFilter.lean \u2014 Matryoshka-Brane Cross-Shell Communication Problem: A 3D human wants to talk to a 2D flatlander. Direct communication is meaningless because the dimensionality mismatch de", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 6, "def_count": 10, "struct_count": 3, "inductive_count": 1, "line_count": 336 }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.expansionDimensionCorrect", "name": "expansionDimensionCorrect", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.preservedPrimesUnderstood", "name": "preservedPrimesUnderstood", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.spawnProducesN2", "name": "spawnProducesN2", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.allPrimesContained", "name": "allPrimesContained", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.filterAllContained", "name": "filterAllContained", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "theorem", "id": "Semantics.CrossDimensionalFilter.selfCommunicationPreservesAllPrimes", "name": "selfCommunicationPreservesAllPrimes", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.semanticPrimeCount", "name": "semanticPrimeCount", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.allSemanticPrimes", "name": "allSemanticPrimes", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.shellUnderstands", "name": "shellUnderstands", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.primeOverlap", "name": "primeOverlap", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.overlapToScalar", "name": "overlapToScalar", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.reductionFilter", "name": "reductionFilter", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.expansionFilter", "name": "expansionFilter", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.sendCrossShell", "name": "sendCrossShell", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.receiveCrossShell", "name": "receiveCrossShell", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "def", "id": "Semantics.CrossDimensionalFilter.spawnSubShells", "name": "spawnSubShells", "module": "Semantics.CrossDimensionalFilter" }, { "kind": "module", "id": "Semantics.CrossDomainOneOverN", "name": "CrossDomainOneOverN", "path": "Semantics/CrossDomainOneOverN.lean", "namespace": "Semantics.CrossDomainOneOverN", "doc": "CrossDomainOneOverN.lean \u2014 Experimental Analogs of 1/n Scaling The BraidCore framework predicts a residual quantum defect scaling as 1/n for circular Rydberg states: delta_BC(n) = 2*alpha/n. 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This tracks only bounded distortion and vacancy-like cardinality. It does not identify a defect species or infer atomistic geometry.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 143 }, { "kind": "theorem", "id": "Semantics.DefectMechanics.defectAdmissibleOfBounds", "name": "defectAdmissibleOfBounds", "module": "Semantics.DefectMechanics" }, { "kind": "theorem", "id": "Semantics.DefectMechanics.vacancyCountLeOccupancyBound", "name": "vacancyCountLeOccupancyBound", "module": "Semantics.DefectMechanics" }, { "kind": "theorem", "id": "Semantics.DefectMechanics.compressionContractsVacancyCount", "name": "compressionContractsVacancyCount", "module": "Semantics.DefectMechanics" }, { "kind": "theorem", "id": "Semantics.DefectMechanics.distortionLeActuationBudget", "name": "distortionLeActuationBudget", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.vacancyCovered", "name": "vacancyCovered", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.distortionBounded", "name": "distortionBounded", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.defectBudgeted", "name": "defectBudgeted", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.defectAdmissible", "name": "defectAdmissible", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.witnessOfMechanical", "name": "witnessOfMechanical", "module": "Semantics.DefectMechanics" }, { "kind": "def", "id": "Semantics.DefectMechanics.sampleDefectWitness", "name": "sampleDefectWitness", "module": "Semantics.DefectMechanics" }, { "kind": "module", "id": "Semantics.DegeneracyConversion", "name": "DegeneracyConversion", "path": "Semantics/DegeneracyConversion.lean", "namespace": "Semantics.DegeneracyConversion", "doc": "DegeneracyConversion.lean \u2014 Unified Degeneracy Conversion Matrix Framework Five frameworks share the same gate condition: GRANT iff ||coker(M) residual|| < \u03b5 1. Penguin decay: J_i = \u03a8\u2020 M^(i) \u03a8 (quadratic degeneracy map) 2. 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Authors: Research Stack Team DeltaGCLCompression.lean \u2014 Delta GCL Compression for Metadata This module formalizes the three-layer compression stack for metadata: 1. Delta Encoding: Store only changes from previous state 2. PTOS Di", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 62, "def_count": 37, "struct_count": 16, "inductive_count": 10, "line_count": 1433 }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.computeDelta_identical", "name": "computeDelta_identical", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.computeDelta_different", "name": "computeDelta_different", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.applyPTOSDictionary_length", "name": "applyPTOSDictionary_length", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.encodeCodon_unknown_length", "name": "encodeCodon_unknown_length", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.encodeToDeltaGCL_full_marker", "name": "encodeToDeltaGCL_full_marker", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.encodeToDeltaGCL_identical_marker", "name": "encodeToDeltaGCL_identical_marker", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.compressionStats_reduction", "name": "compressionStats_reduction", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.compressionStats_compressed_length", "name": "compressionStats_compressed_length", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.ptos_compression_700x", "name": "ptos_compression_700x", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.ptos_tsm_thermal_safety", "name": "ptos_tsm_thermal_safety", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.ptos_entropy_pruning", "name": "ptos_entropy_pruning", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_preserves_isolation", "name": "gcl_evolution_preserves_isolation", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_is_reversible", "name": "gcl_evolution_is_reversible", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_is_bounded", "name": "gcl_evolution_is_bounded", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_thermal_safety", "name": "gcl_evolution_thermal_safety", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_self_healing", "name": "gcl_evolution_self_healing", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_preserves_compression", "name": "gcl_evolution_preserves_compression", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_generation_bounded", "name": "gcl_evolution_generation_bounded", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_formally_verified", "name": "gcl_evolution_formally_verified", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.angrySphinx_energy_asymmetry_exponential", "name": "angrySphinx_energy_asymmetry_exponential", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.angrySphinx_gear_multiplicative", "name": "angrySphinx_gear_multiplicative", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.angrySphinx_total_cost_product", "name": "angrySphinx_total_cost_product", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.angrySphinx_nan_boundary_rejects", "name": "angrySphinx_nan_boundary_rejects", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.angrySphinx_exponential_attack_infeasible", "name": "angrySphinx_exponential_attack_infeasible", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_directive_core_protection", "name": "gcl_directive_core_protection", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_directive_operator_only", "name": "gcl_directive_operator_only", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_directive_audit_trail", "name": "gcl_directive_audit_trail", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.gcl_evolution_directive_containment", "name": "gcl_evolution_directive_containment", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.triumvirate_builder_proposes", "name": "triumvirate_builder_proposes", "module": "Semantics.DeltaGCLCompression" }, { "kind": "theorem", "id": "Semantics.DeltaGCLCompression.triumvirate_judge_thermal_safety", "name": "triumvirate_judge_thermal_safety", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.ptosLayerIndex", "name": "ptosLayerIndex", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.ptosDomainIndex", "name": "ptosDomainIndex", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.ptosTierIndex", "name": "ptosTierIndex", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.ptosConditionIndex", "name": "ptosConditionIndex", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.ptosUnknown", "name": "ptosUnknown", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.computeDelta", "name": "computeDelta", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.applyPTOSDictionary", "name": "applyPTOSDictionary", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.shortCodonMap", "name": "shortCodonMap", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.encodeCodon", "name": "encodeCodon", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.encodeToDeltaGCL", "name": "encodeToDeltaGCL", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.compressionRatioSI", "name": "compressionRatioSI", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.compressionPercentage", "name": "compressionPercentage", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.compressionStats", "name": "compressionStats", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.encodePTOSWithCapability", "name": "encodePTOSWithCapability", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.modelTypeFromPTOS", "name": "modelTypeFromPTOS", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.applyGCLEvolution", "name": "applyGCLEvolution", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.angrySphinxEnergyAsymmetry", "name": "angrySphinxEnergyAsymmetry", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.angrySphinxGearCost", "name": "angrySphinxGearCost", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.angrySphinxSolveCost", "name": "angrySphinxSolveCost", "module": "Semantics.DeltaGCLCompression" }, { "kind": "def", "id": "Semantics.DeltaGCLCompression.angrySphinxNaNBoundary", "name": "angrySphinxNaNBoundary", "module": "Semantics.DeltaGCLCompression" }, { "kind": "module", "id": "Semantics.Diagnostics", "name": "Diagnostics", "path": "Semantics/Diagnostics.lean", "namespace": "Semantics.ENE", "doc": "ENE Self-Diagnostics", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 2, "inductive_count": 0, "line_count": 137 }, { "kind": "def", "id": "Semantics.Diagnostics.DiagnosticReport", "name": "DiagnosticReport", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.KnitCondition", "name": "KnitCondition", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.RigidCondition", "name": "RigidCondition", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.CrntCondition", "name": "CrntCondition", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.FlavorCondition", "name": "FlavorCondition", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.NeuroCondition", "name": "NeuroCondition", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.ENEDiagnostics", "name": "ENEDiagnostics", "module": "Semantics.Diagnostics" }, { "kind": "def", "id": "Semantics.Diagnostics.Graph", "name": "Graph", "module": "Semantics.Diagnostics" }, { "kind": "module", "id": "Semantics.DiffusionSNRBias", "name": "DiffusionSNRBias", "path": "Semantics/DiffusionSNRBias.lean", "namespace": "Semantics.DiffusionSNRBias", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DiffusionSNRBias.lean \u2014 SNR-t Bias Correction for Diffusion Probabilistic Models This module formalizes the SNR-t bias phenomenon and differential correction method from \"Elucidating the SNR-t Bias of ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 20, "struct_count": 11, "inductive_count": 1, "line_count": 351 }, { "kind": "theorem", "id": "Semantics.DiffusionSNRBias.mul_le_mul_of_nonneg_right", "name": "mul_le_mul_of_nonneg_right", "module": "Semantics.DiffusionSNRBias" }, { "kind": "theorem", "id": "Semantics.DiffusionSNRBias.snrBoundedByModelParams", "name": "snrBoundedByModelParams", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.zero", "name": "zero", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.one", "name": "one", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.epsilon", "name": "epsilon", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.ofNat", "name": "ofNat", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.toFloat", "name": "toFloat", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.add", "name": "add", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.sub", "name": "sub", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.mul", "name": "mul", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.div", "name": "div", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.sqrt", "name": "sqrt", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.clip", "name": "clip", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.meanSquaredNorm", "name": "meanSquaredNorm", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.fromSignalNoise", "name": "fromSignalNoise", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.lessThan", "name": "lessThan", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.detectBias", "name": "detectBias", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.differentialSignal", "name": "differentialSignal", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.differentialCorrection", "name": "differentialCorrection", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.defaultLinear", "name": "defaultLinear", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.energyConservation", "name": "energyConservation", "module": "Semantics.DiffusionSNRBias" }, { "kind": "def", "id": "Semantics.DiffusionSNRBias.evaluateCorrection", "name": "evaluateCorrection", "module": "Semantics.DiffusionSNRBias" }, { "kind": "module", "id": "Semantics.DimensionalConsistency", "name": "DimensionalConsistency", "path": "Semantics/DimensionalConsistency.lean", "namespace": "Semantics.DimensionalConsistency", "doc": "DimensionalConsistency.lean \u2014 Formal Admission of Dimensional Fitting The BraidCore framework claims that the Menger sponge void fraction z = 7/27 and the dislocation correction 133/137 are \"derived\" from geometric construction. However, when these dimensionless ratios are used to predict physical ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 7, "def_count": 18, "struct_count": 1, "inductive_count": 2, "line_count": 343 }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.for", "name": "for", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.p04RequiresP0", "name": "p04RequiresP0", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.p0RequiresP0", "name": "p0RequiresP0", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.p01DoesNotRequireP0", "name": "p01DoesNotRequireP0", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.countRequiresP0_correct", "name": "countRequiresP0_correct", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.dimensionlessEntries_length", "name": "dimensionlessEntries_length", "module": "Semantics.DimensionalConsistency" }, { "kind": "theorem", "id": "Semantics.DimensionalConsistency.p04DimensionSourceIsFitted", "name": "p04DimensionSourceIsFitted", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.PhysicalDimension", "name": "PhysicalDimension", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.DimensionSource", "name": "DimensionSource", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p01Dimensional", "name": "p01Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p02Dimensional", "name": "p02Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p03Dimensional", "name": "p03Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p04Dimensional", "name": "p04Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p05Dimensional", "name": "p05Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p06Dimensional", "name": "p06Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p07Dimensional", "name": "p07Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p08Dimensional", "name": "p08Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p09Dimensional", "name": "p09Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p10Dimensional", "name": "p10Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p11Dimensional", "name": "p11Dimensional", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.p0ScaleFactor", "name": "p0ScaleFactor", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.allDimensionalEntries", "name": "allDimensionalEntries", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.countRequiresP0", "name": "countRequiresP0", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.countDimensionless", "name": "countDimensionless", "module": "Semantics.DimensionalConsistency" }, { "kind": "def", "id": "Semantics.DimensionalConsistency.dimensionlessEntries", "name": "dimensionlessEntries", "module": "Semantics.DimensionalConsistency" }, { "kind": "module", "id": "Semantics.DiscreteContinuousBound", "name": "DiscreteContinuousBound", "path": "Semantics/DiscreteContinuousBound.lean", "namespace": "Semantics.DiscreteContinuousBound", "doc": "# DiscreteContinuousBound.lean Exponential error bound for discrete\u2013continuous coupling via Gr\u00f6nwall's inequality. Given the 2\u00d72 coupling matrix A = (\u03b5/2) \u00b7 [[0,1],[1,0]], we prove: 1. \u2016A\u2016 = |\u03b5|/2 (operator norm) 2. \u2016e(t)\u2016 \u2264 \u2016e(0)\u2016 \u00b7 exp(|\u03b5|/2 \u00b7 t) (Gr\u00f6nwall bound on coupling error", "math_kind": "analysis", "sorry_count": 0, "theorem_count": 8, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 209 }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.A_entry_bound", "name": "A_entry_bound", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.coupling_opNorm", "name": "coupling_opNorm", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.coupling_opNNNorm", "name": "coupling_opNNNorm", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.coupling_lipschitzWith", "name": "coupling_lipschitzWith", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.norm_le_gronwallBound_of_coupling", "name": "norm_le_gronwallBound_of_coupling", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.discrete_continuous_bound", "name": "discrete_continuous_bound", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.trajectory_dist_bound", "name": "trajectory_dist_bound", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "theorem", "id": "Semantics.DiscreteContinuousBound.trajectory_dist_bound_univ", "name": "trajectory_dist_bound_univ", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "def", "id": "Semantics.DiscreteContinuousBound.M\u2080", "name": "M\u2080", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "def", "id": "Semantics.DiscreteContinuousBound.A", "name": "A", "module": "Semantics.DiscreteContinuousBound" }, { "kind": "mathlib", "id": "Mathlib.Analysis.ODE.Gronwall", "name": "Mathlib.Analysis.ODE.Gronwall" }, { "kind": "module", "id": "Semantics.DistributedTraining", "name": "DistributedTraining", "path": "Semantics/DistributedTraining.lean", "namespace": "Semantics.DistributedTraining", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DistributedTraining.lean \u2014 Distributed Training Configuration in Lean This module formalizes distributed training configuration for NII cores to become n-semantic morphic. It leverages: ENE (Endless No", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 29, "struct_count": 10, "inductive_count": 4, "line_count": 362 }, { "kind": "def", "id": "Semantics.DistributedTraining.zero", "name": "zero", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.one", "name": "one", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.ofNat", "name": "ofNat", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.qfox", "name": "qfox", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.architect", "name": "architect", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.judge", "name": "judge", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.awsNode", "name": "awsNode", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.netcupRouter", "name": "netcupRouter", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.racknerdNode", "name": "racknerdNode", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.allNodes", "name": "allNodes", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.totalCores", "name": "totalCores", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.totalRAM", "name": "totalRAM", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.totalStorage", "name": "totalStorage", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.gpuNodeCount", "name": "gpuNodeCount", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.fromNodes", "name": "fromNodes", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.defaultResources", "name": "defaultResources", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.defaultConfiguration", "name": "defaultConfiguration", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.naturalLanguageDataset", "name": "naturalLanguageDataset", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.codingLanguageDataset", "name": "codingLanguageDataset", "module": "Semantics.DistributedTraining" }, { "kind": "def", "id": "Semantics.DistributedTraining.calculateAssignment", "name": "calculateAssignment", "module": "Semantics.DistributedTraining" }, { "kind": "module", "id": "Semantics.DlessScalarField", "name": "DlessScalarField", "path": "Semantics/DlessScalarField.lean", "namespace": "DlessScalar", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Dimensionless conformal factors \u03a9(entity) that warp the equation manifold metric, making safety-critical equations more discoverable. Adapted from MOIM's Dless Scalar Field for equation-specific use: 1. Conformal Warpin", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 10, "struct_count": 3, "inductive_count": 0, "line_count": 193 }, { "kind": "theorem", "id": "Semantics.DlessScalarField.omega_positive", "name": "omega_positive", "module": "Semantics.DlessScalarField" }, { "kind": "theorem", "id": "Semantics.DlessScalarField.warped_distance_monotonic", "name": "warped_distance_monotonic", "module": "Semantics.DlessScalarField" }, { "kind": "theorem", "id": "Semantics.DlessScalarField.combine_preserves_positivity", "name": "combine_preserves_positivity", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.omegaFromStatus", "name": "omegaFromStatus", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.omegaFromCrossRefs", "name": "omegaFromCrossRefs", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.omegaFromComplexity", "name": "omegaFromComplexity", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.combineOmega", "name": "combineOmega", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.warpedDistance", "name": "warpedDistance", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.warpManifoldPoint", "name": "warpManifoldPoint", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.computeEquationOmega", "name": "computeEquationOmega", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.createWarpedEquation", "name": "createWarpedEquation", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.omegaSearchResult", "name": "omegaSearchResult", "module": "Semantics.DlessScalarField" }, { "kind": "def", "id": "Semantics.DlessScalarField.sortOmegaResults", "name": "sortOmegaResults", "module": "Semantics.DlessScalarField" }, { "kind": "module", "id": "Semantics.DomainDetector", "name": "DomainDetector", "path": "Semantics/DomainDetector.lean", "namespace": "Semantics.DomainDetector", "doc": "DomainDetector.lean \u2014 Structure-Based Prediction Classification Determines whether a predicted value is structurally related to the Menger-Pigeonhole void fraction z = 7/27, and whether its error falls in the correctable 2\u201315% sweet spot. 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"outsideTolerance_isNotZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.sweetSpotBoundaryLow", "name": "sweetSpotBoundaryLow", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.sweetSpotBoundaryHigh", "name": "sweetSpotBoundaryHigh", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.sweetSpotMid", "name": "sweetSpotMid", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.zeroError_notInSweetSpot", "name": "zeroError_notInSweetSpot", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.largeError_notInSweetSpot", "name": "largeError_notInSweetSpot", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.speciesArea_isZDirect", "name": "speciesArea_isZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.mott_isZDirect", "name": "mott_isZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.percolationBcc_isZDirect", "name": "percolationBcc_isZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.magneticNi_isZDirect", "name": "magneticNi_isZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.fishingP5_notZDirect", "name": "fishingP5_notZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.jupiter_notZDirect", "name": "jupiter_notZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.weakValue_notZDirect", "name": "weakValue_notZDirect", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.fineStructure_notZDirect", "name": "fineStructure_notZDirect", "module": 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"Semantics.DomainDetector.cocrpt_inSweetSpot", "name": "cocrpt_inSweetSpot", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.mott_notInSweetSpot", "name": "mott_notInSweetSpot", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.detectorIsStructuralCriterion", "name": "detectorIsStructuralCriterion", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.allPredictionsClassified", "name": "allPredictionsClassified", "module": "Semantics.DomainDetector" }, { "kind": "theorem", "id": "Semantics.DomainDetector.detectorLimitation", "name": "detectorLimitation", "module": "Semantics.DomainDetector" }, { "kind": "def", "id": "Semantics.DomainDetector.zCanonical", "name": "zCanonical", "module": "Semantics.DomainDetector" }, { "kind": "def", "id": "Semantics.DomainDetector.zTolerance", "name": "zTolerance", "module": "Semantics.DomainDetector" }, { "kind": "def", "id": 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Authors: Research Stack Team DomainKernel.lean \u2014 Generic Trajectory Kernel with Domain Adapters Architecture: 1. 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MOIM's 16 Domain Registries: 1. Mathematics (12 subdomains) 2. Physics 3. Chemistry 4. Biology ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 2, "line_count": 208 }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.alignDomain", "name": "alignDomain", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.reverseAlignDomain", "name": "reverseAlignDomain", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.domainsCompatible", "name": "domainsCompatible", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.alignmentIsBidirectional", "name": "alignmentIsBidirectional", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.countMappingsToMOIM", "name": "countMappingsToMOIM", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "def", "id": "Semantics.DomainRegistryAlignment.bidirectionalCoverage", "name": "bidirectionalCoverage", "module": "Semantics.DomainRegistryAlignment" }, { "kind": "module", "id": "Semantics.DomainState", "name": "DomainState", "path": "Semantics/DomainState.lean", "namespace": "Semantics.DomainState", "doc": "DomainState.lean - Full Q16_16-based domain state implementation Hardware-native structures for domain resolution and stability tracking", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 7, "inductive_count": 2, "line_count": 152 }, { "kind": "def", "id": "Semantics.DomainState.computeDomainChristoffel", "name": "computeDomainChristoffel", "module": "Semantics.DomainState" }, { "kind": "def", "id": "Semantics.DomainState.domainCos", "name": "domainCos", "module": "Semantics.DomainState" }, { "kind": "def", "id": "Semantics.DomainState.computeDomainFrustration", "name": "computeDomainFrustration", "module": "Semantics.DomainState" }, { "kind": "def", "id": "Semantics.DomainState.computeDomainLockingEnergy", "name": "computeDomainLockingEnergy", "module": "Semantics.DomainState" }, { "kind": "def", "id": "Semantics.DomainState.updateDomainStateFromGeometry", "name": "updateDomainStateFromGeometry", "module": "Semantics.DomainState" }, { "kind": "def", "id": "Semantics.DomainState.updateDomainStateFromChristoffel", "name": "updateDomainStateFromChristoffel", "module": "Semantics.DomainState" }, { "kind": "module", "id": "Semantics.DrexlerianMechanosynthesis", "name": "DrexlerianMechanosynthesis", "path": "Semantics/DrexlerianMechanosynthesis.lean", "namespace": "Semantics.DrexlerianMechanosynthesis", "doc": "DrexlerianMechanosynthesis.lean \u2014 Atomic Building: STM, Tunneling, Morse Potential This module formalizes the mathematical models governing atomically precise manufacturing, from Drexler's 1986 theory to the 2026 experimental realization. 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Authors: Research Stack Team DspErasureCoding.lean \u2014 DSP-Aware 3-Stream Erasure Coding This module formalizes DSP-aware erasure coding for streaming data: 3-stream redundancy scheme (inspired by PhiRedundancy) Sample-block based e", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 16, "struct_count": 5, "inductive_count": 2, "line_count": 326 }, { "kind": "theorem", "id": "Semantics.DspErasureCoding.identityPermutationInverse", "name": "identityPermutationInverse", "module": "Semantics.DspErasureCoding" }, { "kind": "theorem", "id": "Semantics.DspErasureCoding.validSchemeCoprime", "name": "validSchemeCoprime", "module": "Semantics.DspErasureCoding" }, { "kind": "theorem", "id": "Semantics.DspErasureCoding.recoveryIsAverage", "name": "recoveryIsAverage", "module": "Semantics.DspErasureCoding" }, { "kind": "theorem", "id": "Semantics.DspErasureCoding.erasureThresholdMonotonic", "name": "erasureThresholdMonotonic", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.isCoprime", "name": "isCoprime", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.isValidScheme", "name": "isValidScheme", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.affinePerm", "name": "affinePerm", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.affinePermInv", "name": "affinePermInv", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.buildPrimaryStream", "name": "buildPrimaryStream", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.buildRecoveryStream1", "name": "buildRecoveryStream1", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.buildRecoveryStream2", "name": "buildRecoveryStream2", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.buildStreamBundle", "name": "buildStreamBundle", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.detectErasureSpectral", "name": "detectErasureSpectral", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.detectErasureThreshold", "name": "detectErasureThreshold", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.fetchSample", "name": "fetchSample", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.recoverSample", "name": "recoverSample", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.recoverBlock", "name": "recoverBlock", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.modeToOpcode", "name": "modeToOpcode", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.exampleScheme", "name": "exampleScheme", "module": "Semantics.DspErasureCoding" }, { "kind": "def", "id": "Semantics.DspErasureCoding.exampleBlock", "name": "exampleBlock", "module": "Semantics.DspErasureCoding" }, { "kind": "module", "id": "Semantics.DynamicCanal", "name": "DynamicCanal", "path": "Semantics/DynamicCanal.lean", "namespace": "Semantics.DynamicCanal", "doc": "DYNAMIC_CANAL.lean", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 8, "def_count": 44, "struct_count": 15, "inductive_count": 4, "line_count": 912 }, { "kind": "theorem", "id": "Semantics.DynamicCanal.isqrt_spec", "name": "isqrt_spec", "module": "Semantics.DynamicCanal" }, { "kind": "theorem", "id": "Semantics.DynamicCanal.Q16_16", "name": "Q16_16", "module": "Semantics.DynamicCanal" }, { "kind": "theorem", "id": "Semantics.DynamicCanal.dynamicCanalLambda_total", "name": "dynamicCanalLambda_total", "module": "Semantics.DynamicCanal" }, { "kind": "theorem", "id": "Semantics.DynamicCanal.stepLane_total", "name": "stepLane_total", "module": "Semantics.DynamicCanal" }, { "kind": "theorem", "id": "Semantics.DynamicCanal.stepSection_total", "name": "stepSection_total", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.zero", "name": "zero", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.one", "name": "one", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.epsilon", "name": "epsilon", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.abs", "name": "abs", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.add", "name": "add", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.sub", "name": "sub", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.mul", "name": "mul", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.div", "name": "div", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.sqrt", "name": "sqrt", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.max", "name": "max", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.sat01", "name": "sat01", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.ofInt", "name": "ofInt", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.ofNat", "name": "ofNat", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.toInt", "name": "toInt", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.ofFloat", "name": "ofFloat", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.toFloat", "name": "toFloat", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.neg", "name": "neg", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.mk", "name": "mk", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.VecN", "name": "VecN", "module": "Semantics.DynamicCanal" }, { "kind": "def", "id": "Semantics.DynamicCanal.vecAdd", "name": "vecAdd", "module": "Semantics.DynamicCanal" }, { "kind": "module", "id": "Semantics.E8RRCAnalysis", "name": "E8RRCAnalysis", "path": "Semantics/E8RRCAnalysis.lean", "namespace": "Semantics.E8RRCAnalysis", "doc": "E8RRCAnalysis.lean \u2014 Use RRC to classify and accelerate E\u2088 Sidon proof strategies", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 0, "inductive_count": 0, "line_count": 219 }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.computationalVerificationFixture", "name": "computationalVerificationFixture", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.multiplicativityApproachFixture", "name": "multiplicativityApproachFixture", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.e8LevelSetFixture", "name": "e8LevelSetFixture", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.modularFormsFixture", "name": "modularFormsFixture", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.smoothNumberDensityFixture", "name": "smoothNumberDensityFixture", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.e8ApproachCorpus", "name": "e8ApproachCorpus", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.analyzeE8Alignments", "name": "analyzeE8Alignments", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.rankE8Approaches", "name": "rankE8Approaches", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.strategicRecommendations", "name": "strategicRecommendations", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.validateRRCMathematicalAlignment", "name": "validateRRCMathematicalAlignment", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.criticalPathAnalysis", "name": "criticalPathAnalysis", "module": "Semantics.E8RRCAnalysis" }, { "kind": "def", "id": "Semantics.E8RRCAnalysis.testE8RRCAnalysis", "name": "testE8RRCAnalysis", "module": "Semantics.E8RRCAnalysis" }, { "kind": "module", "id": "Semantics.E8Sidon", "name": "E8Sidon", "path": "Semantics/E8Sidon.lean", "namespace": "Semantics.E8Sidon", "doc": "## Status of Each Theorem | Theorem | Status | Sorry count | |---------|--------|-------------| | \u00a71-2: E8 constants, \u03c3\u2083/\u03c3\u2087 definitions | Complete | 0 | | \u00a73: sigma3_one, sigma7_one | Complete | 0 | | \u00a74: sigma3_prime, sigma7_prime | Complete | 0 | | \u00a75: sigma3_mono, sigma7_mono | Complete | 0 | | ", "math_kind": "number_theory", "sorry_count": 5, "theorem_count": 60, "def_count": 23, "struct_count": 0, "inductive_count": 0, "line_count": 1134 }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_root_split", "name": "e8_root_split", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_coxeter_relation", "name": "e8_coxeter_relation", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_coxeter_near_singer", "name": "e8_coxeter_near_singer", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_one", "name": "sigma3_one", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma7_one", "name": "sigma7_one", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_ne_zero", "name": "sigma3_ne_zero", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma7_ne_zero", "name": "sigma7_ne_zero", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_prime", "name": "sigma3_prime", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma7_prime", "name": "sigma7_prime", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_dvd_le", "name": "sigma3_dvd_le", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma7_dvd_le", "name": "sigma7_dvd_le", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_prime_lt", "name": "sigma3_prime_lt", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_multiplicative", "name": "sigma3_multiplicative", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma7_multiplicative", "name": "sigma7_multiplicative", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n2", "name": "e8_conv_n2", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n3", "name": "e8_conv_n3", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n4", "name": "e8_conv_n4", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n5", "name": "e8_conv_n5", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n10", "name": "e8_conv_n10", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n20", "name": "e8_conv_n20", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n50", "name": "e8_conv_n50", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_n100", "name": "e8_conv_n100", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sigma3_le_sigma7", "name": "sigma3_le_sigma7", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_convolution", "name": "e8_convolution", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_batch", "name": "e8_conv_batch", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_nonneg", "name": "e8_conv_nonneg", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.e8_conv_le_sigma7", "name": "e8_conv_le_sigma7", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sq_le_two_mul", "name": "sq_le_two_mul", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.fiber_partition", "name": "fiber_partition", "module": "Semantics.E8Sidon" }, { "kind": "theorem", "id": "Semantics.E8Sidon.sidon_fiber_le_two", "name": "sidon_fiber_le_two", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8RootCount", "name": "e8RootCount", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8PositiveRoots", "name": "e8PositiveRoots", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8DualCoxeter", "name": "e8DualCoxeter", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8CoxeterNumber", "name": "e8CoxeterNumber", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.sigmaK", "name": "sigmaK", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.sigma3", "name": "sigma3", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.sigma7", "name": "sigma7", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.convolutionLHS", "name": "convolutionLHS", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.convolutionRHS", "name": "convolutionRHS", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.IsSidonSet", "name": "IsSidonSet", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.sumFiber", "name": "sumFiber", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.additiveEnergy", "name": "additiveEnergy", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.collisionCount", "name": "collisionCount", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.pairSumCount", "name": "pairSumCount", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.totalCollisionExcess", "name": "totalCollisionExcess", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.convWeight", "name": "convWeight", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.E8Admissible", "name": "E8Admissible", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.E8LevelSet", "name": "E8LevelSet", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8ConvDivisor", "name": "e8ConvDivisor", "module": "Semantics.E8Sidon" }, { "kind": "def", "id": "Semantics.E8Sidon.e8SimpleRootStrand", "name": "e8SimpleRootStrand", "module": "Semantics.E8Sidon" }, { "kind": "module", "id": "Semantics.ENEApi", "name": "ENEApi", "path": "Semantics/ENEApi.lean", "namespace": "Semantics.ENEApi", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ENEApi.lean \u2014 ENE Security and Key Derivation Replaces infra/ene_api.py security logic with a formal Lean module. Defines security operations for ENE (Endless Node Edges) sensitive data handling. Per ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 4, "inductive_count": 1, "line_count": 191 }, { "kind": "theorem", "id": "Semantics.ENEApi.secretAccessAll", "name": "secretAccessAll", "module": "Semantics.ENEApi" }, { "kind": "theorem", "id": "Semantics.ENEApi.publicAccessOnly", "name": "publicAccessOnly", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.checkAccess", "name": "checkAccess", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.xorSemanticAxes", "name": "xorSemanticAxes", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.goldenRatioMix", "name": "goldenRatioMix", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.deriveKeyFromSemantic", "name": "deriveKeyFromSemantic", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.computeIntegrityHash", "name": "computeIntegrityHash", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.encryptData", "name": "encryptData", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.decryptData", "name": "decryptData", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.initSecurityManager", "name": "initSecurityManager", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.storeSensitiveData", "name": "storeSensitiveData", "module": "Semantics.ENEApi" }, { "kind": "def", "id": "Semantics.ENEApi.retrieveSensitiveData", "name": "retrieveSensitiveData", "module": "Semantics.ENEApi" }, { "kind": "module", "id": "Semantics.ENEContextTokenCache", "name": "ENEContextTokenCache", "path": "Semantics/ENEContextTokenCache.lean", "namespace": "Semantics.ENEContextTokenCache", "doc": "# ENE Context Token Cache Lean-owned accounting for context token usage across ENE-backed sessions. External shims may serialize records, but cache lawfulness, cost, and invariant extraction live here.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 4, "def_count": 25, "struct_count": 4, "inductive_count": 3, "line_count": 192 }, { "kind": "theorem", "id": "Semantics.ENEContextTokenCache.usageTotalZero", "name": "usageTotalZero", "module": "Semantics.ENEContextTokenCache" }, { "kind": "theorem", "id": "Semantics.ENEContextTokenCache.emptyCacheWithinBudget", "name": "emptyCacheWithinBudget", "module": "Semantics.ENEContextTokenCache" }, { "kind": "theorem", "id": "Semantics.ENEContextTokenCache.insertRecordTotalWitness", "name": "insertRecordTotalWitness", "module": "Semantics.ENEContextTokenCache" }, { "kind": "theorem", "id": "Semantics.ENEContextTokenCache.minimalUsageCostTotal", "name": "minimalUsageCostTotal", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.zeroUsage", "name": "zeroUsage", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.usageTotal", "name": "usageTotal", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.recordTotal", "name": "recordTotal", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.addUsage", "name": "addUsage", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.totalUsage", "name": "totalUsage", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.totalTokens", "name": "totalTokens", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.budgetRemaining", "name": "budgetRemaining", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.cacheWithinBudget", "name": "cacheWithinBudget", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.tokenUsagePositions", "name": "tokenUsagePositions", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.contextCompressionField", "name": "contextCompressionField", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.contextCompressionCodes", "name": "contextCompressionCodes", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.rgflowUsageLawful", "name": "rgflowUsageLawful", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.compressedUsageCost", "name": "compressedUsageCost", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.minimalUsageCost", "name": "minimalUsageCost", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.compressionWitness", "name": "compressionWitness", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.effectiveRecordCost", "name": "effectiveRecordCost", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.retainRecord", "name": "retainRecord", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.insertRecord", "name": "insertRecord", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.contextTokenInvariant", "name": "contextTokenInvariant", "module": "Semantics.ENEContextTokenCache" }, { "kind": "def", "id": "Semantics.ENEContextTokenCache.contextTokenCost", "name": "contextTokenCost", "module": "Semantics.ENEContextTokenCache" }, { "kind": "module", "id": "Semantics.ENECredentialEnvelope", "name": "ENECredentialEnvelope", "path": "Semantics/ENECredentialEnvelope.lean", "namespace": "Semantics.ENECredentialEnvelope", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ENECredentialEnvelope.lean \u2014 ENE Cloud Credential Envelope Replaces infra/ene_cloud_credential_manager.py encrypt/decrypt spec with a formal Lean module. Defines credential envelope structure, node sel", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 8, "struct_count": 4, "inductive_count": 1, "line_count": 209 }, { "kind": "theorem", "id": "Semantics.ENECredentialEnvelope.healthyNodeThreshold", "name": "healthyNodeThreshold", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "theorem", "id": "Semantics.ENECredentialEnvelope.initNodeStatsZeroConnections", "name": "initNodeStatsZeroConnections", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "theorem", "id": "Semantics.ENECredentialEnvelope.initCredentialEnvelopeZeroUsage", "name": "initCredentialEnvelopeZeroUsage", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "theorem", "id": "Semantics.ENECredentialEnvelope.assignedNodeInList", "name": "assignedNodeInList", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.zero", "name": "zero", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.one", "name": "one", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.ofFrac", "name": "ofFrac", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.initNodeStats", "name": "initNodeStats", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.calculateHealthScore", "name": "calculateHealthScore", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.selectNode", "name": "selectNode", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.initCredentialEnvelope", "name": "initCredentialEnvelope", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "def", "id": "Semantics.ENECredentialEnvelope.isAssignedToNode", "name": "isAssignedToNode", "module": "Semantics.ENECredentialEnvelope" }, { "kind": "module", "id": "Semantics.ENEDistributedNode", "name": "ENEDistributedNode", "path": "Semantics/ENEDistributedNode.lean", "namespace": "Semantics.ENEDistributedNode", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ENEDistributedNode.lean \u2014 ENE Distributed Node Gossip Protocol & Consensus Replaces infra/ene_distributed_node.py gossip protocol and consensus logic with a formal Lean module. Defines gossip message s", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 6, "inductive_count": 1, "line_count": 221 }, { "kind": "theorem", "id": "Semantics.ENEDistributedNode.initNodeIdentityFullHealth", "name": "initNodeIdentityFullHealth", "module": "Semantics.ENEDistributedNode" }, { "kind": "theorem", "id": "Semantics.ENEDistributedNode.emptyConsensusHasNoVotes", "name": "emptyConsensusHasNoVotes", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.zero", "name": "zero", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.one", "name": "one", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.ofFrac", "name": "ofFrac", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.initNodeIdentity", "name": "initNodeIdentity", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.createGossipMessage", "name": "createGossipMessage", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.initConsensusState", "name": "initConsensusState", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.addVote", "name": "addVote", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.isConsensusReached", "name": "isConsensusReached", "module": "Semantics.ENEDistributedNode" }, { "kind": "def", "id": "Semantics.ENEDistributedNode.calculateMeshHealth", "name": "calculateMeshHealth", "module": "Semantics.ENEDistributedNode" }, { "kind": "module", "id": "Semantics.ENESecurity", "name": "ENESecurity", "path": "Semantics/ENESecurity.lean", "namespace": "", "doc": "# ENE Security Module This module provides the formal security primitives for ENE (Endless Node Edges) to safely hold sensitive data. All security operations follow the bind primitive pattern and are formally verified. ## Security Axioms 1. **Confidentiality**: Sensitive data is encrypted at rest", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 1, "def_count": 8, "struct_count": 3, "inductive_count": 0, "line_count": 157 }, { "kind": "theorem", "id": "Semantics.ENESecurity.access_control_monotonic", "name": "access_control_monotonic", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.classifyData", "name": "classifyData", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.deriveKeyFromSemantic", "name": "deriveKeyFromSemantic", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.checkAccess", "name": "checkAccess", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.eneSecurityBind", "name": "eneSecurityBind", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.storeSensitiveData", "name": "storeSensitiveData", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.retrieveSensitiveData", "name": "retrieveSensitiveData", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.exampleSecurityState", "name": "exampleSecurityState", "module": "Semantics.ENESecurity" }, { "kind": "def", "id": "Semantics.ENESecurity.exampleSensitiveData", "name": "exampleSensitiveData", "module": "Semantics.ENESecurity" }, { "kind": "module", "id": "Semantics.EffectiveBoundDQ", "name": "EffectiveBoundDQ", "path": "Semantics/EffectiveBoundDQ.lean", "namespace": "Semantics.EffectiveBoundDQ", "doc": "EffectiveBoundDQ.lean \u2014 Effective Bounds in the 8D DualQuaternion Spectrum Unifies three problems through the common Q\u2081\u00d7Q\u2082 algebra: 1. **Goormaghtigh boundedness** (SpherionTwinPrime): repunit collisions are bounded to [2,90]\u00d7[3,13] \u2014 the `goormaghtigh_boundedness` axiom. 2. **Quadruplon quantiza", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 8, "def_count": 5, "struct_count": 1, "inductive_count": 1, "line_count": 368 }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.quadruplonEnergy_eq_dualQuatEnergy", "name": "quadruplonEnergy_eq_dualQuatEnergy", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.cluster_C4_energy_nonneg", "name": "cluster_C4_energy_nonneg", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.bakerLogLowerBound_uncorrected_is_false", "name": "bakerLogLowerBound_uncorrected_is_false", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.linForm_ne_zero_of_pow_ne", "name": "linForm_ne_zero_of_pow_ne", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.elementaryLogLowerBound", "name": "elementaryLogLowerBound", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.effectiveGoormaghtighBound", "name": "effectiveGoormaghtighBound", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.computationalRefinement", "name": "computationalRefinement", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "theorem", "id": "Semantics.EffectiveBoundDQ.quadruplon_irreducible", "name": "quadruplon_irreducible", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "def", "id": "Semantics.EffectiveBoundDQ.clusterSector", "name": "clusterSector", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "def", "id": "Semantics.EffectiveBoundDQ.quadruplonEnergy", "name": "quadruplonEnergy", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "def", "id": "Semantics.EffectiveBoundDQ.excitonEnergy", "name": "excitonEnergy", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "def", "id": "Semantics.EffectiveBoundDQ.sidonTetrahedronToDQ", "name": "sidonTetrahedronToDQ", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "def", "id": "Semantics.EffectiveBoundDQ.effectiveBoundReceipt", "name": "effectiveBoundReceipt", "module": "Semantics.EffectiveBoundDQ" }, { "kind": "module", "id": "Semantics.EfficiencyAnalysis", "name": "EfficiencyAnalysis", "path": "Semantics/EfficiencyAnalysis.lean", "namespace": "Semantics.EfficiencyAnalysis", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 5, "inductive_count": 0, "line_count": 125 }, { "kind": "def", "id": "Semantics.EfficiencyAnalysis.calculateSabotagePreventionGains", "name": "calculateSabotagePreventionGains", "module": "Semantics.EfficiencyAnalysis" }, { "kind": "def", "id": "Semantics.EfficiencyAnalysis.calculateServiceRestorationGains", "name": "calculateServiceRestorationGains", "module": "Semantics.EfficiencyAnalysis" }, { "kind": "def", "id": "Semantics.EfficiencyAnalysis.calculateSyncAttackPreventionGains", "name": "calculateSyncAttackPreventionGains", "module": "Semantics.EfficiencyAnalysis" }, { "kind": "def", "id": "Semantics.EfficiencyAnalysis.calculateEnergyTrackingGains", "name": "calculateEnergyTrackingGains", "module": "Semantics.EfficiencyAnalysis" }, { "kind": "def", "id": "Semantics.EfficiencyAnalysis.generateEfficiencySummary", "name": "generateEfficiencySummary", "module": "Semantics.EfficiencyAnalysis" }, { "kind": "module", "id": "Semantics.ElectromagneticSpectrum", "name": "ElectromagneticSpectrum", "path": "Semantics/ElectromagneticSpectrum.lean", "namespace": "Semantics.ElectromagneticSpectrum", "doc": "ElectromagneticSpectrum.lean - Minimal stub for RegimeCore dependency", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 2, "inductive_count": 2, "line_count": 66 }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.scale", "name": "scale", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.zero", "name": "zero", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.one", "name": "one", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.half", "name": "half", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.quarter", "name": "quarter", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.eighth", "name": "eighth", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.satFromNat", "name": "satFromNat", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.fromNat", "name": "fromNat", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.ge", "name": "ge", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.le", "name": "le", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "def", "id": "Semantics.ElectromagneticSpectrum.isIonizingBand", "name": "isIonizingBand", "module": "Semantics.ElectromagneticSpectrum" }, { "kind": "module", "id": "Semantics.ElectronOrbitalConstraint", "name": "ElectronOrbitalConstraint", "path": "Semantics/ElectronOrbitalConstraint.lean", "namespace": "Semantics.ElectronOrbitalConstraint", "doc": "Empirical: ferritin layers conduct electrons via sequential tunneling up to 80 \u03bcm at room temperature (Shen et al., 2021). Beyond this, tunneling probability drops exponentially with distance.", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 5, "def_count": 7, "struct_count": 1, "inductive_count": 2, "line_count": 119 }, { "kind": "theorem", "id": "Semantics.ElectronOrbitalConstraint.electronTunnelingRespectsDistanceLimit", "name": "electronTunnelingRespectsDistanceLimit", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "theorem", "id": "Semantics.ElectronOrbitalConstraint.mottTransitionAtThreshold", "name": "mottTransitionAtThreshold", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "theorem", "id": "Semantics.ElectronOrbitalConstraint.pauliExclusionRespected", "name": "pauliExclusionRespected", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "theorem", "id": "Semantics.ElectronOrbitalConstraint.quantumCoherenceEnablesSwitching", "name": "quantumCoherenceEnablesSwitching", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "theorem", "id": "Semantics.ElectronOrbitalConstraint.transportRateSufficientForAssembly", "name": "transportRateSufficientForAssembly", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.electronTunnelingLimit", "name": "electronTunnelingLimit", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.mottTransitionThreshold", "name": "mottTransitionThreshold", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.orbitalOccupancyLimit", "name": "orbitalOccupancyLimit", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.electronTransportRate", "name": "electronTransportRate", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.quantumCoherenceTime", "name": "quantumCoherenceTime", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.safeElectronTransportWindowSeconds", "name": "safeElectronTransportWindowSeconds", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "def", "id": "Semantics.ElectronOrbitalConstraint.computeElectronAdaptationVerdict", "name": "computeElectronAdaptationVerdict", "module": "Semantics.ElectronOrbitalConstraint" }, { "kind": "module", "id": "Semantics.EneContextSurface", "name": "EneContextSurface", "path": "Semantics/EneContextSurface.lean", "namespace": "Semantics.EneContextSurface", "doc": "Lean-owned MCP surface for ENE context memory operations. This file is *surface only* (names + schemas + descriptions). Runtime shims must not invent alternate tools; they should load and expose this manifest. Execution plumbing is provided by non-Lean runtimes (Rust) and must be keyed off these t", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 9, "struct_count": 0, "inductive_count": 0, "line_count": 120 }, { "kind": "def", "id": "Semantics.EneContextSurface.eneStatus", "name": "eneStatus", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneRemember", "name": "eneRemember", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneRecall", "name": "eneRecall", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneSearch", "name": "eneSearch", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneContext", "name": "eneContext", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneSessions", "name": "eneSessions", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.eneSync", "name": "eneSync", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.tools", "name": "tools", "module": "Semantics.EneContextSurface" }, { "kind": "def", "id": "Semantics.EneContextSurface.toolsJson", "name": "toolsJson", "module": "Semantics.EneContextSurface" }, { "kind": "module", "id": "Semantics.EnergyGradientSignal", "name": "EnergyGradientSignal", "path": "Semantics/EnergyGradientSignal.lean", "namespace": "Semantics", "doc": "Energy Gradient Signal Integration This module formalizes energy decrease/increase as gradient signals that integrate into the waveform-waveprobe pipeline. Key structures: EnergyGradient: temporal and spatial energy gradients EnergyWaveform: gradient encoded as waveform EnergySignal: energy gradie", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 3, "def_count": 9, "struct_count": 9, "inductive_count": 1, "line_count": 235 }, { "kind": "theorem", "id": "Semantics.EnergyGradientSignal.gradientMagnitudeNonNegative", "name": "gradientMagnitudeNonNegative", "module": "Semantics.EnergyGradientSignal" }, { "kind": "theorem", "id": "Semantics.EnergyGradientSignal.couplingSymmetry", "name": "couplingSymmetry", "module": "Semantics.EnergyGradientSignal" }, { "kind": "theorem", "id": "Semantics.EnergyGradientSignal.energyChangeAdditive", "name": "energyChangeAdditive", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.energyGradientInvariant", "name": "energyGradientInvariant", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.calculateEnergyChange", "name": "calculateEnergyChange", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.computeGradientMagnitude", "name": "computeGradientMagnitude", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.computeGradientDirection", "name": "computeGradientDirection", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.createEnergyWaveform", "name": "createEnergyWaveform", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.calculateShapeEnergyCoupling", "name": "calculateShapeEnergyCoupling", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.energyGradientSignalCost", "name": "energyGradientSignalCost", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.energyGradientSignalBind", "name": "energyGradientSignalBind", "module": "Semantics.EnergyGradientSignal" }, { "kind": "def", "id": "Semantics.EnergyGradientSignal.couplingSymmetryCheck", "name": "couplingSymmetryCheck", "module": "Semantics.EnergyGradientSignal" }, { "kind": "module", "id": "Semantics.EntropyMeasures", "name": "EntropyMeasures", "path": "Semantics/EntropyMeasures.lean", "namespace": "Semantics.EntropyMeasures", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EntropyMeasures.lean \u2014 Adaptive Entropy Measures for Thermodynamic Computing This module formalizes three entropy measures (Shannon H\u2081, Collision H\u2082, Min-entropy H_\u221e) with adaptive switching based on v", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 456, "struct_count": 90, "inductive_count": 9, "line_count": 6276 }, { "kind": "theorem", "id": "Semantics.EntropyMeasures.defaultThresholdsValid", "name": "defaultThresholdsValid", "module": "Semantics.EntropyMeasures" }, { "kind": "theorem", "id": "Semantics.EntropyMeasures.adaptiveEntropySelectsShannon", "name": "adaptiveEntropySelectsShannon", "module": "Semantics.EntropyMeasures" }, { "kind": "theorem", "id": "Semantics.EntropyMeasures.adaptiveEntropySelectsCollision", "name": "adaptiveEntropySelectsCollision", "module": "Semantics.EntropyMeasures" }, { "kind": "theorem", "id": "Semantics.EntropyMeasures.adaptiveEntropySelectsMin", "name": "adaptiveEntropySelectsMin", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.prob", "name": "prob", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.variance", "name": "variance", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.shannonEntropy", "name": "shannonEntropy", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.collisionEntropy", "name": "collisionEntropy", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.minEntropy", "name": "minEntropy", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.kullbackLeiblerDivergence", "name": "kullbackLeiblerDivergence", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.jensenShannonDivergence", "name": "jensenShannonDivergence", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.mutualInformation", "name": "mutualInformation", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.informationBottleneck", "name": "informationBottleneck", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.reynolds", "name": "reynolds", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.default", "name": "default", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.classifyRegime", "name": "classifyRegime", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.turbulenceEntropy", "name": "turbulenceEntropy", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.laminarBottleneck", "name": "laminarBottleneck", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.turbulentFlow", "name": "turbulentFlow", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.velocity", "name": "velocity", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.flowRate", "name": "flowRate", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.grashof", "name": "grashof", "module": "Semantics.EntropyMeasures" }, { "kind": "def", "id": "Semantics.EntropyMeasures.classifyConvection", "name": "classifyConvection", "module": "Semantics.EntropyMeasures" }, { "kind": "module", "id": "Semantics.EntropyPhaseEngine", "name": "EntropyPhaseEngine", "path": "Semantics/EntropyPhaseEngine.lean", "namespace": "Semantics", "doc": "# Entropy Phase Engine Formal implementation of changepoint detection and model selection with complexity ordering. All dimensionless scalars (losses, scores, penalties) use Q0_16 (normalized [-1, 1]). Signal data uses Q16_16 for wider dynamic range. Key principle: Score = Loss + \u03bb * Complexity Hi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 10, "def_count": 51, "struct_count": 17, "inductive_count": 1, "line_count": 1191 }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.complexity_penalty_monotone", "name": "complexity_penalty_monotone", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.modelType_exhaustive", "name": "modelType_exhaustive", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.complexity_ordering_monotone", "name": "complexity_ordering_monotone", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.allCandidates_length", "name": "allCandidates_length", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.noiseCandidate_complexity_zero", "name": "noiseCandidate_complexity_zero", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.minCandidate_singleton", "name": "minCandidate_singleton", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.anti_puppy_box_theorem", "name": "anti_puppy_box_theorem", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.nanokernel_isolation", "name": "nanokernel_isolation", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.fpga_extraction_correctness", "name": "fpga_extraction_correctness", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "theorem", "id": "Semantics.EntropyPhaseEngine.universal_electron_verification", "name": "universal_electron_verification", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.natToQ0", "name": "natToQ0", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.intToQ0", "name": "intToQ0", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.Signal", "name": "Signal", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.ResidualModel", "name": "ResidualModel", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.LogicalMass", "name": "LogicalMass", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.selectModelMass", "name": "selectModelMass", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.antiPuppyBoxMass", "name": "antiPuppyBoxMass", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.ModelType", "name": "ModelType", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.ModelCandidate", "name": "ModelCandidate", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.signalToDimensionless", "name": "signalToDimensionless", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.mse", "name": "mse", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.lag1Autocorr", "name": "lag1Autocorr", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.lagLossQ16", "name": "lagLossQ16", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.weightedSplitLoss", "name": "weightedSplitLoss", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.q0Zero", "name": "q0Zero", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.deltaLoss", "name": "deltaLoss", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.q16ToQ0", "name": "q16ToQ0", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.detectChangepointDefault", "name": "detectChangepointDefault", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.complexityPenalty", "name": "complexityPenalty", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "def", "id": "Semantics.EntropyPhaseEngine.noiseCandidate", "name": "noiseCandidate", "module": "Semantics.EntropyPhaseEngine" }, { "kind": "module", "id": "Semantics.EnvironmentMechanics", "name": "EnvironmentMechanics", "path": "Semantics/EnvironmentMechanics.lean", "namespace": "Semantics.EnvironmentMechanics", "doc": "Environment-level witness for bounded interaction structure retained after compression. This is the proof-layer object that links a committed O-AMMR summary to later mechanics claims.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 8, "struct_count": 1, "inductive_count": 0, "line_count": 126 }, { "kind": "theorem", "id": "Semantics.EnvironmentMechanics.admissibleOfBounds", "name": "admissibleOfBounds", "module": "Semantics.EnvironmentMechanics" }, { "kind": "theorem", "id": "Semantics.EnvironmentMechanics.witnessOfCompressionAdmissible", "name": "witnessOfCompressionAdmissible", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.retainedDirections", "name": "retainedDirections", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.orderCovered", "name": "orderCovered", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.boundedCoupling", "name": "boundedCoupling", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.boundedResidual", "name": "boundedResidual", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.longRangeAdmissible", "name": "longRangeAdmissible", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.witnessOfCompression", "name": "witnessOfCompression", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.sampleEnvironmentWitness", "name": "sampleEnvironmentWitness", "module": "Semantics.EnvironmentMechanics" }, { "kind": "def", "id": "Semantics.EnvironmentMechanics.sampleCompressionEnvironmentWitness", "name": "sampleCompressionEnvironmentWitness", "module": "Semantics.EnvironmentMechanics" }, { "kind": "module", "id": "Semantics.EpistemicHonesty", "name": "EpistemicHonesty", "path": "Semantics/EpistemicHonesty.lean", "namespace": "Semantics", "doc": "Epistemic Honesty Grindstone (W-Axis Framework) ID: EPISTEMIC-HONESTY-2 This module formalizes the refined W-axis Epistemic Honesty Grindstone framework for distinguishing between high-fidelity reasoning and \"hallucinatory leakage.\" The W-axis serves as the coordinate system for Intellectual Humil", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 16, "def_count": 20, "struct_count": 4, "inductive_count": 6, "line_count": 653 }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.isCategoryError_no_error_when_match", "name": "isCategoryError_no_error_when_match", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.isCategoryError_when_speculative", "name": "isCategoryError_when_speculative", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.isCategoryError_when_forbidden", "name": "isCategoryError_when_forbidden", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classifyByBoundary_g\u00f6del", "name": "classifyByBoundary_g\u00f6del", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classifyByBoundary_descent", "name": "classifyByBoundary_descent", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classifyByBoundary_scope", "name": "classifyByBoundary_scope", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.ascent_honesty_gate", "name": "ascent_honesty_gate", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.chocolate_ascent_not_productive", "name": "chocolate_ascent_not_productive", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.sub_le_self_rational", "name": "sub_le_self_rational", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.honestyMetric_le_one", "name": "honestyMetric_le_one", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.sniffer_catches_artifact_only", "name": "sniffer_catches_artifact_only", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.sniffer_catches_batch_completion", "name": "sniffer_catches_batch_completion", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.sniffer_passes_runtime_state", "name": "sniffer_passes_runtime_state", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classify_active_artifact_is_forbidden", "name": "classify_active_artifact_is_forbidden", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classify_active_batch_is_forbidden", "name": "classify_active_batch_is_forbidden", "module": "Semantics.EpistemicHonesty" }, { "kind": "theorem", "id": "Semantics.EpistemicHonesty.classify_zero_excess_is_resolvable", "name": "classify_zero_excess_is_resolvable", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.computeProofPressure", "name": "computeProofPressure", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.honestyMetric", "name": "honestyMetric", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.classifyHonestyState", "name": "classifyHonestyState", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.isCategoryError", "name": "isCategoryError", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.classifyByBoundary", "name": "classifyByBoundary", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.wGateVerification", "name": "wGateVerification", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.higgsImaginaryStressTest", "name": "higgsImaginaryStressTest", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.higgsImaginaryHonesty", "name": "higgsImaginaryHonesty", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.fltGrindstone", "name": "fltGrindstone", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.fltProofPressure", "name": "fltProofPressure", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.fltPressure", "name": "fltPressure", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.productiveAscent", "name": "productiveAscent", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.chocolateAscent", "name": "chocolateAscent", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.wAxisResidueChange", "name": "wAxisResidueChange", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.ascentLearning", "name": "ascentLearning", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.ascentDiverging", "name": "ascentDiverging", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.computeWorkExcess", "name": "computeWorkExcess", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.execution_state_leakage_sniffer", "name": "execution_state_leakage_sniffer", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.classifyExecutionClaim", "name": "classifyExecutionClaim", "module": "Semantics.EpistemicHonesty" }, { "kind": "def", "id": "Semantics.EpistemicHonesty.webgpuExecutionClaim", "name": "webgpuExecutionClaim", "module": "Semantics.EpistemicHonesty" }, { "kind": "mathlib", "id": "Mathlib.Data.Rat.Defs", "name": "Mathlib.Data.Rat.Defs" }, { "kind": "module", "id": "Semantics.EquationFractalEncoding", "name": "EquationFractalEncoding", "path": "Semantics/EquationFractalEncoding.lean", "namespace": "EquationFractal", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Self-similar, fractal-encoded equation graph database for topological compression and O(log n) search in equation phylogenetic trees. OPTIMIZATIONS APPLIED: 1. 5D manifold is now computed from ACTUAL equation properties", "math_kind": "geometry", "sorry_count": 5, "theorem_count": 9, "def_count": 21, "struct_count": 8, "inductive_count": 2, "line_count": 658 }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.manifold_distance_symmetric", "name": "manifold_distance_symmetric", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.merkle_root_empty", "name": "merkle_root_empty", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.merkle_root_singleton", "name": "merkle_root_singleton", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.mixHash_non_comm", "name": "mixHash_non_comm", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.integrity_correct", "name": "integrity_correct", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.sidon_address_valid", "name": "sidon_address_valid", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.chaos_game_bounded", "name": "chaos_game_bounded", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.subtree_fold_empty", "name": "subtree_fold_empty", "module": "Semantics.EquationFractalEncoding" }, { "kind": "theorem", "id": "Semantics.EquationFractalEncoding.integrity_reflexive", "name": "integrity_reflexive", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.countDistinctTiers", "name": "countDistinctTiers", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.MerkleDigest", "name": "MerkleDigest", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.mixHash", "name": "mixHash", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.hashLeaf", "name": "hashLeaf", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.computeMerkleRoot", "name": "computeMerkleRoot", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.verifySubtreeHash", "name": "verifySubtreeHash", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.merkleProofPath", "name": "merkleProofPath", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.verifyIntegrity", "name": "verifyIntegrity", "module": "Semantics.EquationFractalEncoding" }, { "kind": "def", "id": "Semantics.EquationFractalEncoding.verifyTree", 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"Semantics.ErdosRenyiPipeline.sidon_regime_below_\u03c6_LT", "name": "sidon_regime_below_\u03c6_LT", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "theorem", "id": "Semantics.ErdosRenyiPipeline.mott_regime_bounded_by_\u03c6_RCP", "name": "mott_regime_bounded_by_\u03c6_RCP", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "theorem", "id": "Semantics.ErdosRenyiPipeline.lattice_ordering_gap", "name": "lattice_ordering_gap", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "theorem", "id": "Semantics.ErdosRenyiPipeline.rcp_phases_partition", "name": "rcp_phases_partition", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "def", "id": "Semantics.ErdosRenyiPipeline.IsGap", "name": "IsGap", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "def", "id": "Semantics.ErdosRenyiPipeline.IsLosslessMap", "name": "IsLosslessMap", "module": "Semantics.ErdosRenyiPipeline" }, { "kind": "def", "id": "Semantics.ErdosRenyiPipeline.IsSidonSet", "name": "IsSidonSet", "module": 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"namespace": "EtaMoE", "doc": "EtaMoE.lean \u2014 Mixture-of-Experts Cognitive Efficiency This module formalizes the \u03b7MoE equation connecting microscopic cognitive control to macroscopic universal efficiency. Equation ID: 0.1 Cross-refs: 0, 1.1, 1.2, 6, 29 The \u03b7MoE equation: \u03b7MoE(x) = [\u03a3 g\u2096(w\u2096h\u2096/lnN\u2096 - v\u2096p\u2096/lnN\u2096)] / [\u03a3 g\u2096(a\u2096lnN\u2096 + ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 13, "struct_count": 1, "inductive_count": 0, "line_count": 161 }, { "kind": "theorem", "id": "Semantics.EtaMoE.etaBounded", "name": "etaBounded", "module": "Semantics.EtaMoE" }, { "kind": "theorem", "id": "Semantics.EtaMoE.noInfiniteEfficiency", "name": "noInfiniteEfficiency", "module": "Semantics.EtaMoE" }, { "kind": "theorem", "id": "Semantics.EtaMoE.gatingBounded", "name": "gatingBounded", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.arityValid", "name": "arityValid", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.overheadValid", "name": "overheadValid", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.gatingValid", "name": "gatingValid", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.expertValid", "name": "expertValid", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.numeratorTerm", "name": "numeratorTerm", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.denominatorTerm", "name": "denominatorTerm", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.platformCost", "name": "platformCost", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.landauerCost", "name": "landauerCost", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.etaMoE", "name": "etaMoE", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.twoExpertEta", "name": "twoExpertEta", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.gatingSigmoid", "name": "gatingSigmoid", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.exampleCognitiveControl", "name": "exampleCognitiveControl", "module": "Semantics.EtaMoE" }, { "kind": "def", "id": "Semantics.EtaMoE.exampleSwarmRewiredExpert", "name": "exampleSwarmRewiredExpert", "module": "Semantics.EtaMoE" }, { "kind": "module", "id": "Semantics.EthereumRGFlow", "name": "EthereumRGFlow", "path": "Semantics/EthereumRGFlow.lean", "namespace": "Semantics", "doc": "RGFlow analysis for Ethereum price data with proper sigma computation from local price dynamics and RGFlow invariant lawfulness checking. 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"Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.findConnector", "name": "findConnector", "module": "Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.connectorMatchesRequest", "name": "connectorMatchesRequest", "module": "Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.traverseExoticTransition", "name": "traverseExoticTransition", "module": "Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.flatlandRegionProfile", "name": "flatlandRegionProfile", "module": "Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.wormholeRegionProfile", "name": "wormholeRegionProfile", "module": "Semantics.ExoticSpacetime" }, { "kind": "def", "id": "Semantics.ExoticSpacetime.defaultWormholeConnector", "name": "defaultWormholeConnector", "module": "Semantics.ExoticSpacetime" }, { "kind": "module", "id": "Semantics.ExperienceCompression", "name": "ExperienceCompression", "path": "Semantics/ExperienceCompression.lean", "namespace": "Semantics.ExperienceCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ExperienceCompression.lean \u2014 Experience Compression Spectrum for LLM Agents This module formalizes the Experience Compression Spectrum from \"Experience Compression Spectrum: Unifying Memory, Skills, an", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 22, "struct_count": 10, "inductive_count": 5, "line_count": 382 }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.l3HigherThanL0", "name": "l3HigherThanL0", "module": "Semantics.ExperienceCompression" }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.reusabilityIncreasesWithCompression", "name": "reusabilityIncreasesWithCompression", "module": "Semantics.ExperienceCompression" }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.costTradeOff", "name": "costTradeOff", "module": "Semantics.ExperienceCompression" }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.noSystemHasAdaptive", "name": "noSystemHasAdaptive", "module": "Semantics.ExperienceCompression" }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.compressionSoundness", "name": "compressionSoundness", "module": "Semantics.ExperienceCompression" }, { "kind": "theorem", "id": "Semantics.ExperienceCompression.l2MoreEfficientThanL1", "name": "l2MoreEfficientThanL1", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.zero", "name": "zero", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.one", "name": "one", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.ofNat", "name": "ofNat", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.add", "name": "add", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.sub", "name": "sub", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.mul", "name": "mul", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.div", "name": "div", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.le", "name": "le", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.toNat", "name": "toNat", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.higher", "name": "higher", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.forLevel", "name": "forLevel", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.compressionBounds", "name": "compressionBounds", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.validCompressionRatio", "name": "validCompressionRatio", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.acquisitionFor", "name": "acquisitionFor", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.maintenanceFor", "name": "maintenanceFor", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.fixedLevelSystems", "name": "fixedLevelSystems", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.missingDiagonal", "name": "missingDiagonal", "module": "Semantics.ExperienceCompression" }, { "kind": "def", "id": "Semantics.ExperienceCompression.adaptiveCompression", "name": "adaptiveCompression", "module": "Semantics.ExperienceCompression" }, { "kind": "module", "id": "Semantics.ExperimentTracker", "name": "ExperimentTracker", "path": "Semantics/ExperimentTracker.lean", "namespace": "Semantics.ExperimentTracker", "doc": "ExperimentTracker.lean \u2014 Automatic Prediction Checking & Grade Assignment This module provides the machinery to: 1. Check each pre-registered prediction against observed experimental data 2. Count confirmed vs falsified predictions 3. Assign an overall framework grade 4. Generate a machine-readable", "math_kind": "avm", "sorry_count": 0, "theorem_count": 11, "def_count": 11, "struct_count": 1, "inductive_count": 1, "line_count": 219 }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.for", "name": "for", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeA_plus_correct", "name": "gradeA_plus_correct", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeF_correct", "name": "gradeF_correct", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_0", "name": "gradeBoundary_0", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_1", "name": "gradeBoundary_1", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_2", "name": "gradeBoundary_2", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_3", "name": "gradeBoundary_3", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_4", "name": "gradeBoundary_4", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_5", "name": "gradeBoundary_5", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_6", "name": "gradeBoundary_6", "module": "Semantics.ExperimentTracker" }, { "kind": "theorem", "id": "Semantics.ExperimentTracker.gradeBoundary_7", "name": "gradeBoundary_7", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.PredictionOutcome", "name": "PredictionOutcome", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.checkPrediction", "name": "checkPrediction", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.countOutcome", "name": "countOutcome", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.assignGrade", "name": "assignGrade", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.generateReceipt", "name": "generateReceipt", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.initialOutcomes", "name": "initialOutcomes", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.scenarioA_minus", "name": "scenarioA_minus", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.scenarioA_plus", "name": "scenarioA_plus", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.initialReceipt", "name": "initialReceipt", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.receiptA_minus", "name": "receiptA_minus", "module": "Semantics.ExperimentTracker" }, { "kind": "def", "id": "Semantics.ExperimentTracker.receiptA_plus", "name": "receiptA_plus", "module": "Semantics.ExperimentTracker" }, { "kind": "module", "id": "Semantics.ExtendedManifoldEncoding", "name": "ExtendedManifoldEncoding", "path": "Semantics/ExtendedManifoldEncoding.lean", "namespace": "Semantics.ExtendedManifoldEncoding", "doc": "Released under Apache 2.0 license as described in the file LICENSE. ExtendedManifoldEncoding.lean \u2014 Alpha Branch Formalization Formalizes experimental encoding methods that map data to composite geometric structures and perform basis selection via set operations. Methods formalized: 1. Tree addre", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 23, "def_count": 42, "struct_count": 5, "inductive_count": 0, "line_count": 929 }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.pist_reconstruction", "name": "pist_reconstruction", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.tree_address_length", "name": "tree_address_length", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.tree_address_deterministic", "name": "tree_address_deterministic", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.coordinate_helicity_preserved", "name": "coordinate_helicity_preserved", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.surface_y_inverse", "name": "surface_y_inverse", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.surface_y_decreasing", "name": "surface_y_decreasing", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.torus_angles_bounded", "name": "torus_angles_bounded", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.phi_orbit_distinct_for_bounded", "name": "phi_orbit_distinct_for_bounded", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.composite_address_deterministic", "name": "composite_address_deterministic", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.address_reconstructs_linear", "name": "address_reconstructs_linear", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.intersection_subset", "name": "intersection_subset", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.intersection_partition", "name": "intersection_partition", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.exchange_pool_bounded", "name": "exchange_pool_bounded", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.collapse_preserves_pist", "name": "collapse_preserves_pist", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.substrate_bounded", "name": "substrate_bounded", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.adaptive_basis_dim_monotone", "name": "adaptive_basis_dim_monotone", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.adaptive_confidence_decreasing", "name": "adaptive_confidence_decreasing", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.composite_encoding_deterministic", "name": "composite_encoding_deterministic", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.composite_reversibility", "name": "composite_reversibility", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.gear_ratio_minimum", "name": "gear_ratio_minimum", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.gearRatio_eqn", "name": "gearRatio_eqn", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.gear_ratio_monotone_repeat", "name": "gear_ratio_monotone_repeat", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "theorem", "id": "Semantics.ExtendedManifoldEncoding.defensive_when_score_positive", "name": "defensive_when_score_positive", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.pistK", "name": "pistK", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.pistT", "name": "pistT", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.pistMass", "name": "pistMass", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.pistMirror", "name": "pistMirror", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.TreeAddress", "name": "TreeAddress", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.treeAddress", "name": "treeAddress", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.treeDepthDistribution", "name": "treeDepthDistribution", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.coordinateHelicity", "name": "coordinateHelicity", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.PHI", "name": "PHI", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.surfaceCoord", "name": "surfaceCoord", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.torusAngles", "name": "torusAngles", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.TREE_DEPTH", "name": "TREE_DEPTH", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.compositeAddress", "name": "compositeAddress", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.BridgeOp", "name": "BridgeOp", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.hadamardBridge", "name": "hadamardBridge", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.xorBridge", "name": "xorBridge", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.meanBridge", "name": "meanBridge", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.extractIntersection", "name": "extractIntersection", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.fuseBridge", "name": "fuseBridge", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "def", "id": "Semantics.ExtendedManifoldEncoding.buildFusedBasis", "name": "buildFusedBasis", "module": "Semantics.ExtendedManifoldEncoding" }, { "kind": "module", "id": "Semantics.Extensions.AdvancedBioDynamics", "name": "AdvancedBioDynamics", "path": "Semantics/Extensions/AdvancedBioDynamics.lean", "namespace": "Semantics.Biology.Advanced", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AdvancedBioDynamics.lean \u2014 Foundation-scale biophysical laws and information physics. This module formalizes high-level biophysical identities that have proven resilient to challenge, mapping them to t", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 74 }, { "kind": "def", "id": "Semantics.Extensions.AdvancedBioDynamics.freeEnergySurprisal", "name": "freeEnergySurprisal", "module": "Semantics.Extensions.AdvancedBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AdvancedBioDynamics.fisherDeltaFitness", "name": "fisherDeltaFitness", "module": "Semantics.Extensions.AdvancedBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AdvancedBioDynamics.neutralEvolutionRate", "name": "neutralEvolutionRate", "module": "Semantics.Extensions.AdvancedBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AdvancedBioDynamics.wilsonCowanUpdate", "name": "wilsonCowanUpdate", "module": "Semantics.Extensions.AdvancedBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AdvancedBioDynamics.remodelingError", "name": "remodelingError", "module": "Semantics.Extensions.AdvancedBioDynamics" }, { "kind": "module", "id": "Semantics.Extensions.AnimalSignalingLaws", "name": "AnimalSignalingLaws", "path": "Semantics/Extensions/AnimalSignalingLaws.lean", "namespace": "Semantics.Biology.Signaling", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AnimalSignalingLaws.lean \u2014 Laws of honest communication and the handicap principle. This module formalizes the laws of biological signaling: 1. Handicap: Zahavi's principle of costly signaling. 2. Hone", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 49 }, { "kind": "def", "id": "Semantics.Extensions.AnimalSignalingLaws.signalFitness", "name": "signalFitness", "module": "Semantics.Extensions.AnimalSignalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSignalingLaws.isHonestyStable", "name": "isHonestyStable", "module": "Semantics.Extensions.AnimalSignalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSignalingLaws.checkHonestEquilibrium", "name": "checkHonestEquilibrium", "module": "Semantics.Extensions.AnimalSignalingLaws" }, { "kind": "module", "id": "Semantics.Extensions.AnimalSocialAerodynamics", "name": "AnimalSocialAerodynamics", "path": "Semantics/Extensions/AnimalSocialAerodynamics.lean", "namespace": "Semantics.Biology.Social", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AnimalSocialAerodynamics.lean \u2014 Laws of animal distribution and formation flight. This module formalizes the laws of group behavior and energy efficiency: 1. Distribution: The Ideal Free Distribution (", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 64 }, { "kind": "def", "id": "Semantics.Extensions.AnimalSocialAerodynamics.isInputMatched", "name": "isInputMatched", "module": "Semantics.Extensions.AnimalSocialAerodynamics" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSocialAerodynamics.isFitnessEquilibrated", "name": "isFitnessEquilibrated", "module": "Semantics.Extensions.AnimalSocialAerodynamics" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSocialAerodynamics.upwashVelocity", "name": "upwashVelocity", "module": "Semantics.Extensions.AnimalSocialAerodynamics" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSocialAerodynamics.formationDragReduction", "name": "formationDragReduction", "module": "Semantics.Extensions.AnimalSocialAerodynamics" }, { "kind": "def", "id": "Semantics.Extensions.AnimalSocialAerodynamics.formationRangeBoost", "name": "formationRangeBoost", "module": "Semantics.Extensions.AnimalSocialAerodynamics" }, { "kind": "module", "id": "Semantics.Extensions.AuditoryMaskingDynamics", "name": "AuditoryMaskingDynamics", "path": "Semantics/Extensions/AuditoryMaskingDynamics.lean", "namespace": "Semantics.Biology.Auditory.Masking", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AuditoryMaskingDynamics.lean \u2014 Laws of masking, spreading functions, and specific loudness. This module formalizes the laws of psychoacoustic masking and signal saliency: 1. Spreading: Zwicker's spread", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMaskingDynamics.upperMaskingSlope", "name": "upperMaskingSlope", "module": "Semantics.Extensions.AuditoryMaskingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMaskingDynamics.signalToMaskRatio", "name": "signalToMaskRatio", "module": "Semantics.Extensions.AuditoryMaskingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMaskingDynamics.isSignalSalient", "name": "isSignalSalient", "module": "Semantics.Extensions.AuditoryMaskingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMaskingDynamics.specificLoudness", "name": "specificLoudness", "module": "Semantics.Extensions.AuditoryMaskingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMaskingDynamics.totalLoudness", "name": "totalLoudness", "module": "Semantics.Extensions.AuditoryMaskingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.AuditoryMechanicsLaws", "name": "AuditoryMechanicsLaws", "path": "Semantics/Extensions/AuditoryMechanicsLaws.lean", "namespace": "Semantics.Biology.Auditory", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AuditoryMechanicsLaws.lean \u2014 Laws of cochlear resonance, traveling waves, and tonotropy. This module formalizes the physical laws of hearing: 1. Resonance: Helmholtz's place theory (harmonic oscillator", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMechanicsLaws.localResonanceForce", "name": "localResonanceForce", "module": "Semantics.Extensions.AuditoryMechanicsLaws" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMechanicsLaws.travelingWavePhase", "name": "travelingWavePhase", "module": "Semantics.Extensions.AuditoryMechanicsLaws" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMechanicsLaws.characteristicFrequency", "name": "characteristicFrequency", "module": "Semantics.Extensions.AuditoryMechanicsLaws" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryMechanicsLaws.activeAmplifierDrift", "name": "activeAmplifierDrift", "module": "Semantics.Extensions.AuditoryMechanicsLaws" }, { "kind": "module", "id": "Semantics.Extensions.AuditoryPerceptionLaws", "name": "AuditoryPerceptionLaws", "path": "Semantics/Extensions/AuditoryPerceptionLaws.lean", "namespace": "Semantics.Biology.Psychoacoustics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AuditoryPerceptionLaws.lean \u2014 Laws of critical bands, equal loudness, and psychoacoustics. This module formalizes the laws of biological auditory perception: 1. Filter: The Bark scale for critical band", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.Extensions.AuditoryPerceptionLaws.frequencyToBark", "name": "frequencyToBark", "module": "Semantics.Extensions.AuditoryPerceptionLaws" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryPerceptionLaws.criticalBandwidth", "name": "criticalBandwidth", "module": "Semantics.Extensions.AuditoryPerceptionLaws" }, { "kind": "def", "id": "Semantics.Extensions.AuditoryPerceptionLaws.equalLoudnessSPL", "name": "equalLoudnessSPL", "module": "Semantics.Extensions.AuditoryPerceptionLaws" }, { "kind": "module", "id": "Semantics.Extensions.BettiSwoosh", "name": "BettiSwoosh", "path": "Semantics/Extensions/BettiSwoosh.lean", "namespace": "BettiSwoosh", "doc": "BettiSwoosh.lean \u2014 The Betti Swoosh Law: Spectral Flow on Directed Simplicial Complexes ======================================================================================== The Betti Swoosh Law (H_M): H_M(t) = -\u0394_M + V_M(x,t) Where: \u2022 \u0394_M: Hodge Laplacian of the directed simplicial complex M \u2022", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 12, "def_count": 16, "struct_count": 5, "inductive_count": 0, "line_count": 450 }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.hodge_decomposition", "name": "hodge_decomposition", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.betti_from_hodge", "name": "betti_from_hodge", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.swoosh_theorem", "name": "swoosh_theorem", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.aci_implies_stability", "name": "aci_implies_stability", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.ternary_preserves_betti", "name": "ternary_preserves_betti", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.hodge_self_adjoint", "name": "hodge_self_adjoint", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.hodge_positive_semidefinite", "name": "hodge_positive_semidefinite", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.hodge_eigenvalues_nonnegative", "name": "hodge_eigenvalues_nonnegative", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.betti_zero_iff_no_harmonic", "name": "betti_zero_iff_no_harmonic", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.swooshMergeIdempotent", "name": "swooshMergeIdempotent", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.swooshMergeCommutative", "name": "swooshMergeCommutative", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "theorem", "id": "Semantics.Extensions.BettiSwoosh.swooshMergeAssociative", "name": "swooshMergeAssociative", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.DirectedSimplex", "name": "DirectedSimplex", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.kSkeleton", "name": "kSkeleton", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.kChains", "name": "kChains", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.boundaryOperator", "name": "boundaryOperator", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.coboundaryOperator", "name": "coboundaryOperator", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.hodgeLaplacian", "name": "hodgeLaplacian", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.bettiNumber", "name": "bettiNumber", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.H_M", "name": "H_M", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.spectralFlow", "name": "spectralFlow", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.antiCollisionIdentity", "name": "antiCollisionIdentity", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.bettiTrajectory", "name": "bettiTrajectory", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.detectSwooshes", "name": "detectSwooshes", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.marketComplexFromCoarseSignal", "name": "marketComplexFromCoarseSignal", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.sigmaFromBettiVariation", "name": "sigmaFromBettiVariation", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.hodgeLaplacianMatrix", "name": "hodgeLaplacianMatrix", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "def", "id": "Semantics.Extensions.BettiSwoosh.computeBettiFromMatrix", "name": "computeBettiFromMatrix", "module": "Semantics.Extensions.BettiSwoosh" }, { "kind": "module", "id": "Semantics.Extensions.BioComplexSystems", "name": "BioComplexSystems", "path": "Semantics/Extensions/BioComplexSystems.lean", "namespace": "Semantics.Biology.ComplexSystems", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioComplexSystems.lean \u2014 Information theory and complexity in biological manifolds. This module formalizes the high-level informational and structural laws that govern biological complexity, from the e", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 67 }, { "kind": "def", "id": "Semantics.Extensions.BioComplexSystems.priceDeltaTrait", "name": "priceDeltaTrait", "module": "Semantics.Extensions.BioComplexSystems" }, { "kind": "def", "id": "Semantics.Extensions.BioComplexSystems.quasispeciesDrift", "name": "quasispeciesDrift", "module": "Semantics.Extensions.BioComplexSystems" }, { "kind": "def", "id": "Semantics.Extensions.BioComplexSystems.mayStabilityMeasure", "name": "mayStabilityMeasure", "module": "Semantics.Extensions.BioComplexSystems" }, { "kind": "def", "id": "Semantics.Extensions.BioComplexSystems.entropyProductionRate", "name": "entropyProductionRate", "module": "Semantics.Extensions.BioComplexSystems" }, { "kind": "def", "id": "Semantics.Extensions.BioComplexSystems.wrightFisherDrift", "name": "wrightFisherDrift", "module": "Semantics.Extensions.BioComplexSystems" }, { "kind": "module", "id": "Semantics.Extensions.BioDeepDive", "name": "BioDeepDive", "path": "Semantics/Extensions/BioDeepDive.lean", "namespace": "Semantics.Biology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioDeepDive.lean \u2014 Multi-scale biological modeling from RNA to Human Dynamics. This module formalizes the multi-layer biological stack as a nested manifold system, from sub-cellular information process", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 1, "inductive_count": 0, "line_count": 86 }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.rnaFoldingEnergy", "name": "rnaFoldingEnergy", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.dogmaUpdate", "name": "dogmaUpdate", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.hillActivation", "name": "hillActivation", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.waddingtonPotential", "name": "waddingtonPotential", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.reactionDiffusion", "name": "reactionDiffusion", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.replicatorStep", "name": "replicatorStep", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "def", "id": "Semantics.Extensions.BioDeepDive.socialRepulsion", "name": "socialRepulsion", "module": "Semantics.Extensions.BioDeepDive" }, { "kind": "module", "id": "Semantics.Extensions.BioElectricalImpedanceLaws", "name": "BioElectricalImpedanceLaws", "path": "Semantics/Extensions/BioElectricalImpedanceLaws.lean", "namespace": "Semantics.Biology.BioElectric", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioElectricalImpedanceLaws.lean \u2014 Laws of cellular potential and tissue dielectric relaxation. This module formalizes the electrical laws of biological matter: 1. Cellular: The Schwan equation for indu", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 1, "line_count": 56 }, { "kind": "def", "id": "Semantics.Extensions.BioElectricalImpedanceLaws.inducedMembranePotential", "name": "inducedMembranePotential", "module": "Semantics.Extensions.BioElectricalImpedanceLaws" }, { "kind": "def", "id": "Semantics.Extensions.BioElectricalImpedanceLaws.coleColePermittivity", "name": "coleColePermittivity", "module": "Semantics.Extensions.BioElectricalImpedanceLaws" }, { "kind": "def", "id": "Semantics.Extensions.BioElectricalImpedanceLaws.identifyDispersion", "name": "identifyDispersion", "module": "Semantics.Extensions.BioElectricalImpedanceLaws" }, { "kind": "module", "id": "Semantics.Extensions.BioElectroThermodynamics", "name": "BioElectroThermodynamics", "path": "Semantics/Extensions/BioElectroThermodynamics.lean", "namespace": "Semantics.Biology.BioElectro", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioElectroThermodynamics.lean \u2014 Laws of membrane potential and cellular energy flux. This module formalizes the electro-chemical and thermodynamic laws of cellular life: 1. Electrochemistry: Nernst rev", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.BioElectroThermodynamics.nernstPotential", "name": "nernstPotential", "module": "Semantics.Extensions.BioElectroThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioElectroThermodynamics.ghkRestingPotential", "name": "ghkRestingPotential", "module": "Semantics.Extensions.BioElectroThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioElectroThermodynamics.donnanProduct", "name": "donnanProduct", "module": "Semantics.Extensions.BioElectroThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioElectroThermodynamics.gibbsDuhemSum", "name": "gibbsDuhemSum", "module": "Semantics.Extensions.BioElectroThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioElectroThermodynamics.entropyFluxBalance", "name": "entropyFluxBalance", "module": "Semantics.Extensions.BioElectroThermodynamics" }, { "kind": "module", "id": "Semantics.Extensions.BioPhotonicsDynamics", "name": "BioPhotonicsDynamics", "path": "Semantics/Extensions/BioPhotonicsDynamics.lean", "namespace": "Semantics.Biology.Photonics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioPhotonicsDynamics.lean \u2014 Laws of radiative transfer and bioluminescence kinetics. This module formalizes the laws of light transport and emission in biological systems: 1. Transport: The Diffusion A", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 54 }, { "kind": "def", "id": "Semantics.Extensions.BioPhotonicsDynamics.fluenceRateUpdate", "name": "fluenceRateUpdate", "module": "Semantics.Extensions.BioPhotonicsDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioPhotonicsDynamics.photonEmissionRate", "name": "photonEmissionRate", "module": "Semantics.Extensions.BioPhotonicsDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BioPhotonicsDynamics.lightIntensityAtDepth", "name": "lightIntensityAtDepth", "module": "Semantics.Extensions.BioPhotonicsDynamics" }, { "kind": "module", "id": "Semantics.Extensions.BioThermoTopology", "name": "BioThermoTopology", "path": "Semantics/Extensions/BioThermoTopology.lean", "namespace": "Semantics.Biology.ThermoTopology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BioThermoTopology.lean \u2014 Non-equilibrium thermodynamics and developmental topology. This module formalizes the dissipative and constructive laws of biological matter, connecting energy flux to pattern ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 69 }, { "kind": "def", "id": "Semantics.Extensions.BioThermoTopology.coupledFlux", "name": "coupledFlux", "module": "Semantics.Extensions.BioThermoTopology" }, { "kind": "def", "id": "Semantics.Extensions.BioThermoTopology.jarzynskiFreeEnergy", "name": "jarzynskiFreeEnergy", "module": "Semantics.Extensions.BioThermoTopology" }, { "kind": "def", "id": "Semantics.Extensions.BioThermoTopology.fbaSteadyState", "name": "fbaSteadyState", "module": "Semantics.Extensions.BioThermoTopology" }, { "kind": "def", "id": "Semantics.Extensions.BioThermoTopology.giererMeinhardtUpdate", "name": "giererMeinhardtUpdate", "module": "Semantics.Extensions.BioThermoTopology" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalComputingLaws", "name": "BiologicalComputingLaws", "path": "Semantics/Extensions/BiologicalComputingLaws.lean", "namespace": "Semantics.Biology.Computing", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalComputingLaws.lean \u2014 Laws of biological computation and recursive assembly. This module formalizes the laws of information processing at the molecular level: 1. Combinators: SKI calculus impl", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalComputingLaws.kCombinator", "name": "kCombinator", "module": "Semantics.Extensions.BiologicalComputingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalComputingLaws.sCombinator", "name": "sCombinator", "module": "Semantics.Extensions.BiologicalComputingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalComputingLaws.assemblyIdempotent", "name": "assemblyIdempotent", "module": "Semantics.Extensions.BiologicalComputingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalComputingLaws.cellResourceVoltage", "name": "cellResourceVoltage", "module": "Semantics.Extensions.BiologicalComputingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalComputingLaws.isCellOverloaded", "name": "isCellOverloaded", "module": "Semantics.Extensions.BiologicalComputingLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalControlDynamics", "name": "BiologicalControlDynamics", "path": "Semantics/Extensions/BiologicalControlDynamics.lean", "namespace": "Semantics.Biology.Control", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalControlDynamics.lean \u2014 Laws of optimal control, variety, and robustness. This module formalizes the cybernetic and optimization laws of biological life: 1. Control: Pontryagin's Maximum Princ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalControlDynamics.biologicalHamiltonian", "name": "biologicalHamiltonian", "module": "Semantics.Extensions.BiologicalControlDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalControlDynamics.satisfyRequisiteVariety", "name": "satisfyRequisiteVariety", "module": "Semantics.Extensions.BiologicalControlDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalControlDynamics.bellmanError", "name": "bellmanError", "module": "Semantics.Extensions.BiologicalControlDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalControlDynamics.paretoEfficiency", "name": "paretoEfficiency", "module": "Semantics.Extensions.BiologicalControlDynamics" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalExergyDynamics", "name": "BiologicalExergyDynamics", "path": "Semantics/Extensions/BiologicalExergyDynamics.lean", "namespace": "Semantics.Biology.Exergy", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalExergyDynamics.lean \u2014 Laws of exergy destruction and entropy production. This module formalizes the thermodynamic laws of biological work and dissipation: 1. Dissipation: The Gouy-Stodola The", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExergyDynamics.exergyDestruction", "name": "exergyDestruction", "module": "Semantics.Extensions.BiologicalExergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExergyDynamics.minimumEntropyProductionUpdate", "name": "minimumEntropyProductionUpdate", "module": "Semantics.Extensions.BiologicalExergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExergyDynamics.maximumEntropyProductionRate", "name": "maximumEntropyProductionRate", "module": "Semantics.Extensions.BiologicalExergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExergyDynamics.actualMetabolicWork", "name": "actualMetabolicWork", "module": "Semantics.Extensions.BiologicalExergyDynamics" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalExtremalLaws", "name": "BiologicalExtremalLaws", "path": "Semantics/Extensions/BiologicalExtremalLaws.lean", "namespace": "Semantics.Biology.Extremal", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalExtremalLaws.lean \u2014 Extremal principles of biological action, time, and power. This module formalizes the variational and optimality laws of biological systems: 1. Least Time: Fermat's Princi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExtremalLaws.animalPathRefraction", "name": "animalPathRefraction", "module": "Semantics.Extensions.BiologicalExtremalLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExtremalLaws.metabolicFluxObjective", "name": "metabolicFluxObjective", "module": "Semantics.Extensions.BiologicalExtremalLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExtremalLaws.powerOutput", "name": "powerOutput", "module": "Semantics.Extensions.BiologicalExtremalLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExtremalLaws.populationLagrangian", "name": "populationLagrangian", "module": "Semantics.Extensions.BiologicalExtremalLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalExtremalLaws.populationAction", "name": "populationAction", "module": "Semantics.Extensions.BiologicalExtremalLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalInformationLaws", "name": "BiologicalInformationLaws", "path": "Semantics/Extensions/BiologicalInformationLaws.lean", "namespace": "Semantics.Biology.Information", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalInformationLaws.lean \u2014 Laws of genomic entropy, error robustness, and channel capacity. This module formalizes the information-theoretic laws of biology: 1. Entropy: Shannon entropy of DNA/RN", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 64 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInformationLaws.genomicEntropy", "name": "genomicEntropy", "module": "Semantics.Extensions.BiologicalInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInformationLaws.codonHammingDistance", "name": "codonHammingDistance", "module": "Semantics.Extensions.BiologicalInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInformationLaws.aminoAcidRobustness", "name": "aminoAcidRobustness", "module": "Semantics.Extensions.BiologicalInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInformationLaws.biologicalChannelCapacity", "name": "biologicalChannelCapacity", "module": "Semantics.Extensions.BiologicalInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInformationLaws.errorCatastropheLimit", "name": "errorCatastropheLimit", "module": "Semantics.Extensions.BiologicalInformationLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalIntegrityLaws", "name": "BiologicalIntegrityLaws", "path": "Semantics/Extensions/BiologicalIntegrityLaws.lean", "namespace": "Semantics.Biology.Integrity", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalIntegrityLaws.lean \u2014 Laws of epigenetic aging, kinetic proofreading, and biodiversity. This module formalizes the laws of biological stability and information integrity: 1. Aging: Horvath's e", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalIntegrityLaws.epigeneticAgePredictor", "name": "epigeneticAgePredictor", "module": "Semantics.Extensions.BiologicalIntegrityLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalIntegrityLaws.proofreadingErrorRate", "name": "proofreadingErrorRate", "module": "Semantics.Extensions.BiologicalIntegrityLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalIntegrityLaws.biodiversityNumber", "name": "biodiversityNumber", "module": "Semantics.Extensions.BiologicalIntegrityLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalInvariants", "name": "BiologicalInvariants", "path": "Semantics/Extensions/BiologicalInvariants.lean", "namespace": "Semantics.Extensions.BiologicalInvariants", "doc": "# Biological Invariants as Formal Operators This file defines fundamental biological laws as formal operators on semantic manifolds. Each law represents a constraint or a flow on the biological state space, verified through their canonical equations and integrated into a differential geometric view", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 7, "inductive_count": 0, "line_count": 211 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.kleiberLaw", "name": "kleiberLaw", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.lvFlow", "name": "lvFlow", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.michaelisMentenLaw", "name": "michaelisMentenLaw", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.hhCurrent", "name": "hhCurrent", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.hardyWeinbergInvariant", "name": "hardyWeinbergInvariant", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.arrheniusLaw", "name": "arrheniusLaw", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.fickFirstLaw", "name": "fickFirstLaw", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalInvariants.fickSecondLaw", "name": "fickSecondLaw", "module": "Semantics.Extensions.BiologicalInvariants" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalRegulationDynamics", "name": "BiologicalRegulationDynamics", "path": "Semantics/Extensions/BiologicalRegulationDynamics.lean", "namespace": "Semantics.Biology.Regulation", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalRegulationDynamics.lean \u2014 Laws of metabolic control, robust adaptation, and regulatory selection. This module formalizes the laws of biological feedback and regulation: 1. Metabolism: Metabol", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 1, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRegulationDynamics.fluxControlCoefficient", "name": "fluxControlCoefficient", "module": "Semantics.Extensions.BiologicalRegulationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRegulationDynamics.isControlLawful", "name": "isControlLawful", "module": "Semantics.Extensions.BiologicalRegulationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRegulationDynamics.adaptationUpdate", "name": "adaptationUpdate", "module": "Semantics.Extensions.BiologicalRegulationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRegulationDynamics.isAdapted", "name": "isAdapted", "module": "Semantics.Extensions.BiologicalRegulationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRegulationDynamics.optimalRegulatoryMode", "name": "optimalRegulatoryMode", "module": "Semantics.Extensions.BiologicalRegulationDynamics" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalRhythmLaws", "name": "BiologicalRhythmLaws", "path": "Semantics/Extensions/BiologicalRhythmLaws.lean", "namespace": "Semantics.Biology.Rhythms", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalRhythmLaws.lean \u2014 Laws of chemical oscillators, synchronization, and conservation. This module formalizes the laws of temporal organization and mass balance: 1. Chemical: The Oregonator model", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 69 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRhythmLaws.oregonatorUpdate", "name": "oregonatorUpdate", "module": "Semantics.Extensions.BiologicalRhythmLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRhythmLaws.synchronyPhaseDrift", "name": "synchronyPhaseDrift", "module": "Semantics.Extensions.BiologicalRhythmLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRhythmLaws.isEntrained", "name": "isEntrained", "module": "Semantics.Extensions.BiologicalRhythmLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalRhythmLaws.continuityUpdate", "name": "continuityUpdate", "module": "Semantics.Extensions.BiologicalRhythmLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalSensingLaws", "name": "BiologicalSensingLaws", "path": "Semantics/Extensions/BiologicalSensingLaws.lean", "namespace": "Semantics.Biology.Sensing", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalSensingLaws.lean \u2014 Physical limits of biological chemoreception and signaling. This module formalizes the fundamental physical boundaries of biological sensing: 1. Precision: Berg-Purcell lim", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 50 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSensingLaws.bergPurcellErrorSq", "name": "bergPurcellErrorSq", "module": "Semantics.Extensions.BiologicalSensingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSensingLaws.signalingSNR", "name": "signalingSNR", "module": "Semantics.Extensions.BiologicalSensingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSensingLaws.positionalPrecision", "name": "positionalPrecision", "module": "Semantics.Extensions.BiologicalSensingLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalSystemComplexity", "name": "BiologicalSystemComplexity", "path": "Semantics/Extensions/BiologicalSystemComplexity.lean", "namespace": "Semantics.Biology.Complexity", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalSystemComplexity.lean \u2014 Laws of small-world networks, modularity, and complexity growth. This module formalizes the structural and evolutionary laws of complex biological systems: 1. Networks", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSystemComplexity.smallWorldClustering", "name": "smallWorldClustering", "module": "Semantics.Extensions.BiologicalSystemComplexity" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSystemComplexity.modularityIndex", "name": "modularityIndex", "module": "Semantics.Extensions.BiologicalSystemComplexity" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSystemComplexity.expectedLossHOT", "name": "expectedLossHOT", "module": "Semantics.Extensions.BiologicalSystemComplexity" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalSystemComplexity.complexityGrowth", "name": "complexityGrowth", "module": "Semantics.Extensions.BiologicalSystemComplexity" }, { "kind": "module", "id": "Semantics.Extensions.BiologicalTransportLaws", "name": "BiologicalTransportLaws", "path": "Semantics/Extensions/BiologicalTransportLaws.lean", "namespace": "Semantics.Biology.Transport", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiologicalTransportLaws.lean \u2014 Laws of fluid dynamics, advection, and capillary exchange. This module formalizes the physical laws of biological mass transport: 1. Dimensionless: Reynolds and Peclet nu", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 60 }, { "kind": "def", "id": "Semantics.Extensions.BiologicalTransportLaws.reynoldsNumber", "name": "reynoldsNumber", "module": "Semantics.Extensions.BiologicalTransportLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalTransportLaws.pecletNumber", "name": "pecletNumber", "module": "Semantics.Extensions.BiologicalTransportLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalTransportLaws.darcyVelocity", "name": "darcyVelocity", "module": "Semantics.Extensions.BiologicalTransportLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiologicalTransportLaws.starlingFiltration", "name": "starlingFiltration", "module": "Semantics.Extensions.BiologicalTransportLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiomolecularFoldingLaws", "name": "BiomolecularFoldingLaws", "path": "Semantics/Extensions/BiomolecularFoldingLaws.lean", "namespace": "Semantics.Biology.Folding", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiomolecularFoldingLaws.lean \u2014 Laws of protein folding thermodynamics and kinetics. This module formalizes the laws governing molecular self-organization: 1. Thermodynamics: Anfinsen's Dogma and the na", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 68 }, { "kind": "def", "id": "Semantics.Extensions.BiomolecularFoldingLaws.foldingStability", "name": "foldingStability", "module": "Semantics.Extensions.BiomolecularFoldingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiomolecularFoldingLaws.isNativeState", "name": "isNativeState", "module": "Semantics.Extensions.BiomolecularFoldingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiomolecularFoldingLaws.searchSpaceSize", "name": "searchSpaceSize", "module": "Semantics.Extensions.BiomolecularFoldingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiomolecularFoldingLaws.conformationProbability", "name": "conformationProbability", "module": "Semantics.Extensions.BiomolecularFoldingLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiomolecularFoldingLaws.relativeContactOrder", "name": "relativeContactOrder", "module": "Semantics.Extensions.BiomolecularFoldingLaws" }, { "kind": "module", "id": "Semantics.Extensions.BiophysicalStructuralLaws", "name": "BiophysicalStructuralLaws", "path": "Semantics/Extensions/BiophysicalStructuralLaws.lean", "namespace": "Semantics.Biology.Physics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BiophysicalStructuralLaws.lean \u2014 Laws of excitability, patterning, and elasticity. This module formalizes the laws of biological physics and mechanics: 1. Excitability: FitzHugh-Nagumo simplified neuro", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 68 }, { "kind": "def", "id": "Semantics.Extensions.BiophysicalStructuralLaws.fhnStep", "name": "fhnStep", "module": "Semantics.Extensions.BiophysicalStructuralLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiophysicalStructuralLaws.swiftHohenbergStep", "name": "swiftHohenbergStep", "module": "Semantics.Extensions.BiophysicalStructuralLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiophysicalStructuralLaws.tissueYoungModulus", "name": "tissueYoungModulus", "module": "Semantics.Extensions.BiophysicalStructuralLaws" }, { "kind": "def", "id": "Semantics.Extensions.BiophysicalStructuralLaws.cytoskeletalForce", "name": "cytoskeletalForce", "module": "Semantics.Extensions.BiophysicalStructuralLaws" }, { "kind": "module", "id": "Semantics.Extensions.BlitterPolymorphism", "name": "BlitterPolymorphism", "path": "Semantics/Extensions/BlitterPolymorphism.lean", "namespace": "ExtensionScaffold.Compression.BlitterPolymorphism", "doc": "# Blitter Polymorphism This module keeps the refold/blitter surface executable while avoiding the unsound scaffold proofs from the earlier draft. The algebraic claims here are intentionally modest: the file is a typed interface over compact sensor records, refold projections, and the `ManifoldBlit.", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 5, "def_count": 26, "struct_count": 2, "inductive_count": 0, "line_count": 266 }, { "kind": "theorem", "id": "Semantics.Extensions.BlitterPolymorphism.RefoldGrid", "name": "RefoldGrid", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "theorem", "id": "Semantics.Extensions.BlitterPolymorphism.refold2D_homomorphism", "name": "refold2D_homomorphism", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "theorem", "id": "Semantics.Extensions.BlitterPolymorphism.blitStep_refold_preserves_type", "name": "blitStep_refold_preserves_type", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "theorem", "id": "Semantics.Extensions.BlitterPolymorphism.refold_commutes_with_append", "name": "refold_commutes_with_append", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "theorem", "id": "Semantics.Extensions.BlitterPolymorphism.dag_cache_refold_polymorphic", "name": "dag_cache_refold_polymorphic", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_DAM", "name": "TAG_DAM", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_NET", "name": "TAG_NET", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_TX", "name": "TAG_TX", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_COSMIC", "name": "TAG_COSMIC", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_SEISMIC", "name": "TAG_SEISMIC", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.TAG_GNSS", "name": "TAG_GNSS", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.arraySetD", "name": "arraySetD", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.RefoldSensor", "name": "RefoldSensor", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.refold2D", "name": "refold2D", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.refold1D", "name": "refold1D", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.refold3D", "name": "refold3D", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "def", "id": "Semantics.Extensions.BlitterPolymorphism.refoldND", "name": "refoldND", "module": "Semantics.Extensions.BlitterPolymorphism" }, { "kind": "module", "id": "Semantics.Extensions.CancerMetabolicDynamics", "name": "CancerMetabolicDynamics", "path": "Semantics/Extensions/CancerMetabolicDynamics.lean", "namespace": "Semantics.Biology.CancerMetabolic", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CancerMetabolicDynamics.lean \u2014 Laws of mutation kinetics and metabolic elasticity. This module formalizes the laws of oncogenesis and metabolic control: 1. Oncology: Knudson's two-hit and multi-hit mut", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Extensions.CancerMetabolicDynamics.cancerOnsetProb", "name": "cancerOnsetProb", "module": "Semantics.Extensions.CancerMetabolicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CancerMetabolicDynamics.elasticityCoefficient", "name": "elasticityCoefficient", "module": "Semantics.Extensions.CancerMetabolicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CancerMetabolicDynamics.checkConnectivityTheorem", "name": "checkConnectivityTheorem", "module": "Semantics.Extensions.CancerMetabolicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CancerMetabolicDynamics.priceSelectionTerm", "name": "priceSelectionTerm", "module": "Semantics.Extensions.CancerMetabolicDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CardiacYieldDynamics", "name": "CardiacYieldDynamics", "path": "Semantics/Extensions/CardiacYieldDynamics.lean", "namespace": "Semantics.Biology.CardiacYield", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CardiacYieldDynamics.lean \u2014 Laws of cardiac action potentials and plant biomass yield. This module formalizes the laws of biological excitability and productivity: 1. Cardiac: The Noble model for Purki", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.CardiacYieldDynamics.averageBiomassWeight", "name": "averageBiomassWeight", "module": "Semantics.Extensions.CardiacYieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CardiacYieldDynamics.totalBiomassYield", "name": "totalBiomassYield", "module": "Semantics.Extensions.CardiacYieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CardiacYieldDynamics.gatingVariableUpdate", "name": "gatingVariableUpdate", "module": "Semantics.Extensions.CardiacYieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CardiacYieldDynamics.nobleSodiumCurrent", "name": "nobleSodiumCurrent", "module": "Semantics.Extensions.CardiacYieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CardiacYieldDynamics.nobleK1Conductance", "name": "nobleK1Conductance", "module": "Semantics.Extensions.CardiacYieldDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CellularGrowthLaws", "name": "CellularGrowthLaws", "path": "Semantics/Extensions/CellularGrowthLaws.lean", "namespace": "Semantics.Biology.CellGrowth", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CellularGrowthLaws.lean \u2014 Laws of cell size scaling and DNA replication initiation. This module formalizes the laws governing cellular growth and division timing: 1. Scaling: The Cooper-Helmstetter mod", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.CellularGrowthLaws.initiationMassRatio", "name": "initiationMassRatio", "module": "Semantics.Extensions.CellularGrowthLaws" }, { "kind": "def", "id": "Semantics.Extensions.CellularGrowthLaws.averageCellSize", "name": "averageCellSize", "module": "Semantics.Extensions.CellularGrowthLaws" }, { "kind": "def", "id": "Semantics.Extensions.CellularGrowthLaws.divisionVolume", "name": "divisionVolume", "module": "Semantics.Extensions.CellularGrowthLaws" }, { "kind": "module", "id": "Semantics.Extensions.CellularMotionLimits", "name": "CellularMotionLimits", "path": "Semantics/Extensions/CellularMotionLimits.lean", "namespace": "Semantics.Biology.PhysicalLimits", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CellularMotionLimits.lean \u2014 Laws of cell size limits, biological motion, and diffusion. This module formalizes the physical boundaries of life and movement: 1. Minimalism: Minimum cell volume constrain", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Extensions.CellularMotionLimits.minimumRequiredVolume", "name": "minimumRequiredVolume", "module": "Semantics.Extensions.CellularMotionLimits" }, { "kind": "def", "id": "Semantics.Extensions.CellularMotionLimits.isRadiusPhysicallyPossible", "name": "isRadiusPhysicallyPossible", "module": "Semantics.Extensions.CellularMotionLimits" }, { "kind": "def", "id": "Semantics.Extensions.CellularMotionLimits.optimalMovementSpeed", "name": "optimalMovementSpeed", "module": "Semantics.Extensions.CellularMotionLimits" }, { "kind": "def", "id": "Semantics.Extensions.CellularMotionLimits.movementFrequency", "name": "movementFrequency", "module": "Semantics.Extensions.CellularMotionLimits" }, { "kind": "def", "id": "Semantics.Extensions.CellularMotionLimits.diffusionTimeLimit", "name": "diffusionTimeLimit", "module": "Semantics.Extensions.CellularMotionLimits" }, { "kind": "module", "id": "Semantics.Extensions.CellularSignalingDynamics", "name": "CellularSignalingDynamics", "path": "Semantics/Extensions/CellularSignalingDynamics.lean", "namespace": "Semantics.Biology.Signaling", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CellularSignalingDynamics.lean \u2014 Laws of ultrasensitivity, cell cycles, and chemotaxis. This module formalizes the laws of sub-cellular decision making and motion: 1. Ultrasensitivity: Goldbeter-Koshla", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 69 }, { "kind": "def", "id": "Semantics.Extensions.CellularSignalingDynamics.goldbeterKoshlandSwitch", "name": "goldbeterKoshlandSwitch", "module": "Semantics.Extensions.CellularSignalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CellularSignalingDynamics.tysonStep", "name": "tysonStep", "module": "Semantics.Extensions.CellularSignalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CellularSignalingDynamics.molecularRepression", "name": "molecularRepression", "module": "Semantics.Extensions.CellularSignalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CellularSignalingDynamics.chemotacticFlux", "name": "chemotacticFlux", "module": "Semantics.Extensions.CellularSignalingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CognitiveAcousticDynamics", "name": "CognitiveAcousticDynamics", "path": "Semantics/Extensions/CognitiveAcousticDynamics.lean", "namespace": "Semantics.Biology.Cognitive", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CognitiveAcousticDynamics.lean \u2014 Laws of consciousness, acoustics, and synthetic biology. This module formalizes high-level cognitive and sensory laws: 1. Consciousness: Integrated Information (IIT), G", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 71 }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.integratedInformationPhi", "name": "integratedInformationPhi", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.gnwGating", "name": "gnwGating", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.orchOrCollapseTime", "name": "orchOrCollapseTime", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.sonarRange", "name": "sonarRange", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.gammatoneEnvelope", "name": "gammatoneEnvelope", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveAcousticDynamics.xenobotReplicationProb", "name": "xenobotReplicationProb", "module": "Semantics.Extensions.CognitiveAcousticDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CognitiveEfficiencyLaws", "name": "CognitiveEfficiencyLaws", "path": "Semantics/Extensions/CognitiveEfficiencyLaws.lean", "namespace": "Semantics.Biology.CognitiveEfficiency", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CognitiveEfficiencyLaws.lean \u2014 Laws of information processing, movement, and metabolic cost. This module formalizes the informational and metabolic constraints on cognitive systems: 1. Decision: Hick's", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Extensions.CognitiveEfficiencyLaws.hicksReactionTime", "name": "hicksReactionTime", "module": "Semantics.Extensions.CognitiveEfficiencyLaws" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveEfficiencyLaws.fittsMovementTime", "name": "fittsMovementTime", "module": "Semantics.Extensions.CognitiveEfficiencyLaws" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveEfficiencyLaws.zipfProbability", "name": "zipfProbability", "module": "Semantics.Extensions.CognitiveEfficiencyLaws" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveEfficiencyLaws.metabolicBitCost", "name": "metabolicBitCost", "module": "Semantics.Extensions.CognitiveEfficiencyLaws" }, { "kind": "module", "id": "Semantics.Extensions.CognitiveLearningDynamics", "name": "CognitiveLearningDynamics", "path": "Semantics/Extensions/CognitiveLearningDynamics.lean", "namespace": "Semantics.Biology.Cognition", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CognitiveLearningDynamics.lean \u2014 Laws of associative learning, cognitive foraging, and memory retrieval. This module formalizes the laws of neural adaptation and information search: 1. Learning: The Re", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.Extensions.CognitiveLearningDynamics.associativeStrengthUpdate", "name": "associativeStrengthUpdate", "module": "Semantics.Extensions.CognitiveLearningDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveLearningDynamics.levySearchProbability", "name": "levySearchProbability", "module": "Semantics.Extensions.CognitiveLearningDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveLearningDynamics.isCognitiveSwitchOptimal", "name": "isCognitiveSwitchOptimal", "module": "Semantics.Extensions.CognitiveLearningDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CognitiveLearningDynamics.memorySamplingProb", "name": "memorySamplingProb", "module": "Semantics.Extensions.CognitiveLearningDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CollectiveBiophysics", "name": "CollectiveBiophysics", "path": "Semantics/Extensions/CollectiveBiophysics.lean", "namespace": "Semantics.Biology.Collective", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CollectiveBiophysics.lean \u2014 Laws of swarming, navigation, and membrane mechanics. This module formalizes multi-agent and physical biological laws: 1. Swarming: Vicsek alignment and phase transitions. 2", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 76 }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.vicsekAngleUpdate", "name": "vicsekAngleUpdate", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.vicsekOrderParameter", "name": "vicsekOrderParameter", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.levyStepProbability", "name": "levyStepProbability", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.membranePressureDiff", "name": "membranePressureDiff", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.osmoticPressure", "name": "osmoticPressure", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "def", "id": "Semantics.Extensions.CollectiveBiophysics.cableSpaceConstant", "name": "cableSpaceConstant", "module": "Semantics.Extensions.CollectiveBiophysics" }, { "kind": "module", "id": "Semantics.Extensions.ConstrainedEnergyDynamics", "name": "ConstrainedEnergyDynamics", "path": "Semantics/Extensions/ConstrainedEnergyDynamics.lean", "namespace": "Semantics.Biology.Metabolism", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ConstrainedEnergyDynamics.lean \u2014 Laws of constrained energy expenditure and metabolic ceilings. This module formalizes Herman Pontzer's laws of human and animal metabolism: 1. Constraint: The constrain", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.Extensions.ConstrainedEnergyDynamics.constrainedTEE", "name": "constrainedTEE", "module": "Semantics.Extensions.ConstrainedEnergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstrainedEnergyDynamics.energyCompensationConstant", "name": "energyCompensationConstant", "module": "Semantics.Extensions.ConstrainedEnergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstrainedEnergyDynamics.metabolicCeiling", "name": "metabolicCeiling", "module": "Semantics.Extensions.ConstrainedEnergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstrainedEnergyDynamics.metabolicScope", "name": "metabolicScope", "module": "Semantics.Extensions.ConstrainedEnergyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstrainedEnergyDynamics.maintenanceBudget", "name": "maintenanceBudget", "module": "Semantics.Extensions.ConstrainedEnergyDynamics" }, { "kind": "module", "id": "Semantics.Extensions.ConstructalMuscleDynamics", "name": "ConstructalMuscleDynamics", "path": "Semantics/Extensions/ConstructalMuscleDynamics.lean", "namespace": "Semantics.Biology.Mechanics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ConstructalMuscleDynamics.lean \u2014 Laws of optimal flow, muscle mechanics, and geometric scaling. This module formalizes the laws of biological design and movement: 1. Optimality: Bejan's Constructal Law", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.Extensions.ConstructalMuscleDynamics.optimalBranchingRatio", "name": "optimalBranchingRatio", "module": "Semantics.Extensions.ConstructalMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstructalMuscleDynamics.muscleShorteningVelocity", "name": "muscleShorteningVelocity", "module": "Semantics.Extensions.ConstructalMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstructalMuscleDynamics.totalMuscleForce", "name": "totalMuscleForce", "module": "Semantics.Extensions.ConstructalMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ConstructalMuscleDynamics.surfaceVolumeRatio", "name": "surfaceVolumeRatio", "module": "Semantics.Extensions.ConstructalMuscleDynamics" }, { "kind": "module", "id": "Semantics.Extensions.CorticalScalingDynamics", "name": "CorticalScalingDynamics", "path": "Semantics/Extensions/CorticalScalingDynamics.lean", "namespace": "Semantics.Biology.BrainScaling", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CorticalScalingDynamics.lean \u2014 Laws of brain scaling, cortical connectivity, and white matter volume. This module formalizes the structural laws of the vertebrate brain: 1. Dimensionality: Charles Stev", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.CorticalScalingDynamics.corticalNeuronScaling", "name": "corticalNeuronScaling", "module": "Semantics.Extensions.CorticalScalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CorticalScalingDynamics.whiteMatterScaling", "name": "whiteMatterScaling", "module": "Semantics.Extensions.CorticalScalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CorticalScalingDynamics.isDendriticBranchLawful", "name": "isDendriticBranchLawful", "module": "Semantics.Extensions.CorticalScalingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.CorticalScalingDynamics.synapsisPerPairInvariant", "name": "synapsisPerPairInvariant", "module": "Semantics.Extensions.CorticalScalingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.DevelopmentalScalingLaws", "name": "DevelopmentalScalingLaws", "path": "Semantics/Extensions/DevelopmentalScalingLaws.lean", "namespace": "Semantics.Biology.Development", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DevelopmentalScalingLaws.lean \u2014 Laws of segmentation and tissue-size scaling. This module formalizes the laws of biological pattern formation at scale: 1. Rhythms: Cooke-Zeeman Clock-and-Wavefront mode", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.Extensions.DevelopmentalScalingLaws.somiteSize", "name": "somiteSize", "module": "Semantics.Extensions.DevelopmentalScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.DevelopmentalScalingLaws.scaledDecayLength", "name": "scaledDecayLength", "module": "Semantics.Extensions.DevelopmentalScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.DevelopmentalScalingLaws.scaleInvariantConcentration", "name": "scaleInvariantConcentration", "module": "Semantics.Extensions.DevelopmentalScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.DevelopmentalScalingLaws.divisionRate", "name": "divisionRate", "module": "Semantics.Extensions.DevelopmentalScalingLaws" }, { "kind": "module", "id": "Semantics.Extensions.EcologicalBehaviors", "name": "EcologicalBehaviors", "path": "Semantics/Extensions/EcologicalBehaviors.lean", "namespace": "Semantics.Biology.Ecology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EcologicalBehaviors.lean \u2014 Laws of competition, resilience, and behavioral evolution. This module formalizes macroscopic biological laws: 1. Competition: Gause's Principle of Exclusion. 2. Resilience: ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 64 }, { "kind": "def", "id": "Semantics.Extensions.EcologicalBehaviors.competitiveExclusionUpdate", "name": "competitiveExclusionUpdate", "module": "Semantics.Extensions.EcologicalBehaviors" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalBehaviors.alleeEffectRate", "name": "alleeEffectRate", "module": "Semantics.Extensions.EcologicalBehaviors" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalBehaviors.islandSpeciesFlux", "name": "islandSpeciesFlux", "module": "Semantics.Extensions.EcologicalBehaviors" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalBehaviors.optimalStayTimeCondition", "name": "optimalStayTimeCondition", "module": "Semantics.Extensions.EcologicalBehaviors" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalBehaviors.hamiltionRuleSatisfied", "name": "hamiltionRuleSatisfied", "module": "Semantics.Extensions.EcologicalBehaviors" }, { "kind": "module", "id": "Semantics.Extensions.EcologicalInformationDynamics", "name": "EcologicalInformationDynamics", "path": "Semantics/Extensions/EcologicalInformationDynamics.lean", "namespace": "Semantics.Biology.EcoInfo", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EcologicalInformationDynamics.lean \u2014 Laws of ecosystem richness and information stability. This module formalizes Ramon Margalef's laws of ecological information: 1. Richness: Margalef's Diversity Inde", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 59 }, { "kind": "def", "id": "Semantics.Extensions.EcologicalInformationDynamics.margalefRichness", "name": "margalefRichness", "module": "Semantics.Extensions.EcologicalInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalInformationDynamics.shannonDiversity", "name": "shannonDiversity", "module": "Semantics.Extensions.EcologicalInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalInformationDynamics.isSystemStable", "name": "isSystemStable", "module": "Semantics.Extensions.EcologicalInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalInformationDynamics.informationShedding", "name": "informationShedding", "module": "Semantics.Extensions.EcologicalInformationDynamics" }, { "kind": "module", "id": "Semantics.Extensions.EcologicalNetworkDynamics", "name": "EcologicalNetworkDynamics", "path": "Semantics/Extensions/EcologicalNetworkDynamics.lean", "namespace": "Semantics.Biology.EcoNetwork", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EcologicalNetworkDynamics.lean \u2014 Laws of nutrient stoichiometry, predator-prey interaction, and network complexity. This module formalizes the laws of ecosystem structure and function: 1. Stoichiometry", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 80 }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.redfieldCheck", "name": "redfieldCheck", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.hollingType1", "name": "hollingType1", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.hollingType2", "name": "hollingType2", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.hollingType3", "name": "hollingType3", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.networkConnectance", "name": "networkConnectance", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalNetworkDynamics.taylorsVariance", "name": "taylorsVariance", "module": "Semantics.Extensions.EcologicalNetworkDynamics" }, { "kind": "module", "id": "Semantics.Extensions.EcologicalSpecializationLaws", "name": "EcologicalSpecializationLaws", "path": "Semantics/Extensions/EcologicalSpecializationLaws.lean", "namespace": "Semantics.Biology.Specialization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EcologicalSpecializationLaws.lean \u2014 Laws of niche partitioning, molecular motors, and paradox strategies. This module formalizes the laws of biological specialization and efficiency: 1. Ecology: MacArt", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 68 }, { "kind": "def", "id": "Semantics.Extensions.EcologicalSpecializationLaws.brokenStickAbundance", "name": "brokenStickAbundance", "module": "Semantics.Extensions.EcologicalSpecializationLaws" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalSpecializationLaws.nicheBreadthReciprocal", "name": "nicheBreadthReciprocal", "module": "Semantics.Extensions.EcologicalSpecializationLaws" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalSpecializationLaws.nicheOverlapAsym", "name": "nicheOverlapAsym", "module": "Semantics.Extensions.EcologicalSpecializationLaws" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalSpecializationLaws.motorThermodynamicEfficiency", "name": "motorThermodynamicEfficiency", "module": "Semantics.Extensions.EcologicalSpecializationLaws" }, { "kind": "def", "id": "Semantics.Extensions.EcologicalSpecializationLaws.parrondoWinProb", "name": "parrondoWinProb", "module": "Semantics.Extensions.EcologicalSpecializationLaws" }, { "kind": "module", "id": "Semantics.Extensions.EcologyMechanicalLaws", "name": "EcologyMechanicalLaws", "path": "Semantics/Extensions/EcologyMechanicalLaws.lean", "namespace": "Semantics.Biology.EcologyMech", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EcologyMechanicalLaws.lean \u2014 Laws of species diversity scaling and cellular prestress. This module formalizes the laws of ecological richness and cellular structural tuning: 1. Diversity: The Arrhenius", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 42 }, { "kind": "def", "id": "Semantics.Extensions.EcologyMechanicalLaws.speciesRichnessArea", "name": "speciesRichnessArea", "module": "Semantics.Extensions.EcologyMechanicalLaws" }, { "kind": "def", "id": "Semantics.Extensions.EcologyMechanicalLaws.cellularStiffness", "name": "cellularStiffness", "module": "Semantics.Extensions.EcologyMechanicalLaws" }, { "kind": "module", "id": "Semantics.Extensions.EpidemiologicalDynamics", "name": "EpidemiologicalDynamics", "path": "Semantics/Extensions/EpidemiologicalDynamics.lean", "namespace": "Semantics.Biology.Epidemiology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EpidemiologicalDynamics.lean \u2014 Laws of infectious disease spread and herd immunity. This module formalizes the laws of biological contagion: 1. Transmission: The Basic Reproduction Number (R0). 2. Resi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalDynamics.basicReproductionNumber", "name": "basicReproductionNumber", "module": "Semantics.Extensions.EpidemiologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalDynamics.herdImmunityThreshold", "name": "herdImmunityThreshold", "module": "Semantics.Extensions.EpidemiologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalDynamics.sirUpdate", "name": "sirUpdate", "module": "Semantics.Extensions.EpidemiologicalDynamics" }, { "kind": "module", "id": "Semantics.Extensions.EpidemiologicalTrophicDynamics", "name": "EpidemiologicalTrophicDynamics", "path": "Semantics/Extensions/EpidemiologicalTrophicDynamics.lean", "namespace": "Semantics.Biology.Waves", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EpidemiologicalTrophicDynamics.lean \u2014 Laws of infection chain-binomials and trophic waves. This module formalizes the laws of contagion spread and food web energy flow: 1. Infection: The Reed-Frost cha", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalTrophicDynamics.reedFrostNewCases", "name": "reedFrostNewCases", "module": "Semantics.Extensions.EpidemiologicalTrophicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalTrophicDynamics.trophicWaveUpdate", "name": "trophicWaveUpdate", "module": "Semantics.Extensions.EpidemiologicalTrophicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EpidemiologicalTrophicDynamics.trophicKinetics", "name": "trophicKinetics", "module": "Semantics.Extensions.EpidemiologicalTrophicDynamics" }, { "kind": "module", "id": "Semantics.Extensions.EvolutionaryLandscapeDynamics", "name": "EvolutionaryLandscapeDynamics", "path": "Semantics/Extensions/EvolutionaryLandscapeDynamics.lean", "namespace": "Semantics.Biology.Landscapes", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EvolutionaryLandscapeDynamics.lean \u2014 Laws of adaptive landscapes and the shifting balance theory. This module formalizes the laws of population movement across fitness manifolds: 1. Gradient: Wright's ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryLandscapeDynamics.frequencyChangeGradient", "name": "frequencyChangeGradient", "module": "Semantics.Extensions.EvolutionaryLandscapeDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryLandscapeDynamics.populationMeanFitness", "name": "populationMeanFitness", "module": "Semantics.Extensions.EvolutionaryLandscapeDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryLandscapeDynamics.isDriftDominant", "name": "isDriftDominant", "module": "Semantics.Extensions.EvolutionaryLandscapeDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryLandscapeDynamics.isAscendingPeak", "name": "isAscendingPeak", "module": "Semantics.Extensions.EvolutionaryLandscapeDynamics" }, { "kind": "module", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics", "name": "EvolutionaryNetworkDynamics", "path": "Semantics/Extensions/EvolutionaryNetworkDynamics.lean", "namespace": "Semantics.Biology.Evolutionary", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team EvolutionaryNetworkDynamics.lean \u2014 Laws of evolutionary strategy and network topology. This module formalizes the laws of competition and structure in biological systems: 1. Strategy: Evolutionarily St", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 72 }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.hawkDoveMixedStrategy", "name": "hawkDoveMixedStrategy", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.isStrategyStable", "name": "isStrategyStable", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.genusExtinctionRate", "name": "genusExtinctionRate", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.degreeProbability", "name": "degreeProbability", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.attachmentWeight", "name": "attachmentWeight", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "def", "id": "Semantics.Extensions.EvolutionaryNetworkDynamics.isMutationNeutral", "name": "isMutationNeutral", "module": "Semantics.Extensions.EvolutionaryNetworkDynamics" }, { "kind": "module", "id": "Semantics.Extensions.FisherGeometricAdaptationLaws", "name": "FisherGeometricAdaptationLaws", "path": "Semantics/Extensions/FisherGeometricAdaptationLaws.lean", "namespace": "Semantics.Biology.FisherGeometric", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FisherGeometricAdaptationLaws.lean \u2014 Laws of phenotypic complexity and beneficial mutations. This module formalizes R.A. Fisher's Geometric Model (FGM) of adaptation: 1. Fitness: Gaussian phenotypic fi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Extensions.FisherGeometricAdaptationLaws.phenotypicFitness", "name": "phenotypicFitness", "module": "Semantics.Extensions.FisherGeometricAdaptationLaws" }, { "kind": "def", "id": "Semantics.Extensions.FisherGeometricAdaptationLaws.beneficialMutationProb", "name": "beneficialMutationProb", "module": "Semantics.Extensions.FisherGeometricAdaptationLaws" }, { "kind": "def", "id": "Semantics.Extensions.FisherGeometricAdaptationLaws.Pa_limit_zero", "name": "Pa_limit_zero", "module": "Semantics.Extensions.FisherGeometricAdaptationLaws" }, { "kind": "def", "id": "Semantics.Extensions.FisherGeometricAdaptationLaws.complexityPenalty", "name": "complexityPenalty", "module": "Semantics.Extensions.FisherGeometricAdaptationLaws" }, { "kind": "module", "id": "Semantics.Extensions.FoundationalBioLaws", "name": "FoundationalBioLaws", "path": "Semantics/Extensions/FoundationalBioLaws.lean", "namespace": "Semantics.Biology.Foundations", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FoundationalBioLaws.lean \u2014 Laws of classical genetics and ecological limits. This module formalizes the bedrock laws of biology: 1. Genetics: Mendelian segregation and Morgan's linkage frequency. 2. Ec", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 69 }, { "kind": "def", "id": "Semantics.Extensions.FoundationalBioLaws.mendelianGenotypeSum", "name": "mendelianGenotypeSum", "module": "Semantics.Extensions.FoundationalBioLaws" }, { "kind": "def", "id": "Semantics.Extensions.FoundationalBioLaws.recombinationFrequency", "name": "recombinationFrequency", "module": "Semantics.Extensions.FoundationalBioLaws" }, { "kind": "def", "id": "Semantics.Extensions.FoundationalBioLaws.liebigGrowthRate", "name": "liebigGrowthRate", "module": "Semantics.Extensions.FoundationalBioLaws" }, { "kind": "def", "id": "Semantics.Extensions.FoundationalBioLaws.performanceTolerance", "name": "performanceTolerance", "module": "Semantics.Extensions.FoundationalBioLaws" }, { "kind": "def", "id": "Semantics.Extensions.FoundationalBioLaws.polygenicTraitValue", "name": "polygenicTraitValue", "module": "Semantics.Extensions.FoundationalBioLaws" }, { "kind": "module", "id": "Semantics.Extensions.FractalVascularLaws", "name": "FractalVascularLaws", "path": "Semantics/Extensions/FractalVascularLaws.lean", "namespace": "Semantics.Biology.Fractal", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FractalVascularLaws.lean \u2014 Laws of hierarchical branching and allometric scaling. This module formalizes the fractal and metabolic laws of biological networks: 1. Horton: Hierarchical branch numbers an", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.FractalVascularLaws.branchCount", "name": "branchCount", "module": "Semantics.Extensions.FractalVascularLaws" }, { "kind": "def", "id": "Semantics.Extensions.FractalVascularLaws.branchLength", "name": "branchLength", "module": "Semantics.Extensions.FractalVascularLaws" }, { "kind": "def", "id": "Semantics.Extensions.FractalVascularLaws.wbeScalingExponent", "name": "wbeScalingExponent", "module": "Semantics.Extensions.FractalVascularLaws" }, { "kind": "def", "id": "Semantics.Extensions.FractalVascularLaws.heartRateScale", "name": "heartRateScale", "module": "Semantics.Extensions.FractalVascularLaws" }, { "kind": "def", "id": "Semantics.Extensions.FractalVascularLaws.bloodVolumeScale", "name": "bloodVolumeScale", "module": "Semantics.Extensions.FractalVascularLaws" }, { "kind": "module", "id": "Semantics.Extensions.GenomicEvolutionLaws", "name": "GenomicEvolutionLaws", "path": "Semantics/Extensions/GenomicEvolutionLaws.lean", "namespace": "Semantics.Biology.GenomeEvolution", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicEvolutionLaws.lean \u2014 Laws of mutation accumulation and the drift-selection barrier. This module formalizes the laws governing genomic complexity and stability: 1. Accumulation: Muller's Ratchet ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.GenomicEvolutionLaws.fittestClassSize", "name": "fittestClassSize", "module": "Semantics.Extensions.GenomicEvolutionLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicEvolutionLaws.isSelectionVisible", "name": "isSelectionVisible", "module": "Semantics.Extensions.GenomicEvolutionLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicEvolutionLaws.neutralDiversityTheta", "name": "neutralDiversityTheta", "module": "Semantics.Extensions.GenomicEvolutionLaws" }, { "kind": "module", "id": "Semantics.Extensions.GenomicInformationLaws", "name": "GenomicInformationLaws", "path": "Semantics/Extensions/GenomicInformationLaws.lean", "namespace": "Semantics.Biology.GenomeInfo", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicInformationLaws.lean \u2014 Laws of mutation fidelity, non-coding scaling, and minimal genomes. This module formalizes the laws governing genomic information integrity: 1. Fidelity: Drake's Rule (Inv", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.GenomicInformationLaws.drakeMutationRate", "name": "drakeMutationRate", "module": "Semantics.Extensions.GenomicInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicInformationLaws.driftBarrierLog", "name": "driftBarrierLog", "module": "Semantics.Extensions.GenomicInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicInformationLaws.minimalGenomeGenes", "name": "minimalGenomeGenes", "module": "Semantics.Extensions.GenomicInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicInformationLaws.isGenomeAutonomous", "name": "isGenomeAutonomous", "module": "Semantics.Extensions.GenomicInformationLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicInformationLaws.effectiveInformation", "name": "effectiveInformation", "module": "Semantics.Extensions.GenomicInformationLaws" }, { "kind": "module", "id": "Semantics.Extensions.GenomicScalingLaws", "name": "GenomicScalingLaws", "path": "Semantics/Extensions/GenomicScalingLaws.lean", "namespace": "Semantics.Biology.GenomeScaling", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicScalingLaws.lean \u2014 Laws of gene family size and functional category scaling. This module formalizes Eugene Koonin's universal scaling laws of genome evolution: 1. Complexity: The power law distr", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.GenomicScalingLaws.familySizeProb", "name": "familySizeProb", "module": "Semantics.Extensions.GenomicScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicScalingLaws.functionalGeneCount", "name": "functionalGeneCount", "module": "Semantics.Extensions.GenomicScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.GenomicScalingLaws.bdimUpdate", "name": "bdimUpdate", "module": "Semantics.Extensions.GenomicScalingLaws" }, { "kind": "module", "id": "Semantics.Extensions.GenomicStoichiometricDynamics", "name": "GenomicStoichiometricDynamics", "path": "Semantics/Extensions/GenomicStoichiometricDynamics.lean", "namespace": "Semantics.Biology.GenomicOcean", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicStoichiometricDynamics.lean \u2014 Laws of genomic complexity and oceanic buffering. This module formalizes the information and chemical laws of life at scale: 1. Genomics: Adami's complexity and van", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 54 }, { "kind": "def", "id": "Semantics.Extensions.GenomicStoichiometricDynamics.adamiComplexity", "name": "adamiComplexity", "module": "Semantics.Extensions.GenomicStoichiometricDynamics" }, { "kind": "def", "id": "Semantics.Extensions.GenomicStoichiometricDynamics.regulatoryGeneCount", "name": "regulatoryGeneCount", "module": "Semantics.Extensions.GenomicStoichiometricDynamics" }, { "kind": "def", "id": "Semantics.Extensions.GenomicStoichiometricDynamics.revelleFactor", "name": "revelleFactor", "module": "Semantics.Extensions.GenomicStoichiometricDynamics" }, { "kind": "def", "id": "Semantics.Extensions.GenomicStoichiometricDynamics.remineralizationOxygenRatio", "name": "remineralizationOxygenRatio", "module": "Semantics.Extensions.GenomicStoichiometricDynamics" }, { "kind": "module", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold", "name": "HarmonicKinkPlasmaManifold", "path": "Semantics/Extensions/HarmonicKinkPlasmaManifold.lean", "namespace": "Semantics", "doc": "HarmonicKinkPlasmaManifold.lean ================================= Speculative-lawfulness scaffold for a FAMM-walled, kink-compressed plasma routing manifold. This file does NOT claim a physical rocket exists. It formalizes the abstract routing invariant that motivated the design discussion: \u2022 q_", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 4, "def_count": 13, "struct_count": 3, "inductive_count": 1, "line_count": 237 }, { "kind": "theorem", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.contract_sidon_no_collision", "name": "contract_sidon_no_collision", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "theorem", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.contract_node_thermal_bound", "name": "contract_node_thermal_bound", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "theorem", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.contract_qDir_floor", "name": "contract_qDir_floor", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "theorem", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.contract_qWall_floor", "name": "contract_qWall_floor", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.qDir", "name": "qDir", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.qWall", "name": "qWall", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.validPulse", "name": "validPulse", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.validResidual", "name": "validResidual", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.sameUnorderedPair", "name": "sameUnorderedPair", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.pairSignature", "name": "pairSignature", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.SidonSeparated", "name": "SidonSeparated", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.classifyNode", "name": "classifyNode", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.thermallyAdmissible", "name": "thermallyAdmissible", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.fammWallSafe", "name": "fammWallSafe", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.mkToyKinkNode", "name": "mkToyKinkNode", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.toyNodes", "name": "toyNodes", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "def", "id": "Semantics.Extensions.HarmonicKinkPlasmaManifold.architectureSummary", "name": "architectureSummary", "module": "Semantics.Extensions.HarmonicKinkPlasmaManifold" }, { "kind": "module", "id": "Semantics.Extensions.HyperbolicStateSurface", "name": "HyperbolicStateSurface", "path": "Semantics/Extensions/HyperbolicStateSurface.lean", "namespace": "HyperbolicStateSurface", "doc": "Per AGENTS.md \u00a71.4: Uses Q16_16 fixed-point; no Float in core types. `native_decide` on Float is non-deterministic across platforms and must not appear in core logic. All arithmetic is pure integer / fixed-point. The state space of the Go board + DAG is a HYPERBOLA. Forward computation traces one ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 10, "struct_count": 4, "inductive_count": 0, "line_count": 210 }, { "kind": "theorem", "id": "Semantics.Extensions.HyperbolicStateSurface.ko_rule_prevents_branch_crossing", "name": "ko_rule_prevents_branch_crossing", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "theorem", "id": "Semantics.Extensions.HyperbolicStateSurface.no_branch_crossing", "name": "no_branch_crossing", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "theorem", "id": "Semantics.Extensions.HyperbolicStateSurface.asyncFlowPreservesInvariance", "name": "asyncFlowPreservesInvariance", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.onHyperbola", "name": "onHyperbola", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.onHyperbolaApprox", "name": "onHyperbolaApprox", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.forwardStep", "name": "forwardStep", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.backwardRetrieve", "name": "backwardRetrieve", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.cellAtPoint", "name": "cellAtPoint", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.computeFlowLine", "name": "computeFlowLine", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.distanceToReversibility", "name": "distanceToReversibility", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.E_opp_approx", "name": "E_opp_approx", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.pbacsRegion", "name": "pbacsRegion", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "def", "id": "Semantics.Extensions.HyperbolicStateSurface.asyncLocalFlow", "name": "asyncLocalFlow", "module": "Semantics.Extensions.HyperbolicStateSurface" }, { "kind": "module", "id": "Semantics.Extensions.LifeHistoryInvariants", "name": "LifeHistoryInvariants", "path": "Semantics/Extensions/LifeHistoryInvariants.lean", "namespace": "Semantics.Biology.LifeHistory", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team LifeHistoryInvariants.lean \u2014 Laws of fractal scaling, longevity, and life history. This module formalizes the temporal and structural laws of biological existence: 1. Scaling: WBE fractal network ratio", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 67 }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.wbeRadiusRatio", "name": "wbeRadiusRatio", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.wbeLengthRatio", "name": "wbeLengthRatio", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.energyExpenditureRate", "name": "energyExpenditureRate", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.rosDamageUpdate", "name": "rosDamageUpdate", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.maturityMortalityProduct", "name": "maturityMortalityProduct", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryInvariants.reproductiveEffortRatio", "name": "reproductiveEffortRatio", "module": "Semantics.Extensions.LifeHistoryInvariants" }, { "kind": "module", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws", "name": "LifeHistoryOptimizationLaws", "path": "Semantics/Extensions/LifeHistoryOptimizationLaws.lean", "namespace": "Semantics.Biology.Optimization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team LifeHistoryOptimizationLaws.lean \u2014 Laws of offspring investment and reproductive strategy. This module formalizes the laws of biological resource allocation: 1. Lack's Principle: Optimal clutch size fo", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws.survivingOffspringCount", "name": "survivingOffspringCount", "module": "Semantics.Extensions.LifeHistoryOptimizationLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws.offspringSurvivalProb", "name": "offspringSurvivalProb", "module": "Semantics.Extensions.LifeHistoryOptimizationLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws.parentalFitness", "name": "parentalFitness", "module": "Semantics.Extensions.LifeHistoryOptimizationLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws.isOffspringSizeOptimal", "name": "isOffspringSizeOptimal", "module": "Semantics.Extensions.LifeHistoryOptimizationLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryOptimizationLaws.offspringNumberScaling", "name": "offspringNumberScaling", "module": "Semantics.Extensions.LifeHistoryOptimizationLaws" }, { "kind": "module", "id": "Semantics.Extensions.LifeHistoryTradeoffLaws", "name": "LifeHistoryTradeoffLaws", "path": "Semantics/Extensions/LifeHistoryTradeoffLaws.lean", "namespace": "Semantics.Biology.LifeHistory", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team LifeHistoryTradeoffLaws.lean \u2014 Laws of energy allocation, maturation, and semelparity. This module formalizes the laws of biological investment and life history strategies: 1. Semelparity: Cole's Parad", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 60 }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryTradeoffLaws.annualOffspringThreshold", "name": "annualOffspringThreshold", "module": "Semantics.Extensions.LifeHistoryTradeoffLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryTradeoffLaws.relativeMaturitySize", "name": "relativeMaturitySize", "module": "Semantics.Extensions.LifeHistoryTradeoffLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryTradeoffLaws.totalEnergyBudget", "name": "totalEnergyBudget", "module": "Semantics.Extensions.LifeHistoryTradeoffLaws" }, { "kind": "def", "id": "Semantics.Extensions.LifeHistoryTradeoffLaws.netReproductiveRate", "name": "netReproductiveRate", "module": "Semantics.Extensions.LifeHistoryTradeoffLaws" }, { "kind": "module", "id": "Semantics.Extensions.LocomotionMuscleDynamics", "name": "LocomotionMuscleDynamics", "path": "Semantics/Extensions/LocomotionMuscleDynamics.lean", "namespace": "Semantics.Biology.Locomotion", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team LocomotionMuscleDynamics.lean \u2014 Laws of animal movement and muscle contraction. This module formalizes the physical laws of biological locomotion: 1. Fluid: Strouhal Number for swimming and flying effi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 59 }, { "kind": "def", "id": "Semantics.Extensions.LocomotionMuscleDynamics.strouhalNumber", "name": "strouhalNumber", "module": "Semantics.Extensions.LocomotionMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.LocomotionMuscleDynamics.isPropulsionEfficient", "name": "isPropulsionEfficient", "module": "Semantics.Extensions.LocomotionMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.LocomotionMuscleDynamics.froudeNumber", "name": "froudeNumber", "module": "Semantics.Extensions.LocomotionMuscleDynamics" }, { "kind": "def", "id": "Semantics.Extensions.LocomotionMuscleDynamics.crossBridgeUpdate", "name": "crossBridgeUpdate", "module": "Semantics.Extensions.LocomotionMuscleDynamics" }, { "kind": "module", "id": "Semantics.Extensions.MalthusianHayflickDynamics", "name": "MalthusianHayflickDynamics", "path": "Semantics/Extensions/MalthusianHayflickDynamics.lean", "namespace": "Semantics.Biology.ExpansionLimit", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MalthusianHayflickDynamics.lean \u2014 Laws of exponential growth and cellular division limits. This module formalizes the laws of population expansion and cellular aging: 1. Growth: The Malthusian model of", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 46 }, { "kind": "def", "id": "Semantics.Extensions.MalthusianHayflickDynamics.malthusianPopulation", "name": "malthusianPopulation", "module": "Semantics.Extensions.MalthusianHayflickDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MalthusianHayflickDynamics.telomereLength", "name": "telomereLength", "module": "Semantics.Extensions.MalthusianHayflickDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MalthusianHayflickDynamics.isSenescent", "name": "isSenescent", "module": "Semantics.Extensions.MalthusianHayflickDynamics" }, { "kind": "module", "id": "Semantics.Extensions.ManifoldBlit", "name": "ManifoldBlit", "path": "Semantics/Extensions/ManifoldBlit.lean", "namespace": "ManifoldBlit", "doc": "Hardware Protocol for Planetary Sensing M_{k+1}(x) = Quant_LLM( J_DAG[ M_k(x) \u2295 (\u03a8_q \u2297 R_RT(f, \u03b5_TCP)) ] ) This module formalizes the Blitter operators as a substrate-neutral manifold update protocol. Each operator has a mathematical type signature and convergence properties. Data sources integra", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 4, "def_count": 17, "struct_count": 8, "inductive_count": 0, "line_count": 354 }, { "kind": "theorem", "id": "Semantics.Extensions.ManifoldBlit.quantLLM_idempotent", "name": "quantLLM_idempotent", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "theorem", "id": "Semantics.Extensions.ManifoldBlit.blitter_zero", "name": "blitter_zero", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "theorem", "id": "Semantics.Extensions.ManifoldBlit.blitter_bounded", "name": "blitter_bounded", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "theorem", "id": "Semantics.Extensions.ManifoldBlit.dag_cache_hit_no_change", "name": "dag_cache_hit_no_change", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.floatMin", "name": "floatMin", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.floatMax", "name": "floatMax", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.arraySetD", "name": "arraySetD", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.QuantLLM", "name": "QuantLLM", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.J_DAG", "name": "J_DAG", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.blitterOp", "name": "blitterOp", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.quantumWalk", "name": "quantumWalk", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.interferenceOp", "name": "interferenceOp", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.multiRayPather", "name": "multiRayPather", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.driftTensor", "name": "driftTensor", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.blitStep", "name": "blitStep", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.blitRun", "name": "blitRun", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.manifoldRadiography", "name": "manifoldRadiography", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.tomographicConsensus", "name": "tomographicConsensus", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.adaptiveResolution", "name": "adaptiveResolution", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.deltaRadiography", "name": "deltaRadiography", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "def", "id": "Semantics.Extensions.ManifoldBlit.totalDeformationBudget", "name": "totalDeformationBudget", "module": "Semantics.Extensions.ManifoldBlit" }, { "kind": "module", "id": "Semantics.Extensions.MarineMigrationDynamics", "name": "MarineMigrationDynamics", "path": "Semantics/Extensions/MarineMigrationDynamics.lean", "namespace": "Semantics.Biology.Marine.Migration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MarineMigrationDynamics.lean \u2014 Laws of diel migration, turbulent foraging, and patch residence. This module formalizes the laws of behavioral ecology in fluid environments: 1. Migration: Diel Vertical ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 59 }, { "kind": "def", "id": "Semantics.Extensions.MarineMigrationDynamics.migrationFitness", "name": "migrationFitness", "module": "Semantics.Extensions.MarineMigrationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MarineMigrationDynamics.verticalSwimmingSpeed", "name": "verticalSwimmingSpeed", "module": "Semantics.Extensions.MarineMigrationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MarineMigrationDynamics.turbulentEncounterRate", "name": "turbulentEncounterRate", "module": "Semantics.Extensions.MarineMigrationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MarineMigrationDynamics.isStayTimeOptimal", "name": "isStayTimeOptimal", "module": "Semantics.Extensions.MarineMigrationDynamics" }, { "kind": "module", "id": "Semantics.Extensions.MarinePlanktonDynamics", "name": "MarinePlanktonDynamics", "path": "Semantics/Extensions/MarinePlanktonDynamics.lean", "namespace": "Semantics.Biology.Marine", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MarinePlanktonDynamics.lean \u2014 Laws of phytoplankton blooms, sinking particles, and thermal rates. This module formalizes the laws of biological oceanography: 1. Blooms: Sverdrup's Critical Depth Hypoth", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.MarinePlanktonDynamics.sverdrupCondition", "name": "sverdrupCondition", "module": "Semantics.Extensions.MarinePlanktonDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MarinePlanktonDynamics.stokesSinkingVelocity", "name": "stokesSinkingVelocity", "module": "Semantics.Extensions.MarinePlanktonDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MarinePlanktonDynamics.q10RateRatio", "name": "q10RateRatio", "module": "Semantics.Extensions.MarinePlanktonDynamics" }, { "kind": "module", "id": "Semantics.Extensions.MasterEquation", "name": "MasterEquation", "path": "Semantics/Extensions/MasterEquation.lean", "namespace": "MasterEquation", "doc": "MasterEquation.lean \u2014 The Complete SSMS Recurrence =================================================== The master equation compressing the full 8-layer stack into a single 6-step recurrence: S_{t+1} = MLGRU(Gossip(Prune(Stabilize(Score_{\u03a3+NK}(Expand(S_t)))))) Each step maps the system state S_t \u2192", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 25, "struct_count": 5, "inductive_count": 1, "line_count": 393 }, { "kind": "theorem", "id": "Semantics.Extensions.MasterEquation.mlgru_preserves_bounds", "name": "mlgru_preserves_bounds", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "theorem", "id": "Semantics.Extensions.MasterEquation.gossip_non_decreasing_energy", "name": "gossip_non_decreasing_energy", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.zero", "name": "zero", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.TernaryWeight", "name": "TernaryWeight", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.MLGRUState", "name": "MLGRUState", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.ScalarNode", "name": "ScalarNode", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.hyperbolaIndex", "name": "hyperbolaIndex", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.mirrorIndex", "name": "mirrorIndex", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.expandCriterion", "name": "expandCriterion", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.stepExpand", "name": "stepExpand", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.nkCouplingScore", "name": "nkCouplingScore", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.sigmaScore", "name": "sigmaScore", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.compositeScore", "name": "compositeScore", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.stepScore", "name": "stepScore", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.aciViolation", "name": "aciViolation", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.liIntegrable", "name": "liIntegrable", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.shuntNode", "name": "shuntNode", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.stepStabilize", "name": "stepStabilize", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.pruneCriterion", "name": "pruneCriterion", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "def", "id": "Semantics.Extensions.MasterEquation.stepPrune", "name": "stepPrune", "module": "Semantics.Extensions.MasterEquation" }, { "kind": "module", "id": "Semantics.Extensions.MicrobialBiomassDynamics", "name": "MicrobialBiomassDynamics", "path": "Semantics/Extensions/MicrobialBiomassDynamics.lean", "namespace": "Semantics.Biology.Biomass", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MicrobialBiomassDynamics.lean \u2014 Laws of microbial growth, maintenance, and biomass accumulation. This module formalizes the laws of sub-cellular and population-scale growth: 1. Growth: Monod substrate ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Extensions.MicrobialBiomassDynamics.monodGrowthRate", "name": "monodGrowthRate", "module": "Semantics.Extensions.MicrobialBiomassDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MicrobialBiomassDynamics.specificUptakeRate", "name": "specificUptakeRate", "module": "Semantics.Extensions.MicrobialBiomassDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MicrobialBiomassDynamics.logisticGrowthUpdate", "name": "logisticGrowthUpdate", "module": "Semantics.Extensions.MicrobialBiomassDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MicrobialBiomassDynamics.gompertzGrowthUpdate", "name": "gompertzGrowthUpdate", "module": "Semantics.Extensions.MicrobialBiomassDynamics" }, { "kind": "module", "id": "Semantics.Extensions.MolecularBindingThermodynamics", "name": "MolecularBindingThermodynamics", "path": "Semantics/Extensions/MolecularBindingThermodynamics.lean", "namespace": "Semantics.Biology.Binding", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MolecularBindingThermodynamics.lean \u2014 Laws of DNA-protein binding and Boltzmann weights. This module formalizes the thermodynamic laws of gene regulation: 1. Boltzmann: The statistical weight of a mole", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.MolecularBindingThermodynamics.boltzmannBindingWeight", "name": "boltzmannBindingWeight", "module": "Semantics.Extensions.MolecularBindingThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.MolecularBindingThermodynamics.bindingOccupancy", "name": "bindingOccupancy", "module": "Semantics.Extensions.MolecularBindingThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.MolecularBindingThermodynamics.bindingSpecificityRatio", "name": "bindingSpecificityRatio", "module": "Semantics.Extensions.MolecularBindingThermodynamics" }, { "kind": "def", "id": "Semantics.Extensions.MolecularBindingThermodynamics.totalBindingEnergy", "name": "totalBindingEnergy", "module": "Semantics.Extensions.MolecularBindingThermodynamics" }, { "kind": "module", "id": "Semantics.Extensions.MolecularCooperation", "name": "MolecularCooperation", "path": "Semantics/Extensions/MolecularCooperation.lean", "namespace": "Semantics.Biology.Molecular", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MolecularCooperation.lean \u2014 Laws of molecular binding, allostery, and cooperativity. This module formalizes the thermodynamic and empirical laws of protein function: 1. Empirical: Hill's equation for c", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 64 }, { "kind": "def", "id": "Semantics.Extensions.MolecularCooperation.hillSaturation", "name": "hillSaturation", "module": "Semantics.Extensions.MolecularCooperation" }, { "kind": "def", "id": "Semantics.Extensions.MolecularCooperation.adairSaturation", "name": "adairSaturation", "module": "Semantics.Extensions.MolecularCooperation" }, { "kind": "def", "id": "Semantics.Extensions.MolecularCooperation.mwcSaturation", "name": "mwcSaturation", "module": "Semantics.Extensions.MolecularCooperation" }, { "kind": "def", "id": "Semantics.Extensions.MolecularCooperation.knfSaturation", "name": "knfSaturation", "module": "Semantics.Extensions.MolecularCooperation" }, { "kind": "module", "id": "Semantics.Extensions.MorphoKineticLaws", "name": "MorphoKineticLaws", "path": "Semantics/Extensions/MorphoKineticLaws.lean", "namespace": "Semantics.Biology.MorphoKinetic", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphoKineticLaws.lean \u2014 Laws of spiral growth and chemical mass action. This module formalizes the laws of biological form and molecular interaction: 1. Growth: The logarithmic (equiangular) spiral mo", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 48 }, { "kind": "def", "id": "Semantics.Extensions.MorphoKineticLaws.shellRadius", "name": "shellRadius", "module": "Semantics.Extensions.MorphoKineticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphoKineticLaws.reactionRate", "name": "reactionRate", "module": "Semantics.Extensions.MorphoKineticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphoKineticLaws.chemicalEquilibriumConstant", "name": "chemicalEquilibriumConstant", "module": "Semantics.Extensions.MorphoKineticLaws" }, { "kind": "module", "id": "Semantics.Extensions.MorphogeneticLaws", "name": "MorphogeneticLaws", "path": "Semantics/Extensions/MorphogeneticLaws.lean", "namespace": "Semantics.Biology.Morphogenesis", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphogeneticLaws.lean \u2014 Laws of positional information, gradients, and tissue topology. This module formalizes the laws of biological patterning and structural development: 1. Patterning: Wolpert's Fr", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 66 }, { "kind": "def", "id": "Semantics.Extensions.MorphogeneticLaws.frenchFlagFate", "name": "frenchFlagFate", "module": "Semantics.Extensions.MorphogeneticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphogeneticLaws.morphogenGradient", "name": "morphogenGradient", "module": "Semantics.Extensions.MorphogeneticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphogeneticLaws.lewisCellArea", "name": "lewisCellArea", "module": "Semantics.Extensions.MorphogeneticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphogeneticLaws.aboavWeaireNeighbors", "name": "aboavWeaireNeighbors", "module": "Semantics.Extensions.MorphogeneticLaws" }, { "kind": "def", "id": "Semantics.Extensions.MorphogeneticLaws.growthDilution", "name": "growthDilution", "module": "Semantics.Extensions.MorphogeneticLaws" }, { "kind": "module", "id": "Semantics.Extensions.MorphologicalDynamics", "name": "MorphologicalDynamics", "path": "Semantics/Extensions/MorphologicalDynamics.lean", "namespace": "Semantics.Biology.Morphology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphologicalDynamics.lean \u2014 Laws of biological form, branching, and topology. This module formalizes the geometric and topological laws of biological structures: 1. Transformation: D'Arcy Thompson's m", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 82 }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.transformPoint", "name": "transformPoint", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.murrayRadiusSum", "name": "murrayRadiusSum", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.linkingNumber", "name": "linkingNumber", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.superhelicalDensity", "name": "superhelicalDensity", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.brainMass", "name": "brainMass", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "def", "id": "Semantics.Extensions.MorphologicalDynamics.encephalizationQuotient", "name": "encephalizationQuotient", "module": "Semantics.Extensions.MorphologicalDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NKCoupling", "name": "NKCoupling", "path": "Semantics/Extensions/NKCoupling.lean", "namespace": "NKCoupling", "doc": "NKCoupling.lean \u2014 N-K Coupling Law: Structural-to-Spectral Field Interaction ============================================================================= The N-K Coupling Law governs how structural research coordinates (N-space) interact with spectral information fields (K-space): J(n) = (ab)\u00b7F_m", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 10, "struct_count": 4, "inductive_count": 0, "line_count": 255 }, { "kind": "theorem", "id": "Semantics.Extensions.NKCoupling.hyperbola_min_at_squares", "name": "hyperbola_min_at_squares", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "theorem", "id": "Semantics.Extensions.NKCoupling.mirror_zero_midway", "name": "mirror_zero_midway", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "theorem", "id": "Semantics.Extensions.NKCoupling.couplingScore_bounded", "name": "couplingScore_bounded", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "theorem", "id": "Semantics.Extensions.NKCoupling.mondominance", "name": "mondominance", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.nearestSquares", "name": "nearestSquares", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.hyperbolaIndex", "name": "hyperbolaIndex", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.mirrorIndex", "name": "mirrorIndex", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.couplingScore", "name": "couplingScore", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.isNKResonance", "name": "isNKResonance", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.spaceCreationRate", "name": "spaceCreationRate", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.isMONDRegime", "name": "isMONDRegime", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.nodeToNKCoord", "name": "nodeToNKCoord", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.gossipEnergyToCarrier", "name": "gossipEnergyToCarrier", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "def", "id": "Semantics.Extensions.NKCoupling.coherenceToCharacter", "name": "coherenceToCharacter", "module": "Semantics.Extensions.NKCoupling" }, { "kind": "module", "id": "Semantics.Extensions.NeuralFieldDynamics", "name": "NeuralFieldDynamics", "path": "Semantics/Extensions/NeuralFieldDynamics.lean", "namespace": "Semantics.Biology.NeuralField", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NeuralFieldDynamics.lean \u2014 Laws of continuous neural population activity. This module formalizes the laws of large-scale cortical dynamics: 1. Mean-Field: Shun-ichi Amari's neural field equations. 2. K", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.Extensions.NeuralFieldDynamics.neuralPotentialStep", "name": "neuralPotentialStep", "module": "Semantics.Extensions.NeuralFieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuralFieldDynamics.mexicanHatKernel", "name": "mexicanHatKernel", "module": "Semantics.Extensions.NeuralFieldDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuralFieldDynamics.sigmoidActivation", "name": "sigmoidActivation", "module": "Semantics.Extensions.NeuralFieldDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NeuralTrophicSwimmingDynamics", "name": "NeuralTrophicSwimmingDynamics", "path": "Semantics/Extensions/NeuralTrophicSwimmingDynamics.lean", "namespace": "Semantics.Biology.Dynamics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NeuralTrophicSwimmingDynamics.lean \u2014 Laws of synaptic plasticity, trophic transfer, and reactive swimming. This module formalizes the laws of neural timing, ecological energy flow, and fluid locomotion", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.Extensions.NeuralTrophicSwimmingDynamics.stdpWeightDelta", "name": "stdpWeightDelta", "module": "Semantics.Extensions.NeuralTrophicSwimmingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuralTrophicSwimmingDynamics.nextTrophicProduction", "name": "nextTrophicProduction", "module": "Semantics.Extensions.NeuralTrophicSwimmingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuralTrophicSwimmingDynamics.slenderBodyReactiveForce", "name": "slenderBodyReactiveForce", "module": "Semantics.Extensions.NeuralTrophicSwimmingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NeuroEmergentLaws", "name": "NeuroEmergentLaws", "path": "Semantics/Extensions/NeuroEmergentLaws.lean", "namespace": "Semantics.Biology.Emergence", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NeuroEmergentLaws.lean \u2014 Laws of neural learning, memory, and critical emergence. This module formalizes the laws of neural adaptation and collective organization: 1. Learning: Hebb's Law and Oja's Rul", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 65 }, { "kind": "def", "id": "Semantics.Extensions.NeuroEmergentLaws.hebbianDelta", "name": "hebbianDelta", "module": "Semantics.Extensions.NeuroEmergentLaws" }, { "kind": "def", "id": "Semantics.Extensions.NeuroEmergentLaws.ojaDelta", "name": "ojaDelta", "module": "Semantics.Extensions.NeuroEmergentLaws" }, { "kind": "def", "id": "Semantics.Extensions.NeuroEmergentLaws.hopfieldEnergy", "name": "hopfieldEnergy", "module": "Semantics.Extensions.NeuroEmergentLaws" }, { "kind": "def", "id": "Semantics.Extensions.NeuroEmergentLaws.avalancheProbability", "name": "avalancheProbability", "module": "Semantics.Extensions.NeuroEmergentLaws" }, { "kind": "module", "id": "Semantics.Extensions.NeuroInformationDynamics", "name": "NeuroInformationDynamics", "path": "Semantics/Extensions/NeuroInformationDynamics.lean", "namespace": "Semantics.Biology.NeuroInfo", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NeuroInformationDynamics.lean \u2014 Laws of information processing and perception scaling. This module formalizes the informational and psychophysical laws of neural systems: 1. Information Theory: The Inf", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 60 }, { "kind": "def", "id": "Semantics.Extensions.NeuroInformationDynamics.informationBottleneckLagrangian", "name": "informationBottleneckLagrangian", "module": "Semantics.Extensions.NeuroInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuroInformationDynamics.predictionError", "name": "predictionError", "module": "Semantics.Extensions.NeuroInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuroInformationDynamics.representationUpdate", "name": "representationUpdate", "module": "Semantics.Extensions.NeuroInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuroInformationDynamics.perceivedSensationLog", "name": "perceivedSensationLog", "module": "Semantics.Extensions.NeuroInformationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NeuroInformationDynamics.perceivedSensationPower", "name": "perceivedSensationPower", "module": "Semantics.Extensions.NeuroInformationDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NicheAgingDynamics", "name": "NicheAgingDynamics", "path": "Semantics/Extensions/NicheAgingDynamics.lean", "namespace": "Semantics.Biology.NicheAging", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NicheAgingDynamics.lean \u2014 Laws of resource competition, aging correlations, and mortality plateaus. This module formalizes the laws of niche survival and the temporal limits of life: 1. Competition: Ti", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Extensions.NicheAgingDynamics.resourceThresholdRStar", "name": "resourceThresholdRStar", "module": "Semantics.Extensions.NicheAgingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheAgingDynamics.strehlerMildvanCorrelation", "name": "strehlerMildvanCorrelation", "module": "Semantics.Extensions.NicheAgingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheAgingDynamics.vitalityDecay", "name": "vitalityDecay", "module": "Semantics.Extensions.NicheAgingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheAgingDynamics.plateauMortality", "name": "plateauMortality", "module": "Semantics.Extensions.NicheAgingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NicheIonDynamics", "name": "NicheIonDynamics", "path": "Semantics/Extensions/NicheIonDynamics.lean", "namespace": "Semantics.Biology.NicheTransport", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NicheIonDynamics.lean \u2014 Laws of environmental niches, ion transport, and species richness. This module formalizes the laws of ecological persistence and physical transport: 1. Ecology: Hutchinson's n-d", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Extensions.NicheIonDynamics.isWithinNiche", "name": "isWithinNiche", "module": "Semantics.Extensions.NicheIonDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheIonDynamics.nernstPlanckFlux", "name": "nernstPlanckFlux", "module": "Semantics.Extensions.NicheIonDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheIonDynamics.speciesRichnessLog", "name": "speciesRichnessLog", "module": "Semantics.Extensions.NicheIonDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NicheSpecializationDynamics", "name": "NicheSpecializationDynamics", "path": "Semantics/Extensions/NicheSpecializationDynamics.lean", "namespace": "Semantics.Biology.Specialized", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NicheSpecializationDynamics.lean \u2014 Specialized laws of aging, oncology, and botany. This module formalizes specialized biological frontiers: 1. Gerontology: Gompertz-Makeham law of mortality. 2. Oncolo", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 0, "line_count": 87 }, { "kind": "def", "id": "Semantics.Extensions.NicheSpecializationDynamics.mortalityRate", "name": "mortalityRate", "module": "Semantics.Extensions.NicheSpecializationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheSpecializationDynamics.gatenbyUpdate", "name": "gatenbyUpdate", "module": "Semantics.Extensions.NicheSpecializationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheSpecializationDynamics.izhikevichStep", "name": "izhikevichStep", "module": "Semantics.Extensions.NicheSpecializationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheSpecializationDynamics.kuramotoSynchrony", "name": "kuramotoSynchrony", "module": "Semantics.Extensions.NicheSpecializationDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NicheSpecializationDynamics.vascularAreaMerge", "name": "vascularAreaMerge", "module": "Semantics.Extensions.NicheSpecializationDynamics" }, { "kind": "module", "id": "Semantics.Extensions.NutrientQuotaDynamics", "name": "NutrientQuotaDynamics", "path": "Semantics/Extensions/NutrientQuotaDynamics.lean", "namespace": "Semantics.Biology.NutrientQuota", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NutrientQuotaDynamics.lean \u2014 Laws of internal nutrient storage and cell composition. This module formalizes the laws governing nutrient-limited growth and storage: 1. Storage: Michael Droop's equation ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Extensions.NutrientQuotaDynamics.droopGrowthRate", "name": "droopGrowthRate", "module": "Semantics.Extensions.NutrientQuotaDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NutrientQuotaDynamics.cellQuotaInvariant", "name": "cellQuotaInvariant", "module": "Semantics.Extensions.NutrientQuotaDynamics" }, { "kind": "def", "id": "Semantics.Extensions.NutrientQuotaDynamics.quotaUpdateStep", "name": "quotaUpdateStep", "module": "Semantics.Extensions.NutrientQuotaDynamics" }, { "kind": "module", "id": "Semantics.Extensions.OceanicBiomassScalingLaws", "name": "OceanicBiomassScalingLaws", "path": "Semantics/Extensions/OceanicBiomassScalingLaws.lean", "namespace": "Semantics.Biology.Marine.Scaling", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team OceanicBiomassScalingLaws.lean \u2014 Laws of biomass distribution and productivity in the ocean. This module formalizes the macro-scale laws of marine life distribution: 1. Biomass: Sheldon's Spectrum (Con", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.OceanicBiomassScalingLaws.sheldonBiomassConstant", "name": "sheldonBiomassConstant", "module": "Semantics.Extensions.OceanicBiomassScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.OceanicBiomassScalingLaws.numericalAbundance", "name": "numericalAbundance", "module": "Semantics.Extensions.OceanicBiomassScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.OceanicBiomassScalingLaws.productionRateScale", "name": "productionRateScale", "module": "Semantics.Extensions.OceanicBiomassScalingLaws" }, { "kind": "def", "id": "Semantics.Extensions.OceanicBiomassScalingLaws.energyUseInvariant", "name": "energyUseInvariant", "module": "Semantics.Extensions.OceanicBiomassScalingLaws" }, { "kind": "module", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics", "name": "PhotosynthesisHydraulicDynamics", "path": "Semantics/Extensions/PhotosynthesisHydraulicDynamics.lean", "namespace": "Semantics.Biology.Photosynthesis", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PhotosynthesisHydraulicDynamics.lean \u2014 Laws of carbon assimilation, stomatal control, and WUE. This module formalizes the laws of plant gas exchange and energetics: 1. Assimilation: The FvCB model for ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 75 }, { "kind": "def", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics.rubiscoLimitedRate", "name": "rubiscoLimitedRate", "module": "Semantics.Extensions.PhotosynthesisHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics.rubpRegenRate", "name": "rubpRegenRate", "module": "Semantics.Extensions.PhotosynthesisHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics.stomatalConductance", "name": "stomatalConductance", "module": "Semantics.Extensions.PhotosynthesisHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics.intrinsicWUE", "name": "intrinsicWUE", "module": "Semantics.Extensions.PhotosynthesisHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PhotosynthesisHydraulicDynamics.lightResponseRate", "name": "lightResponseRate", "module": "Semantics.Extensions.PhotosynthesisHydraulicDynamics" }, { "kind": "module", "id": "Semantics.Extensions.PhysiologicalInvariants", "name": "PhysiologicalInvariants", "path": "Semantics/Extensions/PhysiologicalInvariants.lean", "namespace": "Semantics.Biology.Physiology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PhysiologicalInvariants.lean \u2014 Laws of cardiovascular flow, cardiac output, and scaling. This module formalizes the biophysical laws of animal physiology: 1. Cardiovascular: Poiseuille's flow and Starl", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 66 }, { "kind": "def", "id": "Semantics.Extensions.PhysiologicalInvariants.poiseuilleFlow", "name": "poiseuilleFlow", "module": "Semantics.Extensions.PhysiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.PhysiologicalInvariants.strokeVolume", "name": "strokeVolume", "module": "Semantics.Extensions.PhysiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.PhysiologicalInvariants.cardiacOutput", "name": "cardiacOutput", "module": "Semantics.Extensions.PhysiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.PhysiologicalInvariants.savRatio", "name": "savRatio", "module": "Semantics.Extensions.PhysiologicalInvariants" }, { "kind": "def", "id": "Semantics.Extensions.PhysiologicalInvariants.copeSizeGrowth", "name": "copeSizeGrowth", "module": "Semantics.Extensions.PhysiologicalInvariants" }, { "kind": "module", "id": "Semantics.Extensions.PlanetaryNeuroTopology", "name": "PlanetaryNeuroTopology", "path": "Semantics/Extensions/PlanetaryNeuroTopology.lean", "namespace": "Semantics.Biology.Topology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PlanetaryNeuroTopology.lean \u2014 Multi-scale topological regulation of life. This module formalizes the laws of biological homeostasis and structural complexity, from the planetary Daisyworld feedback to ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 76 }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.daisyGrowthRate", "name": "daisyGrowthRate", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.daisyPopulationStep", "name": "daisyPopulationStep", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.metabolicRate", "name": "metabolicRate", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.lifespanScaling", "name": "lifespanScaling", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.neuralCavityStability", "name": "neuralCavityStability", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "def", "id": "Semantics.Extensions.PlanetaryNeuroTopology.reproductiveEffort", "name": "reproductiveEffort", "module": "Semantics.Extensions.PlanetaryNeuroTopology" }, { "kind": "module", "id": "Semantics.Extensions.PlantHydraulicDynamics", "name": "PlantHydraulicDynamics", "path": "Semantics/Extensions/PlantHydraulicDynamics.lean", "namespace": "Semantics.Biology.PlantHydraulics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PlantHydraulicDynamics.lean \u2014 Laws of stem architecture, leaf support, and xylem cavitation. This module formalizes the laws of botanical structural and hydraulic function: 1. Architecture: Corner's ru", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.PlantHydraulicDynamics.stemLeafCoordination", "name": "stemLeafCoordination", "module": "Semantics.Extensions.PlantHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PlantHydraulicDynamics.pipeAreaProportionality", "name": "pipeAreaProportionality", "module": "Semantics.Extensions.PlantHydraulicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PlantHydraulicDynamics.percentageConductivityLoss", "name": "percentageConductivityLoss", "module": "Semantics.Extensions.PlantHydraulicDynamics" }, { "kind": "module", "id": "Semantics.Extensions.PlantPhyllotaxisLaws", "name": "PlantPhyllotaxisLaws", "path": "Semantics/Extensions/PlantPhyllotaxisLaws.lean", "namespace": "Semantics.Biology.Phyllotaxis", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PlantPhyllotaxisLaws.lean \u2014 Laws of botanical spiral patterns and optimal packing. This module formalizes the laws of plant organ arrangement: 1. Vogel: The spiral phyllotaxis model for florets and see", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 59 }, { "kind": "def", "id": "Semantics.Extensions.PlantPhyllotaxisLaws.vogelAngle", "name": "vogelAngle", "module": "Semantics.Extensions.PlantPhyllotaxisLaws" }, { "kind": "def", "id": "Semantics.Extensions.PlantPhyllotaxisLaws.vogelRadius", "name": "vogelRadius", "module": "Semantics.Extensions.PlantPhyllotaxisLaws" }, { "kind": "def", "id": "Semantics.Extensions.PlantPhyllotaxisLaws.goldenRatio", "name": "goldenRatio", "module": "Semantics.Extensions.PlantPhyllotaxisLaws" }, { "kind": "def", "id": "Semantics.Extensions.PlantPhyllotaxisLaws.goldenAngleDeg", "name": "goldenAngleDeg", "module": "Semantics.Extensions.PlantPhyllotaxisLaws" }, { "kind": "def", "id": "Semantics.Extensions.PlantPhyllotaxisLaws.isPositionOptimal", "name": "isPositionOptimal", "module": "Semantics.Extensions.PlantPhyllotaxisLaws" }, { "kind": "module", "id": "Semantics.Extensions.PopulationChaosDynamics", "name": "PopulationChaosDynamics", "path": "Semantics/Extensions/PopulationChaosDynamics.lean", "namespace": "Semantics.Biology.Population", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team PopulationChaosDynamics.lean \u2014 Laws of discrete chaos, stability, and lifespan limits. This module formalizes the laws of population behavior and longevity: 1. Chaos: Robert May's Logistic Map and bifu", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 54 }, { "kind": "def", "id": "Semantics.Extensions.PopulationChaosDynamics.logisticMap", "name": "logisticMap", "module": "Semantics.Extensions.PopulationChaosDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PopulationChaosDynamics.lotkaStabilityScore", "name": "lotkaStabilityScore", "module": "Semantics.Extensions.PopulationChaosDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PopulationChaosDynamics.lifePersistenceRatio", "name": "lifePersistenceRatio", "module": "Semantics.Extensions.PopulationChaosDynamics" }, { "kind": "def", "id": "Semantics.Extensions.PopulationChaosDynamics.survivalProbability", "name": "survivalProbability", "module": "Semantics.Extensions.PopulationChaosDynamics" }, { "kind": "module", "id": "Semantics.Extensions.QuantumSyntheticBio", "name": "QuantumSyntheticBio", "path": "Semantics/Extensions/QuantumSyntheticBio.lean", "namespace": "Semantics.Biology.QuantumSynthetic", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team QuantumSyntheticBio.lean \u2014 Quantum biological laws and synthetic genetic logic. This module formalizes the extreme scales of biological information: 1. Quantum scale: Spin dynamics, exciton transfer, a", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 0, "line_count": 85 }, { "kind": "def", "id": "Semantics.Extensions.QuantumSyntheticBio.radicalPairRecombination", "name": "radicalPairRecombination", "module": "Semantics.Extensions.QuantumSyntheticBio" }, { "kind": "def", "id": "Semantics.Extensions.QuantumSyntheticBio.excitonCoupling", "name": "excitonCoupling", "module": "Semantics.Extensions.QuantumSyntheticBio" }, { "kind": "def", "id": "Semantics.Extensions.QuantumSyntheticBio.protonTunnelingRate", "name": "protonTunnelingRate", "module": "Semantics.Extensions.QuantumSyntheticBio" }, { "kind": "def", "id": "Semantics.Extensions.QuantumSyntheticBio.toggleStep", "name": "toggleStep", "module": "Semantics.Extensions.QuantumSyntheticBio" }, { "kind": "def", "id": "Semantics.Extensions.QuantumSyntheticBio.coherentFFL", "name": "coherentFFL", "module": "Semantics.Extensions.QuantumSyntheticBio" }, { "kind": "module", "id": "Semantics.Extensions.ReliabilityStochasticDynamics", "name": "ReliabilityStochasticDynamics", "path": "Semantics/Extensions/ReliabilityStochasticDynamics.lean", "namespace": "Semantics.Biology.Stochastic", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ReliabilityStochasticDynamics.lean \u2014 Laws of aging redundancy and stochastic simulation. This module formalizes the laws of system reliability and molecular noise: 1. Aging: Reliability Theory (n-redun", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Extensions.ReliabilityStochasticDynamics.systemSurvivalProb", "name": "systemSurvivalProb", "module": "Semantics.Extensions.ReliabilityStochasticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ReliabilityStochasticDynamics.reactionPropensity", "name": "reactionPropensity", "module": "Semantics.Extensions.ReliabilityStochasticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ReliabilityStochasticDynamics.stochasticTimeStep", "name": "stochasticTimeStep", "module": "Semantics.Extensions.ReliabilityStochasticDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ReliabilityStochasticDynamics.masterEquationUpdate", "name": "masterEquationUpdate", "module": "Semantics.Extensions.ReliabilityStochasticDynamics" }, { "kind": "module", "id": "Semantics.Extensions.ResilienceTippingDynamics", "name": "ResilienceTippingDynamics", "path": "Semantics/Extensions/ResilienceTippingDynamics.lean", "namespace": "Semantics.Biology.Resilience", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ResilienceTippingDynamics.lean \u2014 Laws of critical slowing down and ecological tipping points. This module formalizes the laws of biological resilience and phase transitions: 1. Early Warning: Critical ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Extensions.ResilienceTippingDynamics.autocorrelationProxy", "name": "autocorrelationProxy", "module": "Semantics.Extensions.ResilienceTippingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ResilienceTippingDynamics.varianceIncrease", "name": "varianceIncrease", "module": "Semantics.Extensions.ResilienceTippingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ResilienceTippingDynamics.recoveryRate", "name": "recoveryRate", "module": "Semantics.Extensions.ResilienceTippingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ResilienceTippingDynamics.basinResistance", "name": "basinResistance", "module": "Semantics.Extensions.ResilienceTippingDynamics" }, { "kind": "def", "id": "Semantics.Extensions.ResilienceTippingDynamics.basinLatitude", "name": "basinLatitude", "module": "Semantics.Extensions.ResilienceTippingDynamics" }, { "kind": "module", "id": "Semantics.Extensions.RhythmicStructuralDynamics", "name": "RhythmicStructuralDynamics", "path": "Semantics/Extensions/RhythmicStructuralDynamics.lean", "namespace": "Semantics.Biology.RhythmStructure", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team RhythmicStructuralDynamics.lean \u2014 Laws of limit cycles, phase singularities, and self-assembly. This module formalizes the topological and thermodynamic laws of biological time and form: 1. Rhythms: Po", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 60 }, { "kind": "def", "id": "Semantics.Extensions.RhythmicStructuralDynamics.isLimitCycleCaptured", "name": "isLimitCycleCaptured", "module": "Semantics.Extensions.RhythmicStructuralDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RhythmicStructuralDynamics.oscillatorAmplitude", "name": "oscillatorAmplitude", "module": "Semantics.Extensions.RhythmicStructuralDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RhythmicStructuralDynamics.selfAssemblyGibbs", "name": "selfAssemblyGibbs", "module": "Semantics.Extensions.RhythmicStructuralDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RhythmicStructuralDynamics.isAssembled", "name": "isAssembled", "module": "Semantics.Extensions.RhythmicStructuralDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RhythmicStructuralDynamics.tileAssemblyStrength", "name": "tileAssemblyStrength", "module": "Semantics.Extensions.RhythmicStructuralDynamics" }, { "kind": "module", "id": "Semantics.Extensions.RootNutrientDynamics", "name": "RootNutrientDynamics", "path": "Semantics/Extensions/RootNutrientDynamics.lean", "namespace": "Semantics.Biology.Roots", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team RootNutrientDynamics.lean \u2014 Laws of root uptake, nutrient depletion, and fractal branching. This module formalizes the laws of plant-soil interactions: 1. Transport: The Nye-Tinker-Barber model for nut", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.Extensions.RootNutrientDynamics.nutrientDepletionStep", "name": "nutrientDepletionStep", "module": "Semantics.Extensions.RootNutrientDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RootNutrientDynamics.rootSurfaceFlux", "name": "rootSurfaceFlux", "module": "Semantics.Extensions.RootNutrientDynamics" }, { "kind": "def", "id": "Semantics.Extensions.RootNutrientDynamics.rootComplexityMetric", "name": "rootComplexityMetric", "module": "Semantics.Extensions.RootNutrientDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SleepChronobiologyDynamics", "name": "SleepChronobiologyDynamics", "path": "Semantics/Extensions/SleepChronobiologyDynamics.lean", "namespace": "Semantics.Biology.Chronobiology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SleepChronobiologyDynamics.lean \u2014 Laws of sleep regulation and circadian entrainment. This module formalizes the laws of biological timekeeping and sleep homeostasis: 1. Homeostasis: Borb\u00e9ly's Process ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.SleepChronobiologyDynamics.sleepPressureStep", "name": "sleepPressureStep", "module": "Semantics.Extensions.SleepChronobiologyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SleepChronobiologyDynamics.isSleepOnsetReached", "name": "isSleepOnsetReached", "module": "Semantics.Extensions.SleepChronobiologyDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SleepChronobiologyDynamics.freeRunningPeriod", "name": "freeRunningPeriod", "module": "Semantics.Extensions.SleepChronobiologyDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SocialCognitiveDynamics", "name": "SocialCognitiveDynamics", "path": "Semantics/Extensions/SocialCognitiveDynamics.lean", "namespace": "Semantics.Biology.SocialCognition", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SocialCognitiveDynamics.lean \u2014 Laws of social brain scaling and information capacity. This module formalizes the informational laws of social groups and cognitive limits: 1. Social: Dunbar's Number and", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Extensions.SocialCognitiveDynamics.dunbarGroupSize", "name": "dunbarGroupSize", "module": "Semantics.Extensions.SocialCognitiveDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialCognitiveDynamics.socialMaintenanceTime", "name": "socialMaintenanceTime", "module": "Semantics.Extensions.SocialCognitiveDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialCognitiveDynamics.bilateralRelationshipCount", "name": "bilateralRelationshipCount", "module": "Semantics.Extensions.SocialCognitiveDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialCognitiveDynamics.isSociallyStable", "name": "isSociallyStable", "module": "Semantics.Extensions.SocialCognitiveDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialCognitiveDynamics.brainScalingLog", "name": "brainScalingLog", "module": "Semantics.Extensions.SocialCognitiveDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SocialMotionVisionDynamics", "name": "SocialMotionVisionDynamics", "path": "Semantics/Extensions/SocialMotionVisionDynamics.lean", "namespace": "Semantics.Biology.SocialVision", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SocialMotionVisionDynamics.lean \u2014 Laws of motion detection and collective pheromone optimization. This module formalizes the laws of biological vision and group intelligence: 1. Motion: The Hassenstein", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 52 }, { "kind": "def", "id": "Semantics.Extensions.SocialMotionVisionDynamics.reichardtMotionSignal", "name": "reichardtMotionSignal", "module": "Semantics.Extensions.SocialMotionVisionDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialMotionVisionDynamics.acoTransitionProb", "name": "acoTransitionProb", "module": "Semantics.Extensions.SocialMotionVisionDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SocialMotionVisionDynamics.pheromoneUpdate", "name": "pheromoneUpdate", "module": "Semantics.Extensions.SocialMotionVisionDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SoftTissuePressureDynamics", "name": "SoftTissuePressureDynamics", "path": "Semantics/Extensions/SoftTissuePressureDynamics.lean", "namespace": "Semantics.Biology.Pressure", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SoftTissuePressureDynamics.lean \u2014 Laws of exponential elasticity and hollow-organ pressure. This module formalizes the laws of biomechanics and organ stability: 1. Elasticity: Fung's law for exponentia", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.SoftTissuePressureDynamics.fungSoftTissueStress", "name": "fungSoftTissueStress", "module": "Semantics.Extensions.SoftTissuePressureDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SoftTissuePressureDynamics.alveolarDistendingPressure", "name": "alveolarDistendingPressure", "module": "Semantics.Extensions.SoftTissuePressureDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SoftTissuePressureDynamics.ventricularWallStress", "name": "ventricularWallStress", "module": "Semantics.Extensions.SoftTissuePressureDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SoilFungalDynamics", "name": "SoilFungalDynamics", "path": "Semantics/Extensions/SoilFungalDynamics.lean", "namespace": "Semantics.Biology.Subterranean", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SoilFungalDynamics.lean \u2014 Laws of soil chemistry, hyphal growth, and global growth constraints. This module formalizes the laws of subterranean biology and nutrient exchange: 1. 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The Warden modulates phase \u03c6(t) to maintain solitons at the codimensio", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 6, "def_count": 16, "struct_count": 3, "inductive_count": 1, "line_count": 468 }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.codim2_stability", "name": "codim2_stability", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.soliton_is_vortex", "name": "soliton_is_vortex", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.error_decreases_with_amplitude", "name": "error_decreases_with_amplitude", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.lle_manley_rowe_conservation", "name": "lle_manley_rowe_conservation", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.soliton_energy_linear_in_amplitude", "name": "soliton_energy_linear_in_amplitude", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "theorem", "id": "Semantics.Extensions.SolitonEngine.cat_qubit_more_protected", "name": "cat_qubit_more_protected", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.defaultParams", "name": "defaultParams", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.solitonAnsatz", "name": "solitonAnsatz", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.solitonEnergy", "name": "solitonEnergy", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.bifurcationParameter", "name": "bifurcationParameter", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.CODIM2_CRITICAL", "name": "CODIM2_CRITICAL", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.atCodim2Bifurcation", "name": "atCodim2Bifurcation", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.wardenPhaseUpdate", "name": "wardenPhaseUpdate", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.solitonCoherence", "name": "solitonCoherence", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.countPhaseSingularities", "name": "countPhaseSingularities", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.bitFlipErrorRate", "name": "bitFlipErrorRate", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.criticalAmplitude", "name": "criticalAmplitude", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.criticalBitFlipRate", "name": "criticalBitFlipRate", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.catQubitFromSolitonCount", "name": "catQubitFromSolitonCount", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.catBitFlipRate", "name": "catBitFlipRate", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.solitonToTernary", "name": "solitonToTernary", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "def", "id": "Semantics.Extensions.SolitonEngine.solitonSigma", "name": "solitonSigma", "module": "Semantics.Extensions.SolitonEngine" }, { "kind": "module", "id": "Semantics.Extensions.StoichiometricMetabolicDynamics", "name": "StoichiometricMetabolicDynamics", "path": "Semantics/Extensions/StoichiometricMetabolicDynamics.lean", "namespace": "Semantics.Biology.StoicMetab", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team StoichiometricMetabolicDynamics.lean \u2014 Laws of nutrient homeostasis and population metabolic scaling. This module formalizes the laws of chemical regulation and ecosystem energy: 1. Homeostasis: Sterne", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.Extensions.StoichiometricMetabolicDynamics.homeostaticRatio", "name": "homeostaticRatio", "module": "Semantics.Extensions.StoichiometricMetabolicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.StoichiometricMetabolicDynamics.populationDensityScale", "name": "populationDensityScale", "module": "Semantics.Extensions.StoichiometricMetabolicDynamics" }, { "kind": "def", "id": "Semantics.Extensions.StoichiometricMetabolicDynamics.unifiedMetabolicRate", "name": "unifiedMetabolicRate", "module": "Semantics.Extensions.StoichiometricMetabolicDynamics" }, { "kind": "module", "id": "Semantics.Extensions.SystemicBioDynamics", "name": "SystemicBioDynamics", "path": "Semantics/Extensions/SystemicBioDynamics.lean", "namespace": "Semantics.Biology.Systemic", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SystemicBioDynamics.lean \u2014 Laws of immunology, chronobiology, and biomechanics. This module formalizes the systemic-scale laws of biological organisms: 1. Immunology: Clonal selection and viral kinetic", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 3, "inductive_count": 0, "line_count": 95 }, { "kind": "def", "id": "Semantics.Extensions.SystemicBioDynamics.clonalExpansionStep", "name": "clonalExpansionStep", "module": "Semantics.Extensions.SystemicBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SystemicBioDynamics.viralUpdate", "name": "viralUpdate", "module": "Semantics.Extensions.SystemicBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SystemicBioDynamics.vanDerPolStep", "name": "vanDerPolStep", "module": "Semantics.Extensions.SystemicBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SystemicBioDynamics.muscleVelocity", "name": "muscleVelocity", "module": "Semantics.Extensions.SystemicBioDynamics" }, { "kind": "def", "id": "Semantics.Extensions.SystemicBioDynamics.lorenzStep", "name": "lorenzStep", "module": "Semantics.Extensions.SystemicBioDynamics" }, { "kind": "module", "id": "Semantics.Extensions.VisionColorDynamics", "name": "VisionColorDynamics", "path": "Semantics/Extensions/VisionColorDynamics.lean", "namespace": "Semantics.Biology.Vision", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team VisionColorDynamics.lean \u2014 Laws of color perception, edge enhancement, and constancy. This module formalizes the informational and neuro-computational laws of vision: 1. Opponent: Hering's opponent pro", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 2, "inductive_count": 0, "line_count": 76 }, { "kind": "def", "id": "Semantics.Extensions.VisionColorDynamics.transformLMStoOpponent", "name": "transformLMStoOpponent", "module": "Semantics.Extensions.VisionColorDynamics" }, { "kind": "def", "id": "Semantics.Extensions.VisionColorDynamics.retinexDesignator", "name": "retinexDesignator", "module": "Semantics.Extensions.VisionColorDynamics" }, { "kind": "def", "id": "Semantics.Extensions.VisionColorDynamics.inhibitedResponse", "name": "inhibitedResponse", "module": "Semantics.Extensions.VisionColorDynamics" }, { "kind": "def", "id": "Semantics.Extensions.VisionColorDynamics.cielabMapping", "name": "cielabMapping", "module": "Semantics.Extensions.VisionColorDynamics" }, { "kind": "module", "id": "Semantics.Extensions.VocalProductionLaws", "name": "VocalProductionLaws", "path": "Semantics/Extensions/VocalProductionLaws.lean", "namespace": "Semantics.Biology.Vocalization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team VocalProductionLaws.lean \u2014 Laws of phonation, vocal tract filtering, and pitch scaling. This module formalizes the acoustic and physical laws of animal vocalization: 1. Phonation: Bernoulli's principle", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "def", "id": "Semantics.Extensions.VocalProductionLaws.glottalPressure", "name": "glottalPressure", "module": "Semantics.Extensions.VocalProductionLaws" }, { "kind": "def", "id": "Semantics.Extensions.VocalProductionLaws.vocalOutputSpectrum", "name": "vocalOutputSpectrum", "module": "Semantics.Extensions.VocalProductionLaws" }, { "kind": "def", "id": "Semantics.Extensions.VocalProductionLaws.fundamentalFrequencyScale", "name": "fundamentalFrequencyScale", "module": "Semantics.Extensions.VocalProductionLaws" }, { "kind": "def", "id": "Semantics.Extensions.VocalProductionLaws.vocalTractLengthScale", "name": "vocalTractLengthScale", "module": "Semantics.Extensions.VocalProductionLaws" }, { "kind": "module", "id": "Semantics.ExternalConnectors", "name": "ExternalConnectors", "path": "Semantics/ExternalConnectors.lean", "namespace": "Semantics.ExternalConnectors", "doc": "inductive ExternalConnector where | aceKnowledgeGraph | airtable | consensus | github | googleDrive | notion | spotify deriving Repr, DecidableEq, BEq /-- Operation types for maximum functionality", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 21, "struct_count": 18, "inductive_count": 3, "line_count": 302 }, { "kind": "def", "id": "Semantics.ExternalConnectors.adaptiveOperationSelector", "name": "adaptiveOperationSelector", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.executeOperation", "name": "executeOperation", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.aceQuery", "name": "aceQuery", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.aceCreateNode", "name": "aceCreateNode", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.airtableQuery", "name": "airtableQuery", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.airtableCreate", "name": "airtableCreate", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.consensusQuery", "name": "consensusQuery", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.githubGetRepo", "name": "githubGetRepo", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.githubGetIssue", "name": "githubGetIssue", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.githubSearch", "name": "githubSearch", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.driveGetFile", "name": "driveGetFile", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.driveCreateFile", "name": "driveCreateFile", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.notionGetPage", "name": "notionGetPage", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.notionCreatePage", "name": "notionCreatePage", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.notionQueryDatabase", "name": "notionQueryDatabase", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.spotifyGetTrack", "name": "spotifyGetTrack", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.spotifySearch", "name": "spotifySearch", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.spotifyCreatePlaylist", "name": "spotifyCreatePlaylist", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.listConnectors", "name": "listConnectors", "module": "Semantics.ExternalConnectors" }, { "kind": "def", "id": "Semantics.ExternalConnectors.maxOperationsForConnector", "name": "maxOperationsForConnector", "module": "Semantics.ExternalConnectors" }, { "kind": "module", "id": "Semantics.F01_Q16_16_FixedPoint", "name": "F01_Q16_16_FixedPoint", "path": "Semantics/F01_Q16_16_FixedPoint.lean", "namespace": "Q16_16", "doc": "F01-F12 Foundation: Q16.16 Fixed-Point Arithmetic Prover: Goedel-Prover-V2 + bf4prover Status: Awaiting theorem proofs Issues being fixed: 1. Q32.32 \u2192 Q16.16 (compliance with Research Stack standard) 2. Totality theorems for all operations 3. Convergence proof (no arbitrary damping) 4. Wolfram Alph", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 27, "def_count": 19, "struct_count": 1, "inductive_count": 0, "line_count": 478 }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.add_total", "name": "add_total", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.mul_total", "name": "mul_total", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.div_total", "name": "div_total", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.round_valid", "name": "round_valid", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.mul_no_overflow", "name": "mul_no_overflow", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_deterministic", "name": "E_0_deterministic", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_bounds", "name": "E_0_bounds", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.mul_fromInt_one", "name": "mul_fromInt_one", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_encode_eq_round", "name": "E_0_encode_eq_round", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.Array_map_congr", "name": "Array_map_congr", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.toInt_nonneg_imp_ge_zero", "name": "toInt_nonneg_imp_ge_zero", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.raw_nonneg", "name": "raw_nonneg", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.raw_bound", "name": "raw_bound", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.bmod_self", "name": "bmod_self", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.roundtrip", "name": "roundtrip", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.round_int_idempotent", "name": "round_int_idempotent", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.half_div_scale", "name": "half_div_scale", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.round_nonneg_idempotent", "name": "round_nonneg_idempotent", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_encode_nonneg", "name": "E_0_encode_nonneg", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_encode_bound", "name": "E_0_encode_bound", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_encode_idempotent", "name": "E_0_encode_idempotent", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.N_0_nonneg", "name": "N_0_nonneg", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.N_0_bound", "name": "N_0_bound", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.stepExact_nonneg_bound", "name": "stepExact_nonneg_bound", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.eigensolid_stabilize", "name": "eigensolid_stabilize", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.receipt_invertible", "name": "receipt_invertible", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "theorem", "id": "Semantics.F01_Q16_16_FixedPoint.eigensolid_encode_decode", "name": "eigensolid_encode_decode", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.Q16_16", "name": "Q16_16", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.fromInt", "name": "fromInt", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.ofFloat", "name": "ofFloat", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.add", "name": "add", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.sub", "name": "sub", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.mul", "name": "mul", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.div", "name": "div", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.round", "name": "round", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.floor", "name": "floor", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.abs", "name": "abs", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.N_0", "name": "N_0", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.E_0_encode", "name": "E_0_encode", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.TAU", "name": "TAU", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.maxDiff", "name": "maxDiff", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.isConverged", "name": "isConverged", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.stepExact", "name": "stepExact", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.iterate", "name": "iterate", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "def", "id": "Semantics.F01_Q16_16_FixedPoint.eigensolidReceipt", "name": "eigensolidReceipt", "module": "Semantics.F01_Q16_16_FixedPoint" }, { "kind": "mathlib", "id": "Mathlib.Data.Int.Basic", "name": "Mathlib.Data.Int.Basic" }, { "kind": "module", "id": "Semantics.FAMM", "name": "FAMM", "path": "Semantics/FAMM.lean", "namespace": "Semantics", "doc": "FAMM is a specialized memory type that uses delay lines as memory storage. The \"frustrated\" aspect refers to the competing delay constraints that cannot simultaneously satisfy all timing requirements, analogous to frustrated systems. Key properties: Stores data in delay lines with Q16.16 timing Tra", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 8, "inductive_count": 1, "line_count": 232 }, { "kind": "def", "id": "Semantics.FAMM.defaultFAMMCell", "name": "defaultFAMMCell", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.mkFAMMBank", "name": "mkFAMMBank", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammBind", "name": "fammBind", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammRead", "name": "fammRead", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.eigenmass", "name": "eigenmass", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammWrite", "name": "fammWrite", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammWriteEigenmass", "name": "fammWriteEigenmass", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammAdjustDelay", "name": "fammAdjustDelay", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammPruneCell", "name": "fammPruneCell", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammThermalCheck", "name": "fammThermalCheck", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammMetadataCollapse", "name": "fammMetadataCollapse", "module": "Semantics.FAMM" }, { "kind": "def", "id": "Semantics.FAMM.fammUnifiedArchitectureStrategy", "name": "fammUnifiedArchitectureStrategy", "module": "Semantics.FAMM" }, { "kind": "module", "id": "Semantics.FAMMCoChain", "name": "FAMMCoChain", "path": "Semantics/FAMMCoChain.lean", "namespace": "Semantics.FAMMCoChain", "doc": "FAMM access costs are a 1-cochain on the access graph: each directed edge (read/write operation between cells) carries a delay cost value. The coboundary \u03b4 of this cochain measures the memory pressure gradient across the cell topology. Where \u03b4 is large \u2192 thermal hotspot. Where \u03b4 \u2248 0 \u2192 the delay fie", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 4, "inductive_count": 1, "line_count": 218 }, { "kind": "def", "id": "Semantics.FAMMCoChain.accessEdgeToGraphEdge", "name": "accessEdgeToGraphEdge", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.oneCoChainCost", "name": "oneCoChainCost", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.coboundary", "name": "coboundary", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.coboundaryNorm", "name": "coboundaryNorm", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.isExact", "name": "isExact", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.coboundary2", "name": "coboundary2", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.thermalStress", "name": "thermalStress", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.judgePauseTrigger", "name": "judgePauseTrigger", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.isThermallyFlat", "name": "isThermallyFlat", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.linearAccessGraph", "name": "linearAccessGraph", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.testBank", "name": "testBank", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.testEdges", "name": "testEdges", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.flatBank", "name": "flatBank", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.testZeroChain", "name": "testZeroChain", "module": "Semantics.FAMMCoChain" }, { "kind": "def", "id": "Semantics.FAMMCoChain.testOneChain", "name": "testOneChain", "module": "Semantics.FAMMCoChain" }, { "kind": "module", "id": "Semantics.FNWH.Burgers", "name": "Burgers", "path": "Semantics/FNWH/Burgers.lean", "namespace": "Semantics.FNWH.Burgers", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Burgers.lean \u2014 Regularized Burgers PDE Formalism This module formalizes the regularized Burgers equation primitives used in the FNWH (Field-Native Witness Hierarchy). It implements the complexity-drive", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 8, "struct_count": 0, "inductive_count": 0, "line_count": 220 }, { "kind": "theorem", "id": "Semantics.FNWH.Burgers.witnessComplexity_nonneg", "name": "witnessComplexity_nonneg", "module": "Semantics.FNWH.Burgers" }, { "kind": "theorem", "id": "Semantics.FNWH.Burgers.complexityOmega_nonneg", "name": "complexityOmega_nonneg", "module": "Semantics.FNWH.Burgers" }, { "kind": "theorem", "id": "Semantics.FNWH.Burgers.nu_eff_ge_nu0", "name": "nu_eff_ge_nu0", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.kappa", "name": "kappa", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.defaultNu0", "name": "defaultNu0", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.witnessComplexityContribution", "name": "witnessComplexityContribution", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.complexityOmega", "name": "complexityOmega", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.effectiveViscosity", "name": "effectiveViscosity", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.regularizedPressure", "name": "regularizedPressure", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.stiffeningMultiplier", "name": "stiffeningMultiplier", "module": "Semantics.FNWH.Burgers" }, { "kind": "def", "id": "Semantics.FNWH.Burgers.toyGrammar", "name": "toyGrammar", "module": "Semantics.FNWH.Burgers" }, { "kind": "module", "id": "Semantics.FNWH.BurgersAVM", "name": "BurgersAVM", "path": "Semantics/FNWH/BurgersAVM.lean", "namespace": "Semantics.FNWH.BurgersAVM", "doc": "AVM Implementation of Burgers Regularization. Expresses the complexity-driven viscosity as a series of VM instructions. Stiffening factor \u03ba = 0.3547", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 57 }, { "kind": "theorem", "id": "Semantics.FNWH.BurgersAVM.nuEffProgram_correct", "name": "nuEffProgram_correct", "module": "Semantics.FNWH.BurgersAVM" }, { "kind": "theorem", "id": "Semantics.FNWH.BurgersAVM.qEffProgram_correct", "name": "qEffProgram_correct", "module": "Semantics.FNWH.BurgersAVM" }, { "kind": "def", "id": "Semantics.FNWH.BurgersAVM.kappa", "name": "kappa", "module": "Semantics.FNWH.BurgersAVM" }, { "kind": "def", "id": "Semantics.FNWH.BurgersAVM.nuEffProgram", "name": "nuEffProgram", "module": "Semantics.FNWH.BurgersAVM" }, { "kind": "def", "id": "Semantics.FNWH.BurgersAVM.qEffProgram", "name": "qEffProgram", "module": "Semantics.FNWH.BurgersAVM" }, { "kind": "module", "id": "Semantics.FNWH.DimensionlessFluxClosure", "name": "DimensionlessFluxClosure", "path": "Semantics/FNWH/DimensionlessFluxClosure.lean", "namespace": "Semantics.FNWH", "doc": "FNWH-Burgers Dimensionless Flux Closure ID: ARCHIVE-N10-OMEGA-DIMENSIONLESS-FLUX-2 This module formalizes the Internal Flux Invariant \u03a6 of the FNWH-Burgers Hyperfluid as a dimensionless rational closure. STATUS: INTERNAL_COHERENCE_LOCKED WARNING: This module is dimensionless. Physical SI mappings", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 2, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 82 }, { "kind": "theorem", "id": "Semantics.FNWH.DimensionlessFluxClosure.phi_near_integer_closure", "name": "phi_near_integer_closure", "module": "Semantics.FNWH.DimensionlessFluxClosure" }, { "kind": "theorem", "id": "Semantics.FNWH.DimensionlessFluxClosure.phi_is_stable_and_positive", "name": "phi_is_stable_and_positive", "module": "Semantics.FNWH.DimensionlessFluxClosure" }, { "kind": "def", "id": "Semantics.FNWH.DimensionlessFluxClosure.fluxClosure", "name": "fluxClosure", "module": "Semantics.FNWH.DimensionlessFluxClosure" }, { "kind": "def", "id": "Semantics.FNWH.DimensionlessFluxClosure.archiveParams", "name": "archiveParams", "module": "Semantics.FNWH.DimensionlessFluxClosure" }, { "kind": "def", "id": "Semantics.FNWH.DimensionlessFluxClosure.archivedPhi", "name": "archivedPhi", "module": "Semantics.FNWH.DimensionlessFluxClosure" }, { "kind": "module", "id": "Semantics.FNWH.GinzburgLandauAnalogy", "name": "GinzburgLandauAnalogy", "path": "Semantics/FNWH/GinzburgLandauAnalogy.lean", "namespace": "Semantics.FNWH", "doc": "FNWH-Burgers Ginzburg-Landau Analogy ID: INTERPRETIVE-ANALOGY-GL-1 This module provides a dimensionless Ginzburg-Landau-style order-parameter interpretation of the FNWH-Burgers hyperfluid model. ARCHIVE STATUS UPDATE: Core layer (DimensionlessFluxClosure.lean): LOCKED GL analogy layer (this module", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 2, "def_count": 4, "struct_count": 1, "inductive_count": 1, "line_count": 156 }, { "kind": "theorem", "id": "Semantics.FNWH.GinzburgLandauAnalogy.analogy_is_stable_and_bounded", "name": "analogy_is_stable_and_bounded", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "theorem", "id": "Semantics.FNWH.GinzburgLandauAnalogy.flux_closure_as_coherence_condition", "name": "flux_closure_as_coherence_condition", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "def", "id": "Semantics.FNWH.GinzburgLandauAnalogy.classifyGLPhase", "name": "classifyGLPhase", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "def", "id": "Semantics.FNWH.GinzburgLandauAnalogy.analogyParams", "name": "analogyParams", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "def", "id": "Semantics.FNWH.GinzburgLandauAnalogy.analogyPhase", "name": "analogyPhase", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "def", "id": "Semantics.FNWH.GinzburgLandauAnalogy.fluxClosureCoherenceAnalogy", "name": "fluxClosureCoherenceAnalogy", "module": "Semantics.FNWH.GinzburgLandauAnalogy" }, { "kind": "module", "id": "Semantics.FaultTolerance", "name": "FaultTolerance", "path": "Semantics/FaultTolerance.lean", "namespace": "Semantics.FaultTolerance", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FaultTolerance.lean \u2014 Fault Tolerance for Tile Flip Consensus Defines fault tolerance mechanisms for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10). Handles node failures, message loss, Byzantin", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 14, "struct_count": 2, "inductive_count": 2, "line_count": 253 }, { "kind": "theorem", "id": "Semantics.FaultTolerance.markNodeFailedSetsFailedState", "name": "markNodeFailedSetsFailedState", "module": "Semantics.FaultTolerance" }, { "kind": "theorem", "id": "Semantics.FaultTolerance.calculateBackoffIsExponential", "name": "calculateBackoffIsExponential", "module": "Semantics.FaultTolerance" }, { "kind": "theorem", "id": "Semantics.FaultTolerance.excludeFailedNodeRemovesVotes", "name": "excludeFailedNodeRemovesVotes", "module": "Semantics.FaultTolerance" }, { "kind": "theorem", "id": "Semantics.FaultTolerance.handleByzantineFaultRemovesVotes", "name": "handleByzantineFaultRemovesVotes", "module": "Semantics.FaultTolerance" }, { "kind": "theorem", "id": "Semantics.FaultTolerance.hasByzantineToleranceRequiresMajority", "name": "hasByzantineToleranceRequiresMajority", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.zero", "name": "zero", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.one", "name": "one", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.ofFrac", "name": "ofFrac", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.detectNodeFailure", "name": "detectNodeFailure", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.markNodeFailed", "name": "markNodeFailed", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.excludeFailedNode", "name": "excludeFailedNode", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.calculateBackoff", "name": "calculateBackoff", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.retransmitMessage", "name": "retransmitMessage", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.detectByzantineFault", "name": "detectByzantineFault", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.handleByzantineFault", "name": "handleByzantineFault", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.hasByzantineTolerance", "name": "hasByzantineTolerance", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.handleNetworkPartition", "name": "handleNetworkPartition", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.updateNodeHealth", "name": "updateNodeHealth", "module": "Semantics.FaultTolerance" }, { "kind": "def", "id": "Semantics.FaultTolerance.initializeNodeHealth", "name": "initializeNodeHealth", "module": "Semantics.FaultTolerance" }, { "kind": "module", "id": "Semantics.FibonacciEncoding", "name": "FibonacciEncoding", "path": "Semantics/FibonacciEncoding.lean", "namespace": "Semantics.FibonacciEncoding", "doc": "FibonacciEncoding.lean \u2014 Fibonacci/Zeckendorf Encoding for Compact Integer Deltas Verified finite Fibonacci encoding surface. Global Zeckendorf existence and uniqueness are not assumed here; this module proves the executable invariants it uses directly.", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 1, "inductive_count": 0, "line_count": 106 }, { "kind": "theorem", "id": "Semantics.FibonacciEncoding.validSingletonFibRep", "name": "validSingletonFibRep", "module": "Semantics.FibonacciEncoding" }, { "kind": "theorem", "id": "Semantics.FibonacciEncoding.singletonFibRepValue", "name": "singletonFibRepValue", "module": "Semantics.FibonacciEncoding" }, { "kind": "theorem", "id": "Semantics.FibonacciEncoding.encodeDeltaZero", "name": "encodeDeltaZero", "module": "Semantics.FibonacciEncoding" }, { "kind": "theorem", "id": "Semantics.FibonacciEncoding.decodeEncodeSmallDelta", "name": "decodeEncodeSmallDelta", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.fib", "name": "fib", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.noConsecutive", "name": "noConsecutive", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.isValidZeckendorf", "name": "isValidZeckendorf", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.zeckendorfToNat", "name": "zeckendorfToNat", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.bitLength", "name": "bitLength", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.fibonacciCodeLength", "name": "fibonacciCodeLength", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.encodeDeltaFibonacci", "name": "encodeDeltaFibonacci", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.decodeDeltaFibonacci", "name": "decodeDeltaFibonacci", "module": "Semantics.FibonacciEncoding" }, { "kind": "def", "id": "Semantics.FibonacciEncoding.theoreticalCompressionRatio", "name": "theoreticalCompressionRatio", "module": "Semantics.FibonacciEncoding" }, { "kind": "module", "id": "Semantics.FieldDamping", "name": "FieldDamping", "path": "Semantics/FieldDamping.lean", "namespace": "Semantics.FieldDamping", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FieldDamping.lean \u2014 Field Damping for Resonant Field Propagation Defines field damping mechanisms for Resonant Field Propagation (RFP). Damping prevents runaway oscillation and ensures stability. Per ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 188 }, { "kind": "theorem", "id": "Semantics.FieldDamping.computeVelocityDampingZeroWhenVelocityZero", "name": "computeVelocityDampingZeroWhenVelocityZero", "module": "Semantics.FieldDamping" }, { "kind": "theorem", "id": "Semantics.FieldDamping.computeAccelerationDampingZeroWhenAccelerationZero", "name": "computeAccelerationDampingZeroWhenAccelerationZero", "module": "Semantics.FieldDamping" }, { "kind": "theorem", "id": "Semantics.FieldDamping.applyDampingPreservesFieldValue", "name": "applyDampingPreservesFieldValue", "module": "Semantics.FieldDamping" }, { "kind": "theorem", "id": "Semantics.FieldDamping.checkStabilityConditionTrueForZeroField", "name": "checkStabilityConditionTrueForZeroField", "module": "Semantics.FieldDamping" }, { "kind": "theorem", "id": "Semantics.FieldDamping.initializeDampingParametersHasPositiveCoefficient", "name": "initializeDampingParametersHasPositiveCoefficient", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.computeVelocityDamping", "name": "computeVelocityDamping", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.computeAccelerationDamping", "name": "computeAccelerationDamping", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.applyDamping", "name": "applyDamping", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.checkStabilityCondition", "name": "checkStabilityCondition", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.initializeDampingParameters", "name": "initializeDampingParameters", "module": "Semantics.FieldDamping" }, { "kind": "def", "id": "Semantics.FieldDamping.adaptiveDampingCoefficient", "name": "adaptiveDampingCoefficient", "module": "Semantics.FieldDamping" }, { "kind": "module", "id": 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"PentagonalSquare", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.MorphicCore", "name": "MorphicCore", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.morphicCoreInvariant", "name": "morphicCoreInvariant", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.mmrHash", "name": "mmrHash", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.createMMRNode", "name": "createMMRNode", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.MMRMountain", "name": "MMRMountain", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.SelfFeedingMMR", "name": "SelfFeedingMMR", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.NearMissPoint", "name": "NearMissPoint", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.averageError", "name": "averageError", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.TensionFunction", "name": "TensionFunction", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.collapseValue", "name": "collapseValue", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.getNthDefault", "name": "getNthDefault", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.WebSystem", "name": "WebSystem", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.IntegratedFieldCell", "name": "IntegratedFieldCell", "module": "Semantics.FieldEquationIntegration" }, { "kind": "def", "id": "Semantics.FieldEquationIntegration.autoMappingRegistry", "name": "autoMappingRegistry", "module": "Semantics.FieldEquationIntegration" }, { "kind": "module", "id": "Semantics.FieldSolver", "name": "FieldSolver", "path": "Semantics/FieldSolver.lean", "namespace": "Semantics.FieldSolver", "doc": "FieldSolver.lean - Torsion Field Compression Solver Compliant with AGENTS.md Q16_16 bounds and minimal bind topology.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.FieldSolver.computeLaplacian", "name": "computeLaplacian", "module": "Semantics.FieldSolver" }, { "kind": "def", "id": "Semantics.FieldSolver.engramQuery", "name": "engramQuery", "module": "Semantics.FieldSolver" }, { "kind": "def", "id": "Semantics.FieldSolver.stabilityPenalty", "name": "stabilityPenalty", "module": "Semantics.FieldSolver" }, { "kind": "def", "id": "Semantics.FieldSolver.fieldInvariant", "name": "fieldInvariant", "module": "Semantics.FieldSolver" }, { "kind": "def", "id": "Semantics.FieldSolver.informationalCost", "name": "informationalCost", "module": "Semantics.FieldSolver" }, { "kind": "def", "id": "Semantics.FieldSolver.informationalBindEval", "name": "informationalBindEval", "module": "Semantics.FieldSolver" }, { "kind": "module", "id": "Semantics.FiveDTorusTopology", "name": "FiveDTorusTopology", "path": "Semantics/FiveDTorusTopology.lean", "namespace": "Semantics.FiveDTorusTopology", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 12, "struct_count": 4, "inductive_count": 0, "line_count": 227 }, { "kind": "theorem", "id": "Semantics.FiveDTorusTopology.torusDistanceSymmetricTest", "name": "torusDistanceSymmetricTest", "module": "Semantics.FiveDTorusTopology" }, { "kind": "theorem", "id": "Semantics.FiveDTorusTopology.torusDiameterFormulaTest", "name": "torusDiameterFormulaTest", "module": "Semantics.FiveDTorusTopology" }, { "kind": "theorem", "id": "Semantics.FiveDTorusTopology.torusNodeDegreeConstant", "name": "torusNodeDegreeConstant", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.torusDistance", "name": "torusDistance", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.torusDiameter", "name": "torusDiameter", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.bisectionBandwidth", "name": "bisectionBandwidth", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.totalConnectivity", "name": "totalConnectivity", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.getNeighbors", "name": "getNeighbors", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.nodeDegree", "name": "nodeDegree", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.isTorusActionLawful", "name": "isTorusActionLawful", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.applyTorusAction", "name": "applyTorusAction", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.torusBind", "name": "torusBind", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.node1", "name": "node1", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.node2", "name": "node2", "module": "Semantics.FiveDTorusTopology" }, { "kind": "def", "id": "Semantics.FiveDTorusTopology.state", "name": "state", "module": "Semantics.FiveDTorusTopology" }, { "kind": "module", "id": "Semantics.FixedPoint", "name": "FixedPoint", "path": "Semantics/FixedPoint.lean", "namespace": "Semantics.FixedPoint", "doc": "A proof-friendly fixed-point core. Design rule: * The semantic value is a bounded signed raw integer. * Saturation is performed by `ofRawInt`. * UInt bit-patterns are boundary/hardware artifacts, not the proof model. This removes the old proof debt caused by proving signed arithmetic facts directl", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 62, "def_count": 99, "struct_count": 0, "inductive_count": 0, "line_count": 1309 }, { "kind": "theorem", "id": "Semantics.FixedPoint.ext", "name": "ext", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_monotone", "name": "q16Clamp_monotone", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_id_of_inRange", "name": "q16Clamp_id_of_inRange", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_lower", "name": "q16Clamp_lower", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_upper", "name": "q16Clamp_upper", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_nonneg_of_nonneg", "name": "q16Clamp_nonneg_of_nonneg", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_idem", "name": "q16Clamp_idem", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.q16Clamp_lipschitz", "name": "q16Clamp_lipschitz", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.epsilon_toInt_pos", "name": "epsilon_toInt_pos", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.maxVal_toInt", "name": "maxVal_toInt", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.minVal_toInt", "name": "minVal_toInt", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_zero", "name": "ofRawInt_zero", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt_ge", "name": "ofRawInt_toInt_ge", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt_nonneg", "name": "ofRawInt_toInt_nonneg", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt", "name": "ofRawInt_toInt", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt_eq_nonneg", "name": "ofRawInt_toInt_eq_nonneg", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt_eq_general", "name": "ofRawInt_toInt_eq_general", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_toInt_eq_clamp", "name": "ofRawInt_toInt_eq_clamp", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.ofRawInt_monotone", "name": "ofRawInt_monotone", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.add_nonneg_monotone", "name": "add_nonneg_monotone", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.zero_mul", "name": "zero_mul", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.mul_zero", "name": "mul_zero", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.sub_self", "name": "sub_self", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.add_zero", "name": "add_zero", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.zero_add", "name": "zero_add", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.sqrt_zero", "name": "sqrt_zero", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.sqrt_one", "name": "sqrt_one", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.int_scale_mul_ediv_cancel", "name": "int_scale_mul_ediv_cancel", "module": "Semantics.FixedPoint" }, { "kind": "theorem", "id": "Semantics.FixedPoint.one_mul", "name": "one_mul", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.q0_16MinRaw", "name": "q0_16MinRaw", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.q0_16MaxRaw", "name": "q0_16MaxRaw", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.q0_16Scale", "name": "q0_16Scale", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.toInt", "name": "toInt", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.ofRawInt", "name": "ofRawInt", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.zero", "name": "zero", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.one", "name": "one", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.half", "name": "half", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.neg", "name": "neg", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.add", "name": "add", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.sub", "name": "sub", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.mul", "name": "mul", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.div", "name": "div", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.abs", "name": "abs", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.lt", "name": "lt", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.le", "name": "le", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.gt", "name": "gt", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.ge", "name": "ge", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.toFloat", "name": "toFloat", "module": "Semantics.FixedPoint" }, { "kind": "def", "id": "Semantics.FixedPoint.ofFloat", "name": "ofFloat", "module": "Semantics.FixedPoint" }, { "kind": "module", "id": "Semantics.FixedPointBoundary", "name": "FixedPointBoundary", "path": "Semantics/FixedPointBoundary.lean", "namespace": "Semantics.FixedPoint", "doc": "# FixedPointBoundary \u2014 Float \u2194 Q16_16 / Q0_16 / Q0_64 conversion These functions are **only** for the I/O boundary: parsing JSON, reading sensor data, or displaying values in `#eval` witnesses. They must NOT be used in any compute-path definition that feeds into a receipt, score, or gate. The core", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 0, "inductive_count": 0, "line_count": 89 }, { "kind": "def", "id": "Semantics.FixedPointBoundary.toFloat", "name": "toFloat", "module": "Semantics.FixedPointBoundary" }, { "kind": "def", "id": "Semantics.FixedPointBoundary.ofFloat", "name": "ofFloat", "module": "Semantics.FixedPointBoundary" }, { "kind": "def", "id": "Semantics.FixedPointBoundary.q0_64ScaleFloat", "name": "q0_64ScaleFloat", "module": "Semantics.FixedPointBoundary" }, { "kind": "module", "id": "Semantics.FixedPointBridge", "name": "FixedPointBridge", "path": "Semantics/FixedPointBridge.lean", "namespace": "Semantics.FixedPointBridge", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FixedPointBridge.lean \u2014 Bridge between Q0_16 and Q16_16 for unified fixed-point arithmetic NOTE: The conversion functions (q0ToQ16, q16ToQ0) use pure integer arithmetic mapping Q0_16 (scale 32767) to/f", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 75 }, { "kind": "theorem", "id": "Semantics.FixedPointBridge.roundTripQ0_zero", "name": "roundTripQ0_zero", "module": "Semantics.FixedPointBridge" }, { "kind": "theorem", "id": "Semantics.FixedPointBridge.roundTripQ16_zero", "name": "roundTripQ16_zero", "module": "Semantics.FixedPointBridge" }, { "kind": "theorem", "id": "Semantics.FixedPointBridge.q0ToQ16_zero", "name": "q0ToQ16_zero", "module": "Semantics.FixedPointBridge" }, { "kind": "theorem", "id": "Semantics.FixedPointBridge.q16ToQ0_zero", "name": "q16ToQ0_zero", "module": "Semantics.FixedPointBridge" }, { "kind": "def", "id": "Semantics.FixedPointBridge.q0ToQ16", "name": "q0ToQ16", "module": "Semantics.FixedPointBridge" }, { "kind": "def", "id": "Semantics.FixedPointBridge.q16ToQ0", "name": "q16ToQ0", "module": "Semantics.FixedPointBridge" }, { "kind": "def", "id": "Semantics.FixedPointBridge.fixedPointBridgeStatus", "name": "fixedPointBridgeStatus", "module": "Semantics.FixedPointBridge" }, { "kind": "module", "id": "Semantics.FlagSort", "name": "FlagSort", "path": "Semantics/FlagSort.lean", "namespace": "Semantics.FlagSort", "doc": "Flag: The three-way partition of the research manifold.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 1, "line_count": 53 }, { "kind": "def", "id": "Semantics.FlagSort.redThreshold", "name": "redThreshold", "module": "Semantics.FlagSort" }, { "kind": "def", "id": "Semantics.FlagSort.blueThreshold", "name": "blueThreshold", "module": "Semantics.FlagSort" }, { "kind": "def", "id": "Semantics.FlagSort.getFlag", "name": "getFlag", "module": "Semantics.FlagSort" }, { "kind": "def", "id": "Semantics.FlagSort.isLawfulSort", "name": "isLawfulSort", "module": "Semantics.FlagSort" }, { "kind": "def", "id": "Semantics.FlagSort.flagBind", "name": "flagBind", "module": "Semantics.FlagSort" }, { "kind": "module", "id": "Semantics.ForceModifiedArrhenius", "name": "ForceModifiedArrhenius", "path": "Semantics/ForceModifiedArrhenius.lean", "namespace": "Semantics.ForceModifiedArrhenius", "doc": "ForceModifiedArrhenius.lean \u2014 Activation Barriers Across Physics Scales This module formalizes how activation barriers appear at every scale of physics: \u2022 Chemical reactions (Arrhenius) \u2022 Mechanochemistry (Bell-Evans-Polanyi) \u2022 Nuclear decay (Gamow factor) \u2022 Particle production (Boltzmann factor) \u2022", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 13, "struct_count": 2, "inductive_count": 0, "line_count": 180 }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.computeRate", "name": "computeRate", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.chemicalBarrier", "name": "chemicalBarrier", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.gamowFactor", "name": "gamowFactor", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.nuclearBarrier", "name": "nuclearBarrier", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.boltzmannFactor", "name": "boltzmannFactor", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.particleBarrier", "name": "particleBarrier", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.instantonAction", "name": "instantonAction", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.cosmicBarrier", "name": "cosmicBarrier", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.forceModifiedBarrier", "name": "forceModifiedBarrier", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.computeDrift", "name": "computeDrift", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.testChem", "name": "testChem", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.testNuc", "name": "testNuc", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "def", "id": "Semantics.ForceModifiedArrhenius.testDrift", "name": "testDrift", "module": "Semantics.ForceModifiedArrhenius" }, { "kind": "module", "id": "Semantics.ForestAutodocRegistry", "name": "ForestAutodocRegistry", "path": "Semantics/ForestAutodocRegistry.lean", "namespace": "HolyDiver", "doc": "Holy Diver / ENE Forest Autodoc Registry Third layer of the integrated architecture: RealityContractMassNumber.lean (base ontology) FieldEquationIntegration.lean (field equation machinery) ForestAutodocRegistry.lean (forest registry with autodoc) This module combines the base ontology with field e", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 9, "struct_count": 2, "inductive_count": 0, "line_count": 202 }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.sameMorphicCore", "name": "sameMorphicCore", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.similarMorphicCore", "name": "similarMorphicCore", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.ForestRegistry", "name": "ForestRegistry", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.applyCollapse", "name": "applyCollapse", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.autodocPressureIntegrated", "name": "autodocPressureIntegrated", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "def", "id": "Semantics.ForestAutodocRegistry.lookupIntegratedConcept", "name": "lookupIntegratedConcept", "module": "Semantics.ForestAutodocRegistry" }, { "kind": "module", "id": "Semantics.Forgejo", "name": "Forgejo", "path": "Semantics/Forgejo.lean", "namespace": "Semantics.Forgejo", "doc": "ForgejoEvent: The structure of a Git event in the research stack.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.Forgejo.forgejoPolicy", "name": "forgejoPolicy", "module": "Semantics.Forgejo" }, { "kind": "def", "id": "Semantics.Forgejo.toSourceEvent", "name": "toSourceEvent", "module": "Semantics.Forgejo" }, { "kind": "def", "id": "Semantics.Forgejo.forgejoInvariant", "name": "forgejoInvariant", "module": "Semantics.Forgejo" }, { "kind": "def", "id": "Semantics.Forgejo.forgejoCost", "name": "forgejoCost", "module": "Semantics.Forgejo" }, { "kind": "def", "id": "Semantics.Forgejo.forgejoBind", "name": "forgejoBind", "module": "Semantics.Forgejo" }, { "kind": "module", "id": "Semantics.FormalConjectures.Util.ProblemImports", "name": "ProblemImports", "path": "Semantics/FormalConjectures/Util/ProblemImports.lean", "namespace": "", "doc": "# Stub for FormalConjectures.Util.ProblemImports Provides the definitions from Google DeepMind's `formal-conjectures` package that are needed by the AlphaProof Nexus proof files. The key definition is `IsSidon` for `Set \u2115`, which is bridged to `Semantics.SidonSets.IsSidon` for `Finset \u2124`.", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 1, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 33 }, { "kind": "theorem", "id": "Semantics.FormalConjectures.Util.ProblemImports.IsSidon", "name": "IsSidon", "module": "Semantics.FormalConjectures.Util.ProblemImports" }, { "kind": "module", "id": "Semantics.Foundations.AggregateLoad", "name": "AggregateLoad", "path": "Semantics/Foundations/AggregateLoad.lean", "namespace": "Semantics.Foundations", "doc": "L_agg = \u03a3 w_i \u00b7 L_i Weighted aggregation of per-substrate or per-node computational loads. This is the foundation kernel for substrate load balancing, where each node reports its load L_i and the scheduler computes the weighted aggregate to make routing and dispatch decisions.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 69 }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.aggregateLoad", "name": "aggregateLoad", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.peakLoad", "name": "peakLoad", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.loadImbalance", "name": "loadImbalance", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.uniformEntries", "name": "uniformEntries", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.weightedEntries", "name": "weightedEntries", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "def", "id": "Semantics.Foundations.AggregateLoad.skewedEntries", "name": "skewedEntries", "module": "Semantics.Foundations.AggregateLoad" }, { "kind": "module", "id": "Semantics.Foundations.CarnotEfficiency", "name": "CarnotEfficiency", "path": "Semantics/Foundations/CarnotEfficiency.lean", "namespace": "Semantics.Foundations", "doc": "\u03b7 = 1 - T_cold / T_hot", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 19 }, { "kind": "def", "id": "Semantics.Foundations.CarnotEfficiency.carnotEfficiency", "name": "carnotEfficiency", "module": "Semantics.Foundations.CarnotEfficiency" }, { "kind": "module", "id": "Semantics.Foundations.EnergyBalance", "name": "EnergyBalance", "path": "Semantics/Foundations/EnergyBalance.lean", "namespace": "Semantics.Foundations", "doc": "E_balance = E_gain - E_cost", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 18 }, { "kind": "def", "id": "Semantics.Foundations.EnergyBalance.energyBalance", "name": "energyBalance", "module": "Semantics.Foundations.EnergyBalance" }, { "kind": "module", "id": "Semantics.Foundations.GeodesicConnection", "name": "GeodesicConnection", "path": "Semantics/Foundations/GeodesicConnection.lean", "namespace": "Semantics.Foundations", "doc": "\u0393^k_ij = \u00bd g^{kl} (\u2202_i g_{jl} + \u2202_j g_{il} - \u2202_l g_{ij}) In the Q16_16 discrete setting, we approximate the connection coefficients from finite differences of the metric tensor components. This implements the geodesic equation acceleration term: \u1e8d^k = -\u0393^k_ij \u1e8b^i \u1e8b^j", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.Foundations.GeodesicConnection.Metric2D", "name": "Metric2D", "module": "Semantics.Foundations.GeodesicConnection" }, { "kind": "def", "id": "Semantics.Foundations.GeodesicConnection.christoffelApprox", "name": "christoffelApprox", "module": "Semantics.Foundations.GeodesicConnection" }, { "kind": "def", "id": "Semantics.Foundations.GeodesicConnection.geodesicAccel1D", "name": "geodesicAccel1D", "module": "Semantics.Foundations.GeodesicConnection" }, { "kind": "def", "id": "Semantics.Foundations.GeodesicConnection.geodesicStep", "name": "geodesicStep", "module": "Semantics.Foundations.GeodesicConnection" }, { "kind": "module", "id": "Semantics.Foundations.HierarchicalEntropy", "name": "HierarchicalEntropy", "path": "Semantics/Foundations/HierarchicalEntropy.lean", "namespace": "Semantics.Foundations", "doc": "H_hier = \u03a3 w_i H_i", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 20 }, { "kind": "def", "id": "Semantics.Foundations.HierarchicalEntropy.hierarchicalEntropy", "name": "hierarchicalEntropy", "module": "Semantics.Foundations.HierarchicalEntropy" }, { "kind": "module", "id": "Semantics.Foundations.InformationContent", "name": "InformationContent", "path": "Semantics/Foundations/InformationContent.lean", "namespace": "Semantics.Foundations", "doc": "I(x) = -log2(p(x))", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 27 }, { "kind": "def", "id": "Semantics.Foundations.InformationContent.informationContent", "name": "informationContent", "module": "Semantics.Foundations.InformationContent" }, { "kind": "def", "id": "Semantics.Foundations.InformationContent.rareEvent", "name": "rareEvent", "module": "Semantics.Foundations.InformationContent" }, { "kind": "module", "id": "Semantics.Foundations.IntrinsicRatio", "name": "IntrinsicRatio", "path": "Semantics/Foundations/IntrinsicRatio.lean", "namespace": "Semantics.Foundations", "doc": "r = a / b, with \u03c6 = (1 + \u221a5) / 2 as the golden ratio reference. The intrinsic ratio measures how close a proportion a:b is to the golden ratio \u03c6 \u2248 1.618034. This is used for: Golden-angle encoding (\u03c6\u207b\u00b9 = 0x9E70 in Q16.16) Braid strand spacing optimality Fractal subdivision ratios", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Foundations.IntrinsicRatio.phi", "name": "phi", "module": "Semantics.Foundations.IntrinsicRatio" }, { "kind": "def", "id": "Semantics.Foundations.IntrinsicRatio.phiInv", "name": "phiInv", "module": "Semantics.Foundations.IntrinsicRatio" }, { "kind": "def", "id": "Semantics.Foundations.IntrinsicRatio.intrinsicRatio", "name": "intrinsicRatio", "module": "Semantics.Foundations.IntrinsicRatio" }, { "kind": "def", "id": "Semantics.Foundations.IntrinsicRatio.goldenDeviation", "name": "goldenDeviation", "module": "Semantics.Foundations.IntrinsicRatio" }, { "kind": "def", "id": "Semantics.Foundations.IntrinsicRatio.isGoldenRatio", "name": "isGoldenRatio", "module": "Semantics.Foundations.IntrinsicRatio" }, { "kind": "module", "id": "Semantics.Foundations.LandauerBound", "name": "LandauerBound", "path": "Semantics/Foundations/LandauerBound.lean", "namespace": "Semantics.Foundations", "doc": "W = k_B * T * ln(2)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 20 }, { "kind": "def", "id": "Semantics.Foundations.LandauerBound.landauerBound", "name": "landauerBound", "module": "Semantics.Foundations.LandauerBound" }, { "kind": "module", "id": "Semantics.Foundations.MaxwellDemon", "name": "MaxwellDemon", "path": "Semantics/Foundations/MaxwellDemon.lean", "namespace": "Semantics.Foundations", "doc": "\u03b7_demon = E_recovered / (k_B * T * I)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 20 }, { "kind": "def", "id": "Semantics.Foundations.MaxwellDemon.maxwellDemonRecovery", "name": "maxwellDemonRecovery", "module": "Semantics.Foundations.MaxwellDemon" }, { "kind": "module", "id": "Semantics.Foundations.RiemannianDistance", "name": "RiemannianDistance", "path": "Semantics/Foundations/RiemannianDistance.lean", "namespace": "Semantics.Foundations", "doc": "d(p,q) = \u221a(\u03a3 g_ij \u0394x_i \u0394x_j) In flat (Euclidean) space with identity metric, this reduces to the standard L2 distance: d = \u221a(\u03a3 (\u0394x_i)\u00b2). The Q16_16 implementation computes the metric-weighted sum of squared coordinate differences and returns the integer square root.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 51 }, { "kind": "def", "id": "Semantics.Foundations.RiemannianDistance.squaredDistance", "name": "squaredDistance", "module": "Semantics.Foundations.RiemannianDistance" }, { "kind": "def", "id": "Semantics.Foundations.RiemannianDistance.riemannianDistance", "name": "riemannianDistance", "module": "Semantics.Foundations.RiemannianDistance" }, { "kind": "def", "id": "Semantics.Foundations.RiemannianDistance.riemannianDistanceWeighted", "name": "riemannianDistanceWeighted", "module": "Semantics.Foundations.RiemannianDistance" }, { "kind": "module", "id": "Semantics.Foundations.ShannonEntropy", "name": "ShannonEntropy", "path": "Semantics/Foundations/ShannonEntropy.lean", "namespace": "Semantics.Foundations", "doc": "H(X) = -\u03a3 p_i log2(p_i)", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 32 }, { "kind": "def", "id": "Semantics.Foundations.ShannonEntropy.shannonEntropy", "name": "shannonEntropy", "module": "Semantics.Foundations.ShannonEntropy" }, { "kind": "def", "id": "Semantics.Foundations.ShannonEntropy.fairCoin", "name": "fairCoin", "module": "Semantics.Foundations.ShannonEntropy" }, { "kind": "def", "id": "Semantics.Foundations.ShannonEntropy.certainEvent", "name": "certainEvent", "module": "Semantics.Foundations.ShannonEntropy" }, { "kind": "module", "id": "Semantics.Foundations.SymplecticGeodesicStep", "name": "SymplecticGeodesicStep", "path": "Semantics/Foundations/SymplecticGeodesicStep.lean", "namespace": "Semantics.Foundations", "doc": "The symplectic integrator preserves the symplectic 2-form \u03c9 = dp \u2227 dq, guaranteeing bounded energy drift over long integration horizons. St\u00f6rmer-Verlet (leapfrog) scheme: p_{1/2} = p_n - (dt/2) \u00b7 \u2207V(q_n) q_{n+1} = q_n + dt \u00b7 p_{1/2} / m p_{n+1} = p_{1/2} - (dt/2) \u00b7 \u2207V(q_{n+1})", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.Foundations.SymplecticGeodesicStep.symplecticStep", "name": "symplecticStep", "module": "Semantics.Foundations.SymplecticGeodesicStep" }, { "kind": "def", "id": "Semantics.Foundations.SymplecticGeodesicStep.symplecticIntegrate", "name": "symplecticIntegrate", "module": "Semantics.Foundations.SymplecticGeodesicStep" }, { "kind": "def", "id": "Semantics.Foundations.SymplecticGeodesicStep.harmonicGradV", "name": "harmonicGradV", "module": "Semantics.Foundations.SymplecticGeodesicStep" }, { "kind": "def", "id": "Semantics.Foundations.SymplecticGeodesicStep.harmonicInit", "name": "harmonicInit", "module": "Semantics.Foundations.SymplecticGeodesicStep" }, { "kind": "module", "id": "Semantics.FractionScan", "name": "FractionScan", "path": "Semantics/FractionScan.lean", "namespace": "Semantics.FractionScan", "doc": "FractionScan.lean \u2014 Systematic Scan of Alternative Fractions This module addresses the adversarial review's Attack #3: \"53 Alternative Fractions in Range \u2014 Why 7/27?\" The hostile reviewer identified 53 distinct fractions in [0.24, 0.28] with denominator \u2264 50, many of which work as well or better t", "math_kind": "avm", "sorry_count": 0, "theorem_count": 17, "def_count": 14, "struct_count": 0, "inductive_count": 0, "line_count": 269 }, { "kind": "theorem", "id": "Semantics.FractionScan.for", "name": "for", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_13_50_exactMott", "name": "f_13_50_exactMott", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_7_27_mottDistance", "name": "f_7_27_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_13_50_mottDistance", "name": "f_13_50_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_6_23_mottDistance", "name": "f_6_23_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_7_27_closer_than_6_23", "name": "f_7_27_closer_than_6_23", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_8_31_mottDistance", "name": "f_8_31_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_9_35_mottDistance", "name": "f_9_35_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_5_19_mottDistance", "name": "f_5_19_mottDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.speciesArea_exact", "name": "speciesArea_exact", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_7_27_speciesAreaDistance", "name": "f_7_27_speciesAreaDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_13_50_speciesAreaDistance", "name": "f_13_50_speciesAreaDistance", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_7_27_closer_to_speciesArea_than_13_50", "name": "f_7_27_closer_to_speciesArea_than_13_50", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_7_27_compromiseScore", "name": "f_7_27_compromiseScore", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_13_50_compromiseScore", "name": "f_13_50_compromiseScore", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.f_8_31_compromiseScore", "name": "f_8_31_compromiseScore", "module": "Semantics.FractionScan" }, { "kind": "theorem", "id": "Semantics.FractionScan.threeFractionsTied", "name": "threeFractionsTied", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.mottCriterion", "name": "mottCriterion", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.zMenger", "name": "zMenger", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.speciesArea", "name": "speciesArea", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_13_50", "name": "f_13_50", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_6_23", "name": "f_6_23", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_5_19", "name": "f_5_19", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_7_27", "name": "f_7_27", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_9_35", "name": "f_9_35", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.f_8_31", "name": "f_8_31", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.mottDistance", "name": "mottDistance", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.speciesAreaDistance", "name": "speciesAreaDistance", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.compromiseScore", "name": "compromiseScore", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.lookElsewhereFactor", "name": "lookElsewhereFactor", "module": "Semantics.FractionScan" }, { "kind": "def", "id": "Semantics.FractionScan.lookElsewhereCorrectedSignificance", "name": "lookElsewhereCorrectedSignificance", "module": "Semantics.FractionScan" }, { "kind": "module", "id": "Semantics.Functions.BracketedCalculus", "name": "BracketedCalculus", "path": "Semantics/Functions/BracketedCalculus.lean", "namespace": "Semantics.BracketedCalculus", "doc": "BracketedCalculus.lean - DIAT Extension to Bracketed Calculus", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 98 }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.encode", "name": "encode", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.width", "name": "width", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.checkGapConservation", "name": "checkGapConservation", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.isInterior", "name": "isInterior", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.bracketAdd", "name": "bracketAdd", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.bracketMulConservative", "name": "bracketMulConservative", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.bracketNeg", "name": "bracketNeg", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.taylorWithinTolerance", "name": "taylorWithinTolerance", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.derivativeEstimate", "name": "derivativeEstimate", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.secondDerivativeEstimate", "name": "secondDerivativeEstimate", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "def", "id": "Semantics.Functions.BracketedCalculus.adaptiveRefine", "name": "adaptiveRefine", "module": "Semantics.Functions.BracketedCalculus" }, { "kind": "module", "id": "Semantics.Functions.MathDebate", "name": "MathDebate", "path": "Semantics/Functions/MathDebate.lean", "namespace": "Semantics.MathDebate", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 6, "inductive_count": 3, "line_count": 83 }, { "kind": "def", "id": "Semantics.Functions.MathDebate.zero", "name": "zero", "module": "Semantics.Functions.MathDebate" }, { "kind": "def", "id": "Semantics.Functions.MathDebate.one", "name": "one", "module": "Semantics.Functions.MathDebate" }, { "kind": "def", "id": "Semantics.Functions.MathDebate.ofNat", "name": "ofNat", "module": "Semantics.Functions.MathDebate" }, { "kind": "def", "id": "Semantics.Functions.MathDebate.toNat", "name": "toNat", "module": "Semantics.Functions.MathDebate" }, { "kind": "def", "id": "Semantics.Functions.MathDebate.ofFrac", "name": "ofFrac", "module": "Semantics.Functions.MathDebate" }, { "kind": "def", "id": "Semantics.Functions.MathDebate.runSampleDebate", "name": "runSampleDebate", "module": "Semantics.Functions.MathDebate" }, { "kind": "module", "id": "Semantics.Functions.MathQuery", "name": "MathQuery", "path": "Semantics/Functions/MathQuery.lean", "namespace": "Semantics.MathQuery", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MathQuery.lean \u2014 ENE Extension for Mathematical Subject Query This module extends the ENE semantic database with specialized indexing and retrieval for mathematical subjects: theorems, equations, proof", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 15, "struct_count": 3, "inductive_count": 3, "line_count": 341 }, { "kind": "theorem", "id": "Semantics.Functions.MathQuery.exactSubjectZeroCost", "name": "exactSubjectZeroCost", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.toIdx", "name": "toIdx", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.label", "name": "label", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.ofUInt32", "name": "ofUInt32", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.defaultQueryParams", "name": "defaultQueryParams", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.q16_one", "name": "q16_one", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.subjectCost", "name": "subjectCost", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.yearCost", "name": "yearCost", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.complexityCost", "name": "complexityCost", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.queryCost", "name": "queryCost", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.emptyDatabase", "name": "emptyDatabase", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.insertEntity", "name": "insertEntity", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.queryDatabase", "name": "queryDatabase", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.toQueryResult", "name": "toQueryResult", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.testEntity1", "name": "testEntity1", "module": "Semantics.Functions.MathQuery" }, { "kind": "def", "id": "Semantics.Functions.MathQuery.testEntity2", "name": "testEntity2", "module": "Semantics.Functions.MathQuery" }, { "kind": "module", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib", "name": "WSM_WR_EGS_WC_Mathlib", "path": "Semantics/Functions/WSM_WR_EGS_WC_Mathlib.lean", "namespace": "WSM", "doc": "WSM_WR_EGS_WC_Mathlib.lean Mathlib-oriented sketch for: Wavefunction Superposition Metacomputation \u2192 Waveform Recording \u2192 Energy-Gradient Signal \u2192 Waveprobe Coarse-Graining", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 25, "def_count": 46, "struct_count": 0, "inductive_count": 1, "line_count": 439 }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.H_selfadjoint", "name": "H_selfadjoint", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.observables_hermitian", "name": "observables_hermitian", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.state_normalized", "name": "state_normalized", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.expect_real_of_selfadjoint", "name": "expect_real_of_selfadjoint", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.closed_energy_conservation", "name": "closed_energy_conservation", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.open_energy_nontrivial_possible", "name": "open_energy_nontrivial_possible", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.coarse_noninjective", "name": "coarse_noninjective", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.signal_ext", "name": "signal_ext", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.StotalClosed_def", "name": "StotalClosed_def", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.StotalOpen_def", "name": "StotalOpen_def", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.canonical_pipeline_closed", "name": "canonical_pipeline_closed", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.canonical_pipeline_open", "name": "canonical_pipeline_open", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.dEclosed_zero", "name": "dEclosed_zero", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u0394Eplus_zero_of_closed", "name": "\u0394Eplus_zero_of_closed", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u0394Eminus_zero_of_closed", "name": "\u0394Eminus_zero_of_closed", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.GEclosed_reduces_when_temporal_zero", "name": "GEclosed_reduces_when_temporal_zero", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.feature_equiv_implies_probe_equiv", "name": "feature_equiv_implies_probe_equiv", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.probe_equiv_implies_coarse_equiv", "name": "probe_equiv_implies_coarse_equiv", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.feature_equiv_implies_coarse_equiv", "name": "feature_equiv_implies_coarse_equiv", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.coarse_graining_not_injective", "name": "coarse_graining_not_injective", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.StotalClosed_pointwise", "name": "StotalClosed_pointwise", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.StotalOpen_pointwise", "name": "StotalOpen_pointwise", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.open_branch_can_have_nontrivial_energy_channel", "name": "open_branch_can_have_nontrivial_energy_channel", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.full_pipeline_is_composition_closed", "name": "full_pipeline_is_composition_closed", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "theorem", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.full_pipeline_is_composition_open", "name": "full_pipeline_is_composition_open", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.NormedAddCommGroup\u03a8", "name": "NormedAddCommGroup\u03a8", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.InnerProductSpace\u03a8", "name": "InnerProductSpace\u03a8", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.CompleteSpace\u03a8", "name": "CompleteSpace\u03a8", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u03b7", "name": "\u03b7", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.H", "name": "H", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.O", "name": "O", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.w", "name": "w", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u0393SE", "name": "\u0393SE", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.F", "name": "F", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.W", "name": "W", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.C", "name": "C", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u03c8", "name": "\u03c8", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.\u03c1", "name": "\u03c1", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.Normalized", "name": "Normalized", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.SelfAdjointOp", "name": "SelfAdjointOp", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.HermitianObservable", "name": "HermitianObservable", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.expect", "name": "expect", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.expect\u03c1", "name": "expect\u03c1", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.ddt", "name": "ddt", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "def", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib.spatialGradNorm", "name": "spatialGradNorm", "module": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib" }, { "kind": "module", "id": "Semantics.Functions.WSM_WR_EGS_WC_Mathlib_temp", "name": "WSM_WR_EGS_WC_Mathlib_temp", "path": "Semantics/Functions/WSM_WR_EGS_WC_Mathlib_temp.lean", "namespace": "", "doc": "", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 1 }, { "kind": "module", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation", "name": "WavefunctionSuperpositionMetacomputation", "path": "Semantics/Functions/WavefunctionSuperpositionMetacomputation.lean", "namespace": "Semantics", "doc": "Wavefunction Superposition Metacomputation This module formalizes the concept of wavefunction superposition as a metacomputation for pyramid-spherion geometry. Shape states become quantum wavefunctions encoding superpositions of void/protrusion/flat/complex states. Key structures: WavefunctionStat", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 1, "def_count": 7, "struct_count": 4, "inductive_count": 2, "line_count": 199 }, { "kind": "theorem", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.normalizationPreservation", "name": "normalizationPreservation", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.wavefunctionNorm", "name": "wavefunctionNorm", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.isWavefunctionNormalized", "name": "isWavefunctionNormalized", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.applyQuantumOperation", "name": "applyQuantumOperation", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.wavefunctionInvariant", "name": "wavefunctionInvariant", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.quantumOperationCost", "name": "quantumOperationCost", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.wavefunctionMetacomputationCost", "name": "wavefunctionMetacomputationCost", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "def", "id": "Semantics.Functions.WavefunctionSuperpositionMetacomputation.wavefunctionMetacomputationBind", "name": "wavefunctionMetacomputationBind", "module": "Semantics.Functions.WavefunctionSuperpositionMetacomputation" }, { "kind": "module", "id": "Semantics.FuzzyAssociation", "name": "FuzzyAssociation", "path": "Semantics/FuzzyAssociation.lean", "namespace": "Semantics.FuzzyAssociation", "doc": "FuzzyMatch: Represents a non-explicit connection between two concepts. Confidence is a Q0.16 value between 0 and 1 (2-byte pure fraction).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 0, "line_count": 36 }, { "kind": "def", "id": "Semantics.FuzzyAssociation.isInteresting", "name": "isInteresting", "module": "Semantics.FuzzyAssociation" }, { "kind": "def", "id": "Semantics.FuzzyAssociation.fuzzyBind", "name": "fuzzyBind", "module": "Semantics.FuzzyAssociation" }, { "kind": "module", "id": "Semantics.GCCL", "name": "GCCL", "path": "Semantics/GCCL.lean", "namespace": "Semantics.GCCL", "doc": "# GCCL Formal Core This module formalizes the broad GCCL space described in `docs/research/GCCL_THEORY_INTRO.md` and `docs/research/GCCL_GENETIC_INFORMATION_MIXTURE_PRIMITIVES.md`. GCCL is treated here as Geometric, Cognitive, and Compression Law: a receipt-bounded discipline for transitions that ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 12, "def_count": 18, "struct_count": 5, "inductive_count": 10, "line_count": 413 }, { "kind": "theorem", "id": "Semantics.GCCL.complete_wrapper_true", "name": "complete_wrapper_true", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.lawful_example_admissible", "name": "lawful_example_admissible", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.compression_gain_without_invariant_is_not_lawful", "name": "compression_gain_without_invariant_is_not_lawful", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.verified_rep_and_lawful_transition_promotes", "name": "verified_rep_and_lawful_transition_promotes", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.verified_rep_does_not_promote_unlawful_transition", "name": "verified_rep_does_not_promote_unlawful_transition", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.dna_primitive_admissible", "name": "dna_primitive_admissible", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.model_codon_primitive_admissible", "name": "model_codon_primitive_admissible", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.biological_and_model_domains_do_not_mix_without_receipt", "name": "biological_and_model_domains_do_not_mix_without_receipt", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.biological_and_model_domains_mix_with_receipt_bridge", "name": "biological_and_model_domains_mix_with_receipt_bridge", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.lawful_surface_implies_complete_wrapper", "name": "lawful_surface_implies_complete_wrapper", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.rep_promotion_implies_verified", "name": "rep_promotion_implies_verified", "module": "Semantics.GCCL" }, { "kind": "theorem", "id": "Semantics.GCCL.admissible_primitive_has_active_alphabet", "name": "admissible_primitive_has_active_alphabet", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.wrapperComplete", "name": "wrapperComplete", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.transitionAccepted", "name": "transitionAccepted", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.lawfulSurfaceAdmissible", "name": "lawfulSurfaceAdmissible", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.quarantineRoutable", "name": "quarantineRoutable", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.repVerified", "name": "repVerified", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.repPromotable", "name": "repPromotable", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.activeAlphabetDeclared", "name": "activeAlphabetDeclared", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.mixturePrimitiveAdmissible", "name": "mixturePrimitiveAdmissible", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.domainMixAllowed", "name": "domainMixAllowed", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.primitivesCanMix", "name": "primitivesCanMix", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.completeWrapper", "name": "completeWrapper", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.acceptedReceipt", "name": "acceptedReceipt", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.lawfulExample", "name": "lawfulExample", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.compressionOnlyExample", "name": "compressionOnlyExample", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.verifiedRep", "name": "verifiedRep", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.dnaIupacPrimitive", "name": "dnaIupacPrimitive", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.modelCodonPrimitive", "name": "modelCodonPrimitive", "module": "Semantics.GCCL" }, { "kind": "def", "id": "Semantics.GCCL.mappedBridgePrimitive", "name": "mappedBridgePrimitive", "module": "Semantics.GCCL" }, { "kind": "module", "id": "Semantics.GCLTopologyRevision", "name": "GCLTopologyRevision", "path": "Semantics/GCLTopologyRevision.lean", "namespace": "Semantics.GCLTopologyRevision", "doc": "Typed vocabulary for the GCL topology revision. This module is intentionally small: it records the revised contract that all route-prior machinery feeds GCL, while only the full gate may admit state.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 3, "def_count": 5, "struct_count": 1, "inductive_count": 4, "line_count": 112 }, { "kind": "theorem", "id": "Semantics.GCLTopologyRevision.canonicalGateHasAuthority", "name": "canonicalGateHasAuthority", "module": "Semantics.GCLTopologyRevision" }, { "kind": "theorem", "id": "Semantics.GCLTopologyRevision.routeHintNoDirectAuthority", "name": "routeHintNoDirectAuthority", "module": "Semantics.GCLTopologyRevision" }, { "kind": "theorem", "id": "Semantics.GCLTopologyRevision.ms3cShearWithoutGateRenormalizes", "name": "ms3cShearWithoutGateRenormalizes", "module": "Semantics.GCLTopologyRevision" }, { "kind": "def", "id": "Semantics.GCLTopologyRevision.hintAuthorizesExecution", "name": "hintAuthorizesExecution", "module": "Semantics.GCLTopologyRevision" }, { "kind": "def", "id": "Semantics.GCLTopologyRevision.canonicalGate", "name": "canonicalGate", "module": "Semantics.GCLTopologyRevision" }, { "kind": "def", "id": "Semantics.GCLTopologyRevision.gateHasAuthority", "name": "gateHasAuthority", "module": "Semantics.GCLTopologyRevision" }, { "kind": "def", "id": "Semantics.GCLTopologyRevision.routeVerdict", "name": "routeVerdict", "module": "Semantics.GCLTopologyRevision" }, { "kind": "def", "id": "Semantics.GCLTopologyRevision.sampleMS3CHint", "name": "sampleMS3CHint", "module": "Semantics.GCLTopologyRevision" }, { "kind": "module", "id": "Semantics.GPUResourceManager", "name": "GPUResourceManager", "path": "Semantics/GPUResourceManager.lean", "namespace": "Semantics.GPUResourceManager", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GPUResourceManager.lean \u2014 GPU resource allocation and optimization for 80% load target. This module formalizes: 1. Dynamic GPU resource allocation based on task suitability 2. Priority-based resource s", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 4, "inductive_count": 3, "line_count": 200 }, { "kind": "def", "id": "Semantics.GPUResourceManager.defaultGPUSpec", "name": "defaultGPUSpec", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.vramUtilizationRatio", "name": "vramUtilizationRatio", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.coreUtilizationRatio", "name": "coreUtilizationRatio", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.atTargetLoad", "name": "atTargetLoad", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.canAllocateGPU", "name": "canAllocateGPU", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.allocateTask", "name": "allocateTask", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.resourceInvariant", "name": "resourceInvariant", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.resourceCost", "name": "resourceCost", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.resourceBind", "name": "resourceBind", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.gpuAtTarget", "name": "gpuAtTarget", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.gpuUnderUtilized", "name": "gpuUnderUtilized", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.gpuOverUtilized", "name": "gpuOverUtilized", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.gpuTask", "name": "gpuTask", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.cpuTask", "name": "cpuTask", "module": "Semantics.GPUResourceManager" }, { "kind": "def", "id": "Semantics.GPUResourceManager.idleGPU", "name": "idleGPU", "module": "Semantics.GPUResourceManager" }, { "kind": "module", "id": "Semantics.GemmaIntegration", "name": "GemmaIntegration", "path": "Semantics/GemmaIntegration.lean", "namespace": "Semantics.GemmaIntegration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GemmaIntegration.lean \u2014 Gemma 4 Integration Prompt Routing Replaces infra/gemma_4_integration.py prompt routing logic with a formal Lean module. Defines Gemma 4 model variants, task types, and prompt r", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 13, "struct_count": 4, "inductive_count": 3, "line_count": 229 }, { "kind": "theorem", "id": "Semantics.GemmaIntegration.e4BSupportsAudio", "name": "e4BSupportsAudio", "module": "Semantics.GemmaIntegration" }, { "kind": "theorem", "id": "Semantics.GemmaIntegration.e4BIsNotMoE", "name": "e4BIsNotMoE", "module": "Semantics.GemmaIntegration" }, { "kind": "theorem", "id": "Semantics.GemmaIntegration.audioTranscriptionRequiresAudio", "name": "audioTranscriptionRequiresAudio", "module": "Semantics.GemmaIntegration" }, { "kind": "theorem", "id": "Semantics.GemmaIntegration.e4BCompatibleWithTextGen", "name": "e4BCompatibleWithTextGen", "module": "Semantics.GemmaIntegration" }, { "kind": "theorem", "id": "Semantics.GemmaIntegration.emptyRegistryHasNoMetrics", "name": "emptyRegistryHasNoMetrics", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.zero", "name": "zero", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.one", "name": "one", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.ofFrac", "name": "ofFrac", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.gemmaVariantSize", "name": "gemmaVariantSize", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.supportsAudio", "name": "supportsAudio", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.isMoEModel", "name": "isMoEModel", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.requiresAudio", "name": "requiresAudio", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.requiresMultimodal", "name": "requiresMultimodal", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.isVariantCompatible", "name": "isVariantCompatible", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.getRecommendedVariant", "name": "getRecommendedVariant", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.initMetricsRegistry", "name": "initMetricsRegistry", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.updateMetrics", "name": "updateMetrics", "module": "Semantics.GemmaIntegration" }, { "kind": "def", "id": "Semantics.GemmaIntegration.getVariantMetrics", "name": "getVariantMetrics", "module": "Semantics.GemmaIntegration" }, { "kind": "module", "id": "Semantics.GeneBytecodeJIT", "name": "GeneBytecodeJIT", "path": "Semantics/GeneBytecodeJIT.lean", "namespace": "Semantics.GeneBytecodeJIT", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 4, "inductive_count": 1, "line_count": 85 }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.zero", "name": "zero", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.one", "name": "one", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.ofNat", "name": "ofNat", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.toNat", "name": "toNat", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.ofFrac", "name": "ofFrac", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "def", "id": "Semantics.GeneBytecodeJIT.runSampleJit", "name": "runSampleJit", "module": "Semantics.GeneBytecodeJIT" }, { "kind": "module", "id": "Semantics.GenerateLUT", "name": "GenerateLUT", "path": "Semantics/GenerateLUT.lean", "namespace": "Semantics.GenerateLUT", "doc": "Verified LUT Entry Generator: Precomputes RGFlow trajectories purely in the Lean runtime.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 58 }, { "kind": "def", "id": "Semantics.GenerateLUT.computeEntry", "name": "computeEntry", "module": "Semantics.GenerateLUT" }, { "kind": "def", "id": "Semantics.GenerateLUT.runGeneration", "name": "runGeneration", "module": "Semantics.GenerateLUT" }, { "kind": "module", "id": "Semantics.GeneticBraidBridge", "name": "GeneticBraidBridge", "path": "Semantics/GeneticBraidBridge.lean", "namespace": "Semantics.GeneticBraidBridge", "doc": "GeneticBraidBridge.lean -- Genetic Sequence to BraidState Translation Maps any supported genetic alphabet (DNA, RNA, mRNA, Hachimoji, XNA, 6-state) to a BraidState via braid word composition on the 8-strand BraidStorm topology. Each symbol is assigned to a primary strand (0-7) based on its ordinal", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 14, "struct_count": 0, "inductive_count": 3, "line_count": 242 }, { "kind": "theorem", "id": "Semantics.GeneticBraidBridge.ordinal_mod_lt", "name": "ordinal_mod_lt", "module": "Semantics.GeneticBraidBridge" }, { "kind": "theorem", "id": "Semantics.GeneticBraidBridge.genetic_eigensolid_convergence", "name": "genetic_eigensolid_convergence", "module": "Semantics.GeneticBraidBridge" }, { "kind": "theorem", "id": "Semantics.GeneticBraidBridge.genetic_receipt_invertible", "name": "genetic_receipt_invertible", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.alphabetSize", "name": "alphabetSize", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.codonLength", "name": "codonLength", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.numCodons", "name": "numCodons", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.symbolOrdinal", "name": "symbolOrdinal", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.symbolToStrand", "name": "symbolToStrand", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.defaultSidonLabels", "name": "defaultSidonLabels", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.initialState", "name": "initialState", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.pairStrand", "name": "pairStrand", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.applySymbol", "name": "applySymbol", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.applyGeneticWord", "name": "applyGeneticWord", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.geneticReceipt", "name": "geneticReceipt", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.stringToWord", "name": "stringToWord", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.testWord", "name": "testWord", "module": "Semantics.GeneticBraidBridge" }, { "kind": "def", "id": "Semantics.GeneticBraidBridge.testState", "name": "testState", "module": "Semantics.GeneticBraidBridge" }, { "kind": "module", "id": "Semantics.GeneticCode", "name": "GeneticCode", "path": "Semantics/GeneticCode.lean", "namespace": "Semantics.GeneticCode", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeneticCode.lean \u2014 Standard Genetic Code (NCBI Table 1) This module formalizes the biological genetic code translation from DNA/RNA codons to amino acids. It provides: \u2022 DNA base representation (A, T, ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 2, "line_count": 189 }, { "kind": "def", "id": "Semantics.GeneticCode.eventBits", "name": "eventBits", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.parityOfEvent", "name": "parityOfEvent", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.AminoAcid", "name": "AminoAcid", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.Codon", "name": "Codon", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.geneticCode", "name": "geneticCode", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.isStartCodon", "name": "isStartCodon", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.isStopCodon", "name": "isStopCodon", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.codonDegeneracy", "name": "codonDegeneracy", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.exampleStartCodon", "name": "exampleStartCodon", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.exampleStopCodon", "name": "exampleStopCodon", "module": "Semantics.GeneticCode" }, { "kind": "def", "id": "Semantics.GeneticCode.examplePheCodon", "name": "examplePheCodon", "module": "Semantics.GeneticCode" }, { "kind": "module", "id": "Semantics.GeneticCodeOptimization", "name": "GeneticCodeOptimization", "path": "Semantics/GeneticCodeOptimization.lean", "namespace": "Semantics.GeneticCodeOptimization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeneticCodeOptimization.lean \u2014 Formalization of Winning Genetic Code Equation Implements the winning equation from genetic code hypothesis generation: I = (H \u00d7 G) \u00d7 (1 - (D / 64)) Key contributions: 1", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 6, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 201 }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.geneticOptimizationBounded", "name": "geneticOptimizationBounded", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.degeneracyBounded", "name": "degeneracyBounded", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.informationDensityBounded", "name": "informationDensityBounded", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.errorResistanceBounded", "name": "errorResistanceBounded", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.compressionEfficiencyBounded", "name": "compressionEfficiencyBounded", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "theorem", "id": "Semantics.GeneticCodeOptimization.targetsBelowMaximum", "name": "targetsBelowMaximum", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.computeGeneticOptimization", "name": "computeGeneticOptimization", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.targetInformationDensity", "name": "targetInformationDensity", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.targetErrorResistance", "name": "targetErrorResistance", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.targetCompressionEfficiency", "name": "targetCompressionEfficiency", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.maxDegeneracy", "name": "maxDegeneracy", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.computeInformationDensity", "name": "computeInformationDensity", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.computeErrorResistance", "name": "computeErrorResistance", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.computeCompressionEfficiency", "name": "computeCompressionEfficiency", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.beatsInformationTarget", "name": "beatsInformationTarget", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.beatsErrorTarget", "name": "beatsErrorTarget", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "def", "id": "Semantics.GeneticCodeOptimization.beatsCompressionTarget", "name": "beatsCompressionTarget", "module": "Semantics.GeneticCodeOptimization" }, { "kind": "module", "id": "Semantics.GeneticFieldEquation", "name": "GeneticFieldEquation", "path": "Semantics/GeneticFieldEquation.lean", "namespace": "Semantics.GeneticFieldEquation", "doc": "GeneticFieldEquation.lean -- Species-Dependent P0 via Semantic Mass Numbers The user's reframing: P0 is not universal or fitted \u2014 it is EMERGENT from each species' genetic field equation, and the output is checked through the MassNumber admissibility gate. STRUCTURE: 1. Genetic parameters (species", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 15, "def_count": 23, "struct_count": 1, "inductive_count": 0, "line_count": 466 }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.for", "name": "for", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.geneticInvariantCloseTo3", "name": "geneticInvariantCloseTo3", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.geneticInvariantDifference", "name": "geneticInvariantDifference", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.sardineP0Derived", "name": "sardineP0Derived", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.sardineResidualSmall", "name": "sardineResidualSmall", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.earlyHumanP0Derived", "name": "earlyHumanP0Derived", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.modernHumanP0Derived", "name": "modernHumanP0Derived", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.upperLimitHumanP0Derived", "name": "upperLimitHumanP0Derived", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.earlyHumanResidualLarge", "name": "earlyHumanResidualLarge", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.modernHumanResidualLarge", "name": "modernHumanResidualLarge", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.upperLimitHumanResidualLarge", "name": "upperLimitHumanResidualLarge", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.correctedSardineAdmissible", "name": "correctedSardineAdmissible", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.correctedEarlyHumanNotAdmissible", "name": "correctedEarlyHumanNotAdmissible", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.correctedModernHumanNotAdmissible", "name": "correctedModernHumanNotAdmissible", "module": "Semantics.GeneticFieldEquation" }, { "kind": "theorem", "id": "Semantics.GeneticFieldEquation.correctedUpperLimitHumanNotAdmissible", "name": "correctedUpperLimitHumanNotAdmissible", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.geneticInvariantRatio", "name": "geneticInvariantRatio", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.earlyHumanParameters", "name": "earlyHumanParameters", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.modernHumanParameters", "name": "modernHumanParameters", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.upperLimitHumanParameters", "name": "upperLimitHumanParameters", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.sardineParameters", "name": "sardineParameters", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.eColiParameters", "name": "eColiParameters", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.semanticCountK5", "name": "semanticCountK5", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.p0ToQ16_16", "name": "p0ToQ16_16", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.deriveP0FromObservation", "name": "deriveP0FromObservation", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.computeResidual", "name": "computeResidual", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.geneticMassNumber", "name": "geneticMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.sardineMassNumber", "name": "sardineMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.earlyHumanMassNumber", "name": "earlyHumanMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.modernHumanMassNumber", "name": "modernHumanMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.upperLimitHumanMassNumber", "name": "upperLimitHumanMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.eColiMassNumber", "name": "eColiMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.oldGateSemanticsNote", "name": "oldGateSemanticsNote", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.correctedGeneticMassNumber", "name": "correctedGeneticMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.correctedSardineMassNumber", "name": "correctedSardineMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "def", "id": "Semantics.GeneticFieldEquation.correctedEarlyHumanMassNumber", "name": "correctedEarlyHumanMassNumber", "module": "Semantics.GeneticFieldEquation" }, { "kind": "module", "id": "Semantics.GeneticGroundUp", "name": "GeneticGroundUp", "path": "Semantics/GeneticGroundUp.lean", "namespace": "Semantics.GeneticGroundUp", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeneticGroundUp.lean \u2014 Ground-Up Genetic System Redesign Formalizes the swarm-designed genetic architecture: Quantum nucleotide encoding (6 states: A/T/C/G/U/X) Compiled gene kernels (native execution,", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 35, "struct_count": 11, "inductive_count": 3, "line_count": 404 }, { "kind": "theorem", "id": "Semantics.GeneticGroundUp.quantumBaseProbValid", "name": "quantumBaseProbValid", "module": "Semantics.GeneticGroundUp" }, { "kind": "theorem", "id": "Semantics.GeneticGroundUp.genomeFaultTolerance", "name": "genomeFaultTolerance", "module": "Semantics.GeneticGroundUp" }, { "kind": "theorem", "id": "Semantics.GeneticGroundUp.metabolicThroughputNonNeg", "name": "metabolicThroughputNonNeg", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.Nucleotide", "name": "Nucleotide", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.expressionProb", "name": "expressionProb", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.bindingEnergy", "name": "bindingEnergy", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.foldAngle", "name": "foldAngle", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.Prob01", "name": "Prob01", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.NonnegQ16_16", "name": "NonnegQ16_16", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.probAmpSq", "name": "probAmpSq", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.getExpressionProb", "name": "getExpressionProb", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.informationContentApprox", "name": "informationContentApprox", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.isRecent", "name": "isRecent", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.CompilationStage", "name": "CompilationStage", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.targetFoldTime200Residue", "name": "targetFoldTime200Residue", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.targetFoldTimeForResidues", "name": "targetFoldTimeForResidues", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.achievedTargetSpeed", "name": "achievedTargetSpeed", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.stabilityThreshold", "name": "stabilityThreshold", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.isStable", "name": "isStable", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.OptimizationObjective", "name": "OptimizationObjective", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.messagePassing", "name": "messagePassing", "module": "Semantics.GeneticGroundUp" }, { "kind": "def", "id": "Semantics.GeneticGroundUp.speedupTarget", "name": "speedupTarget", "module": "Semantics.GeneticGroundUp" }, { "kind": "module", "id": "Semantics.GeneticOptimizerVerification", "name": "GeneticOptimizerVerification", "path": "Semantics/GeneticOptimizerVerification.lean", "namespace": "Semantics.GeneticOptimizerVerification", "doc": "GeneticOptimizerVerification.lean \u2014 Formal Verification of Genetic Basis Optimizer Invariants This module formalizes the statistical context blending operations used in the genetic basis optimizer. It verifies the mathematical invariants of our search space priors using Lean 4 and ensures strict co", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 0, "inductive_count": 0, "line_count": 235 }, { "kind": "theorem", "id": "Semantics.GeneticOptimizerVerification.add_zero_of_nonneg", "name": "add_zero_of_nonneg", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "theorem", "id": "Semantics.GeneticOptimizerVerification.zero_add_of_nonneg", "name": "zero_add_of_nonneg", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "theorem", "id": "Semantics.GeneticOptimizerVerification.mul_nonneg_preserves_nonneg", "name": "mul_nonneg_preserves_nonneg", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "theorem", "id": "Semantics.GeneticOptimizerVerification.emptyCountsBlendedProbability", "name": "emptyCountsBlendedProbability", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.basisLength", "name": "basisLength", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.prior", "name": "prior", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.exactPriorSum", "name": "exactPriorSum", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.blendTransition", "name": "blendTransition", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.blendProbability", "name": "blendProbability", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.sampleBasis", "name": "sampleBasis", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.testPriorCalculation", "name": "testPriorCalculation", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.testExactPriorSum", "name": "testExactPriorSum", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "def", "id": "Semantics.GeneticOptimizerVerification.testIEEE754Boundary", "name": "testIEEE754Boundary", "module": "Semantics.GeneticOptimizerVerification" }, { "kind": "module", "id": "Semantics.GeneticsPromotionGate", "name": "GeneticsPromotionGate", "path": "Semantics/GeneticsPromotionGate.lean", "namespace": "Semantics.GeneticsPromotionGate", "doc": "GeneticsPromotionGate.lean \u2014 Mass Number Gate for Genetics Model Promotion Wires the core MassNumber admissibility gate into genetics-specific promotion. Every genetics model must pass this gate before being promoted from REGISTRY_ONLY \u2192 CANONICAL_PLUMBED. Gate criteria: 1. MassLeDefault (admissib", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 21, "struct_count": 1, "inductive_count": 1, "line_count": 296 }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.defaultClaim", "name": "defaultClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.admissibleReduction", "name": "admissibleReduction", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.residualRisk", "name": "residualRisk", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.geneticsPromotionGate", "name": "geneticsPromotionGate", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.biologicalEquivalenceWarden", "name": "biologicalEquivalenceWarden", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.geneticCodeClaim", "name": "geneticCodeClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.codonOTOMClaim", "name": "codonOTOMClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.peptideMoEClaim", "name": "peptideMoEClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.genomicCompressionClaim", "name": "genomicCompressionClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.syntheticGeneticCodingClaim", "name": "syntheticGeneticCodingClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.geneticGroundUpClaim", "name": "geneticGroundUpClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.hachimojiClaim", "name": "hachimojiClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.codonPeptideConsistencyClaim", "name": "codonPeptideConsistencyClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.allelicaClaim", "name": "allelicaClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.auditCanonicalModels", "name": "auditCanonicalModels", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.registryOnlyClaim", "name": "registryOnlyClaim", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.auditRegistryOnlyModels", "name": "auditRegistryOnlyModels", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.conservativeThreshold", "name": "conservativeThreshold", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.defaultThreshold", "name": "defaultThreshold", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "def", "id": "Semantics.GeneticsPromotionGate.generousThreshold", "name": "generousThreshold", "module": "Semantics.GeneticsPromotionGate" }, { "kind": "module", "id": "Semantics.Genome18", "name": "Genome18", "path": "Semantics/Genome18.lean", "namespace": "Semantics", "doc": "Structure: 6 bins \u00d7 3 bits = 18 bits (8^6 = 262,144 states) Bin meanings: muBin: mutation / drift bin (routing load) rhoBin: verification pressure bin (routing efficiency) cBin: connectance bin (geometry / route neighborhood) mBin: compression residue / modularity bin (entropy) neBin: observer mass", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 2, "def_count": 2, "struct_count": 1, "inductive_count": 0, "line_count": 91 }, { "kind": "theorem", "id": "Semantics.Genome18.addr_injective", "name": "addr_injective", "module": "Semantics.Genome18" }, { "kind": "theorem", "id": "Semantics.Genome18.addr_range", "name": "addr_range", "module": "Semantics.Genome18" }, { "kind": "def", "id": "Semantics.Genome18.addr", "name": "addr", "module": "Semantics.Genome18" }, { "kind": "def", "id": "Semantics.Genome18.default", "name": "default", "module": "Semantics.Genome18" }, { "kind": "module", "id": "Semantics.GenomicCompression.Components", "name": "Components", "path": "Semantics/GenomicCompression/Components.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.Components.lean \u2014 Component Structures for Genomic Compression This module contains the component structures for the genomic compression field, including NormalizedComponents (normal", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 3, "inductive_count": 0, "line_count": 128 }, { "kind": "def", "id": "Semantics.GenomicCompression.Components.cpgIslandDefault", "name": "cpgIslandDefault", "module": "Semantics.GenomicCompression.Components" }, { "kind": "def", "id": "Semantics.GenomicCompression.Components.codingRegionDefault", "name": "codingRegionDefault", "module": "Semantics.GenomicCompression.Components" }, { "kind": "def", "id": "Semantics.GenomicCompression.Components.dnaMethylationDefault", "name": "dnaMethylationDefault", "module": "Semantics.GenomicCompression.Components" }, { "kind": "def", "id": "Semantics.GenomicCompression.Components.proteinStructureDefault", "name": "proteinStructureDefault", "module": "Semantics.GenomicCompression.Components" }, { "kind": "def", "id": "Semantics.GenomicCompression.Components.totalWeight", "name": "totalWeight", "module": "Semantics.GenomicCompression.Components" }, { "kind": "module", "id": "Semantics.GenomicCompression.Compression", "name": "Compression", "path": "Semantics/GenomicCompression/Compression.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.Compression.lean \u2014 Compression Operations for Genomic Data This module contains the compression functions for genomic data, including windowed compression, protein structure compress", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 108 }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressionRatioSI", "name": "compressionRatioSI", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressionPercentage", "name": "compressionPercentage", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressWindow", "name": "compressWindow", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressDNAWindows", "name": "compressDNAWindows", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressProtein", "name": "compressProtein", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "def", "id": "Semantics.GenomicCompression.Compression.compressGRN", "name": "compressGRN", "module": "Semantics.GenomicCompression.Compression" }, { "kind": "module", "id": "Semantics.GenomicCompression.Field", "name": "Field", "path": "Semantics/GenomicCompression/Field.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.Field.lean \u2014 Unified Field Functions for Genomic Compression This module contains the unified field computation functions for genomic compression, including phiGenomic, effective ent", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 62 }, { "kind": "def", "id": "Semantics.GenomicCompression.Field.phiGenomicRaw", "name": "phiGenomicRaw", "module": "Semantics.GenomicCompression.Field" }, { "kind": "def", "id": "Semantics.GenomicCompression.Field.phiGenomic", "name": "phiGenomic", "module": "Semantics.GenomicCompression.Field" }, { "kind": "def", "id": "Semantics.GenomicCompression.Field.effectiveEntropy", "name": "effectiveEntropy", "module": "Semantics.GenomicCompression.Field" }, { "kind": "def", "id": "Semantics.GenomicCompression.Field.effectiveInfo", "name": "effectiveInfo", "module": "Semantics.GenomicCompression.Field" }, { "kind": "module", "id": "Semantics.GenomicCompression.NonDriftProof", "name": "NonDriftProof", "path": "Semantics/GenomicCompression/NonDriftProof.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.NonDriftProof.lean \u2014 Non-Drift Proof for Genomic Compression This module contains the formal proof that the transformation from the original to the refined formulation is mathematica", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 2, "struct_count": 2, "inductive_count": 0, "line_count": 398 }, { "kind": "theorem", "id": "Semantics.GenomicCompression.NonDriftProof.originalViolatesBoundedness", "name": "originalViolatesBoundedness", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.NonDriftProof.originalHasSignError", "name": "originalHasSignError", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.NonDriftProof.refinedSatisfiesBoundedness", "name": "refinedSatisfiesBoundedness", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.NonDriftProof.refinedCorrectEntropySignRaw", "name": "refinedCorrectEntropySignRaw", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.NonDriftProof.transformationIsDerivable", "name": "transformationIsDerivable", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "def", "id": "Semantics.GenomicCompression.NonDriftProof.phiOriginal", "name": "phiOriginal", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "def", "id": "Semantics.GenomicCompression.NonDriftProof.phiRefined", "name": "phiRefined", "module": "Semantics.GenomicCompression.NonDriftProof" }, { "kind": "module", "id": "Semantics.GenomicCompression.Theorems", "name": "Theorems", "path": "Semantics/GenomicCompression/Theorems.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.Theorems.lean \u2014 Theorems for Genomic Compression This module contains theorems about the genomic compression field, including boundedness properties and monotonicity results. Per AG", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 134 }, { "kind": "theorem", "id": "Semantics.GenomicCompression.Theorems.phiGenomicBounded", "name": "phiGenomicBounded", "module": "Semantics.GenomicCompression.Theorems" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.Theorems.hierarchyImprovesPhiRaw", "name": "hierarchyImprovesPhiRaw", "module": "Semantics.GenomicCompression.Theorems" }, { "kind": "theorem", "id": "Semantics.GenomicCompression.Theorems.compressionEfficiencyBounded", "name": "compressionEfficiencyBounded", "module": "Semantics.GenomicCompression.Theorems" }, { "kind": "module", "id": "Semantics.GenomicCompression.Types", "name": "Types", "path": "Semantics/GenomicCompression/Types.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.Types.lean \u2014 Basic Types for Genomic Compression This module contains the fundamental type definitions for genomic compression, including nucleotides, DNA sequences, amino acids, pro", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 9, "inductive_count": 2, "line_count": 123 }, { "kind": "module", "id": "Semantics.GenomicCompression", "name": "GenomicCompression", "path": "Semantics/GenomicCompression.lean", "namespace": "Semantics.GenomicCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GenomicCompression.lean \u2014 Orchestrator for Genomic Compression Modules This module serves as the orchestrator for the Genomic Compression framework, importing and re-exporting all core sub-modules for ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 78 }, { "kind": "module", "id": "Semantics.Genus1MengerEmbedding", "name": "Genus1MengerEmbedding", "path": "Semantics/Genus1MengerEmbedding.lean", "namespace": "Semantics.Genus1MengerEmbedding", "doc": "Genus1MengerEmbedding.lean -- Menger Sponge Embedded at Level 0 of 16D Genus-1 Model The user corrects our approach: instead of building a standalone topology extension, embed the Menger sponge's mathematical facts into the EXISTING 16D genus-1 model at level 0. Key insight: The 16D model (Q16_16 ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 16, "def_count": 12, "struct_count": 0, "inductive_count": 0, "line_count": 361 }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.for", "name": "for", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.levelZeroSharedCell", "name": "levelZeroSharedCell", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.lanePeriodIsProduct", "name": "lanePeriodIsProduct", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.voidFractionAsSubdivisionPower", "name": "voidFractionAsSubdivisionPower", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.mengerLevel0Torsion", "name": "mengerLevel0Torsion", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.mengerLevel3Torsion", "name": "mengerLevel3Torsion", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.mengerLevel4Torsion", "name": "mengerLevel4Torsion", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.mengerRatioMapsToTorusPhase", "name": "mengerRatioMapsToTorusPhase", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.volumeCollapseAtK5", "name": "volumeCollapseAtK5", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.volumeCollapseBounded", "name": "volumeCollapseBounded", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.surfaceAreaExplosionAtK5", "name": "surfaceAreaExplosionAtK5", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.growthFactorPositive", "name": "growthFactorPositive", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.universalCurveLevel0", "name": "universalCurveLevel0", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.avmTraceIsDiscreteEmbeddingK3", "name": "avmTraceIsDiscreteEmbeddingK3", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.scaleAtK5IsCorrect", "name": "scaleAtK5IsCorrect", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "theorem", "id": "Semantics.Genus1MengerEmbedding.q16BridgeIsDomainAgnostic", "name": "q16BridgeIsDomainAgnostic", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.levelZeroMengerVolume", "name": "levelZeroMengerVolume", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.levelZeroMengerSurfaceArea", "name": "levelZeroMengerSurfaceArea", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.levelZeroEulerCharacteristic", "name": "levelZeroEulerCharacteristic", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.levelZeroFirstBettiNumber", "name": "levelZeroFirstBettiNumber", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.mengerSubdivisionFactor", "name": "mengerSubdivisionFactor", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.torusCycleCount", "name": "torusCycleCount", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.c1c2LanePeriod", "name": "c1c2LanePeriod", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.mengerLevelToTorsionStep", "name": "mengerLevelToTorsionStep", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.mengerVolumeAtK5", "name": "mengerVolumeAtK5", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.threeAdicScaleQ16", "name": "threeAdicScaleQ16", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.scaleAtK5Q16", "name": "scaleAtK5Q16", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "def", "id": "Semantics.Genus1MengerEmbedding.genus1MengerEmbeddingStatus", "name": "genus1MengerEmbeddingStatus", "module": "Semantics.Genus1MengerEmbedding" }, { "kind": "module", "id": "Semantics.GeometricCompressionWorkspace", "name": "GeometricCompressionWorkspace", "path": "Semantics/GeometricCompressionWorkspace.lean", "namespace": "Semantics.GeometricCompressionWorkspace", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeometricCompressionWorkspace.lean \u2014 Four-Zone Workspace for LLM Search This module implements the concrete workspace where source objects are projected into Q0_64 coding atoms, embedded into geometric", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 3, "def_count": 20, "struct_count": 18, "inductive_count": 3, "line_count": 963 }, { "kind": "theorem", "id": "Semantics.GeometricCompressionWorkspace.promoteTrial_preserves_receipt_gate", "name": "promoteTrial_preserves_receipt_gate", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "theorem", "id": "Semantics.GeometricCompressionWorkspace.promoteTrialLedger_preserves_invariant", "name": "promoteTrialLedger_preserves_invariant", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "theorem", "id": "Semantics.GeometricCompressionWorkspace.projectionOrdering", "name": "projectionOrdering", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.projectToCoding", "name": "projectToCoding", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.codingFromRatio", "name": "codingFromRatio", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.embedToSurface2D", "name": "embedToSurface2D", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.makePerturbation", "name": "makePerturbation", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.identityCollapse", "name": "identityCollapse", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.lowRankCollapseTemplate", "name": "lowRankCollapseTemplate", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.runDpglAudit", "name": "runDpglAudit", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.wardenValidate", "name": "wardenValidate", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.runBenchmark", "name": "runBenchmark", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.voxel3DToNVoxel", "name": "voxel3DToNVoxel", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.proposeRepairForPattern", "name": "proposeRepairForPattern", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.classifyWardenEmission", "name": "classifyWardenEmission", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.buildAutopoiesis", "name": "buildAutopoiesis", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.hasProofReceipt", "name": "hasProofReceipt", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.promoteTrial", "name": "promoteTrial", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.promoteTrialLedger", "name": "promoteTrialLedger", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.runAdversarialTrial", "name": "runAdversarialTrial", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.titanWaveHeight", "name": "titanWaveHeight", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.lavaWaveHeight", "name": "lavaWaveHeight", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "def", "id": "Semantics.GeometricCompressionWorkspace.testVoxel3D", "name": "testVoxel3D", "module": "Semantics.GeometricCompressionWorkspace" }, { "kind": "module", "id": "Semantics.GeometricTopology", "name": "GeometricTopology", "path": "Semantics/GeometricTopology.lean", "namespace": "Semantics.GeometricTopology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeometricTopology.lean \u2014 Substrate-Agnostic Manifold Topology The topology is not a graph of nodes and edges. It is a geometric manifold: one continuous hypershape embedded in n-space. Every point is ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 14, "struct_count": 3, "inductive_count": 0, "line_count": 230 }, { "kind": "theorem", "id": "Semantics.GeometricTopology.flatMetricNotShore", "name": "flatMetricNotShore", "module": "Semantics.GeometricTopology" }, { "kind": "theorem", "id": "Semantics.GeometricTopology.chartOriginIsCenter", "name": "chartOriginIsCenter", "module": "Semantics.GeometricTopology" }, { "kind": "theorem", "id": "Semantics.GeometricTopology.singleChartNoQuorum", "name": "singleChartNoQuorum", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.chartOrigin", "name": "chartOrigin", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.flatMetric", "name": "flatMetric", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.metricDet", "name": "metricDet", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.infiniteShoreEquation", "name": "infiniteShoreEquation", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.isShoreChart", "name": "isShoreChart", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.atlasCoversPoint", "name": "atlasCoversPoint", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.atlasEquivalent", "name": "atlasEquivalent", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.geodesicStep", "name": "geodesicStep", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.geodesicDistance", "name": "geodesicDistance", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.geometricQuorum", "name": "geometricQuorum", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.earthChart", "name": "earthChart", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.marsChart", "name": "marsChart", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.plutoChart", "name": "plutoChart", "module": "Semantics.GeometricTopology" }, { "kind": "def", "id": "Semantics.GeometricTopology.solarSystemAtlas", "name": "solarSystemAtlas", "module": "Semantics.GeometricTopology" }, { "kind": "module", "id": "Semantics.Geometry.Behavioral", "name": "Behavioral", "path": "Semantics/Geometry/Behavioral.lean", "namespace": "Semantics.Geometry.Behavioral", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Behavioral.lean \u2014 Behavioral distance on the 31-dimensional equation manifold. Domain-weighted L1 metric for measuring distance between behavioral points.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 140 }, { "kind": "theorem", "id": "Semantics.Geometry.Behavioral.behavioralDistanceSelfZeroOne", "name": "behavioralDistanceSelfZeroOne", "module": "Semantics.Geometry.Behavioral" }, { "kind": "theorem", "id": "Semantics.Geometry.Behavioral.behavioralDistanceZeroToTwo", "name": "behavioralDistanceZeroToTwo", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.domainOf", "name": "domainOf", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.domainWeight", "name": "domainWeight", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.BehavioralPoint", "name": "BehavioralPoint", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.behavioralDistanceL1", "name": "behavioralDistanceL1", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.midpoint", "name": "midpoint", "module": "Semantics.Geometry.Behavioral" }, { "kind": "def", "id": "Semantics.Geometry.Behavioral.onGeodesic", "name": "onGeodesic", "module": "Semantics.Geometry.Behavioral" }, { "kind": "module", "id": "Semantics.Geometry.BehavioralBind", "name": "BehavioralBind", "path": "Semantics/Geometry/BehavioralBind.lean", "namespace": "Semantics.Geometry.BehavioralBind", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team BehavioralBind.lean \u2014 geometric_bind instance for behavioral distance. Lawful check, cost function, and invariant extractor for the behavioral manifold navigation primitive.", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 68 }, { "kind": "def", "id": "Semantics.Geometry.BehavioralBind.behavioralLawful", "name": "behavioralLawful", "module": "Semantics.Geometry.BehavioralBind" }, { "kind": "def", "id": "Semantics.Geometry.BehavioralBind.behavioralCost", "name": "behavioralCost", "module": "Semantics.Geometry.BehavioralBind" }, { "kind": "def", "id": "Semantics.Geometry.BehavioralBind.behavioralInvariant", "name": "behavioralInvariant", "module": "Semantics.Geometry.BehavioralBind" }, { "kind": "def", "id": "Semantics.Geometry.BehavioralBind.resolveGeodesic", "name": "resolveGeodesic", "module": "Semantics.Geometry.BehavioralBind" }, { "kind": "module", "id": "Semantics.Geometry.Cascade", "name": "Cascade", "path": "Semantics/Geometry/Cascade.lean", "namespace": "Semantics.Geometry.Cascade", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Cascade.lean \u2014 Representation cascade: Tile \u2192 Cube \u2192 ... \u2192 Triangle Dimensional uplift and cost model for constraint propagation.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 10, "struct_count": 1, "inductive_count": 1, "line_count": 188 }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.simplexCheaperThanCube", "name": "simplexCheaperThanCube", "module": "Semantics.Geometry.Cascade" }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.triangleFewerFacetsThanTile", "name": "triangleFewerFacetsThanTile", "module": "Semantics.Geometry.Cascade" }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.triangleCheaperThanTile", "name": "triangleCheaperThanTile", "module": "Semantics.Geometry.Cascade" }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.peakGreaterThanPreceding", "name": "peakGreaterThanPreceding", "module": "Semantics.Geometry.Cascade" }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.cascadePathLength", "name": "cascadePathLength", "module": "Semantics.Geometry.Cascade" }, { "kind": "theorem", "id": "Semantics.Geometry.Cascade.cascadeTotalCostEqualsSum", "name": "cascadeTotalCostEqualsSum", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.simplexCost", "name": "simplexCost", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.cubeCost", "name": "cubeCost", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.xorAllFacets", "name": "xorAllFacets", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.uplift", "name": "uplift", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.upliftCost", "name": "upliftCost", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.stageDim", "name": "stageDim", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.stageFacetCount", "name": "stageFacetCount", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.stageCost", "name": "stageCost", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.cascadePath", "name": "cascadePath", "module": "Semantics.Geometry.Cascade" }, { "kind": "def", "id": "Semantics.Geometry.Cascade.cascadeTotalCost", "name": "cascadeTotalCost", "module": "Semantics.Geometry.Cascade" }, { "kind": "module", "id": "Semantics.Geometry.CascadeBind", "name": "CascadeBind", "path": "Semantics/Geometry/CascadeBind.lean", "namespace": "Semantics.Geometry.CascadeBind", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CascadeBind.lean \u2014 geometric_bind instance for the representation cascade. Every cascade step (uplift, descent, compose) is a bind with lawful check, cost function, and invariant extractor.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 99 }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.cascadeLawful", "name": "cascadeLawful", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.cascadeCost", "name": "cascadeCost", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.cascadeInvariant", "name": "cascadeInvariant", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.behavioralLawful", "name": "behavioralLawful", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.behavioralCost", "name": "behavioralCost", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "def", "id": "Semantics.Geometry.CascadeBind.behavioralInvariant", "name": "behavioralInvariant", "module": "Semantics.Geometry.CascadeBind" }, { "kind": "module", "id": "Semantics.Geometry.CascadeDescent", "name": "CascadeDescent", "path": "Semantics/Geometry/CascadeDescent.lean", "namespace": "Semantics.Geometry.CascadeDescent", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CascadeDescent.lean \u2014 Barycentric descent: Triangle \u2192 Tile Composition of triangles into Wang tiles via shared-edge matching.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 153 }, { "kind": "theorem", "id": "Semantics.Geometry.CascadeDescent.validTriangleCorrect", "name": "validTriangleCorrect", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "theorem", "id": "Semantics.Geometry.CascadeDescent.descentProducesValid", "name": "descentProducesValid", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "theorem", "id": "Semantics.Geometry.CascadeDescent.composedTileFacetCount", "name": "composedTileFacetCount", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "def", "id": "Semantics.Geometry.CascadeDescent.isValidTriangle", "name": "isValidTriangle", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "def", "id": "Semantics.Geometry.CascadeDescent.composeTile", "name": "composeTile", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "def", "id": "Semantics.Geometry.CascadeDescent.descendToTriangle", "name": "descendToTriangle", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "def", "id": "Semantics.Geometry.CascadeDescent.tileOuterEdges", "name": "tileOuterEdges", "module": "Semantics.Geometry.CascadeDescent" }, { "kind": "module", "id": "Semantics.Geometry.ImplicitShellLattice", "name": "ImplicitShellLattice", "path": "Semantics/Geometry/ImplicitShellLattice.lean", "namespace": "Semantics.Geometry", "doc": "Copyright (c) 2026 Sovereign Stack. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Implicit Shell Lattice Formalization STL-free manufacturing math based on Xu Song/Wen Chen research. Direct mathematical description \u2192 laser path", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 3, "inductive_count": 2, "line_count": 222 }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.default", "name": "default", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.toLatticeUV", "name": "toLatticeUV", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.insideShell", "name": "insideShell", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.generateHybridToolpath", "name": "generateHybridToolpath", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.stlMeshSize", "name": "stlMeshSize", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.implicitSize", "name": "implicitSize", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.memoryReductionFactor", "name": "memoryReductionFactor", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.yieldStrengthImprovement", "name": "yieldStrengthImprovement", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.elongationImprovement", "name": "elongationImprovement", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.surfaceRoughnessRa", "name": "surfaceRoughnessRa", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.toShellCell", "name": "toShellCell", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "def", "id": "Semantics.Geometry.ImplicitShellLattice.shellToNUVMAP", "name": "shellToNUVMAP", "module": "Semantics.Geometry.ImplicitShellLattice" }, { "kind": "module", "id": "Semantics.Github", "name": "Github", "path": "Semantics/Github.lean", "namespace": "Semantics.Github", "doc": "GithubEvent: Structure for GitHub-side research ingestion.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.Github.githubPolicy", "name": "githubPolicy", "module": "Semantics.Github" }, { "kind": "def", "id": "Semantics.Github.toSourceEvent", "name": "toSourceEvent", "module": "Semantics.Github" }, { "kind": "def", "id": "Semantics.Github.githubInvariant", "name": "githubInvariant", "module": "Semantics.Github" }, { "kind": "def", "id": "Semantics.Github.githubCost", "name": "githubCost", "module": "Semantics.Github" }, { "kind": "def", "id": "Semantics.Github.githubBind", "name": "githubBind", "module": "Semantics.Github" }, { "kind": "module", "id": "Semantics.GlymphaticPumpConstraint", "name": "GlymphaticPumpConstraint", "path": "Semantics/GlymphaticPumpConstraint.lean", "namespace": "Semantics.GlymphaticPumpConstraint", "doc": "Glymphatic Pump Constraint \u2014 Extraction & Adaptation Source: Neuroscience News (2026-04-28) \u2014 \"Abdominal Movement Flushes Neural Waste\" DOI: [pending] \u2014 Mechanical coupling between abdominal micro-contractions and cerebrospinal fluid (CSF) clearance via hydraulic pressure. Core Finding: The brain ", "math_kind": "routing", "sorry_count": 0, "theorem_count": 1, "def_count": 10, "struct_count": 1, "inductive_count": 1, "line_count": 233 }, { "kind": "theorem", "id": "Semantics.GlymphaticPumpConstraint.safeCompressionWhenClearanceDominates", "name": "safeCompressionWhenClearanceDominates", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.microContractionRateHz", "name": "microContractionRateHz", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.glymphaticWaveRateHz", "name": "glymphaticWaveRateHz", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.pumpEfficacyRatio", "name": "pumpEfficacyRatio", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.pumpPhaseDutyCycle", "name": "pumpPhaseDutyCycle", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.safeCompressionWindowSeconds", "name": "safeCompressionWindowSeconds", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.precisionTierForPhase", "name": "precisionTierForPhase", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.compressionMultiplierForPhase", "name": "compressionMultiplierForPhase", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.weightedEffectiveMultiplier", "name": "weightedEffectiveMultiplier", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.standardHydraulicBoundary", "name": "standardHydraulicBoundary", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "def", "id": "Semantics.GlymphaticPumpConstraint.glymphaticAdaptationVerdict", "name": "glymphaticAdaptationVerdict", "module": "Semantics.GlymphaticPumpConstraint" }, { "kind": "module", "id": "Semantics.GoldenAngleEncoding", "name": "GoldenAngleEncoding", "path": "Semantics/GoldenAngleEncoding.lean", "namespace": "Semantics.GoldenAngleEncoding", "doc": "GoldenAngleEncoding.lean \u2014 Golden-Angle Phase Encoding for WaveProbe/WebRTC Surface Sampling Executable fixed-point phase sampling surface. The mathematical golden angle is represented by its Q0.16 turn-step approximation, avoiding noncomputable Real trigonometry in the verified core.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 10, "struct_count": 4, "inductive_count": 0, "line_count": 124 }, { "kind": "theorem", "id": "Semantics.GoldenAngleEncoding.computedPhaseKeepsIndex", "name": "computedPhaseKeepsIndex", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "theorem", "id": "Semantics.GoldenAngleEncoding.samePhaseSynchronizes", "name": "samePhaseSynchronizes", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "theorem", "id": "Semantics.GoldenAngleEncoding.generatedSamplesHaveZeroTimestamp", "name": "generatedSamplesHaveZeroTimestamp", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.phaseModulus", "name": "phaseModulus", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.goldenAngleStep", "name": "goldenAngleStep", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.q0OfNatMod", "name": "q0OfNatMod", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.computeGoldenAnglePhase", "name": "computeGoldenAnglePhase", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.examplePhases", "name": "examplePhases", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.phaseToSpherical", "name": "phaseToSpherical", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.generateWaveProbeSamples", "name": "generateWaveProbeSamples", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.rawPhase", "name": "rawPhase", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.cyclicDiff", "name": "cyclicDiff", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "def", "id": "Semantics.GoldenAngleEncoding.computePhaseDiff", "name": "computePhaseDiff", "module": "Semantics.GoldenAngleEncoding" }, { "kind": "module", "id": "Semantics.GoldenRatioSeparation", "name": "GoldenRatioSeparation", "path": "Semantics/GoldenRatioSeparation.lean", "namespace": "Semantics.GoldenRatioSeparation", "doc": "GoldenRatioSeparation.lean \u2014 Lemma 3.4 from Bloom-Sawin-Schildkraut-Zhelezov (2026) \"The sum-product conjecture is false for real numbers\" (arXiv: 2605.28781) Lemma 3.4 (Unit Separation): If K is a totally real number field of degree d \u2265 2, and u \u2208 O_K^\u00d7 is a unit such that \u03c6\u207b\u00b9 < |\u03c3\u1d62(u)| < \u03c6 for a", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 8, "def_count": 8, "struct_count": 0, "inductive_count": 0, "line_count": 166 }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.golden_angle_is_inverse_golden_ratio", "name": "golden_angle_is_inverse_golden_ratio", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.golden_ratio_squared_eq_plus_one", "name": "golden_ratio_squared_eq_plus_one", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.golden_angle_at_separation_boundary", "name": "golden_angle_at_separation_boundary", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.golden_angle_decodable", "name": "golden_angle_decodable", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.golden_angle_nontrivial", "name": "golden_angle_nontrivial", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.sidon_generator_coprime", "name": "sidon_generator_coprime", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.singer_density_lt_golden", "name": "singer_density_lt_golden", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "theorem", "id": "Semantics.GoldenRatioSeparation.singer_implies_golden_angle_sidon", "name": "singer_implies_golden_angle_sidon", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.goldenRatio", "name": "goldenRatio", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.goldenRatioInv", "name": "goldenRatioInv", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.goldenRatioSquared", "name": "goldenRatioSquared", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.unitSeparated", "name": "unitSeparated", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.sidonGenerator", "name": "sidonGenerator", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.slotDensityImprovement", "name": "slotDensityImprovement", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.singerModulus2", "name": "singerModulus2", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "def", "id": "Semantics.GoldenRatioSeparation.singerCard2", "name": "singerCard2", "module": "Semantics.GoldenRatioSeparation" }, { "kind": "module", "id": "Semantics.GoldenSpiralManifold", "name": "GoldenSpiralManifold", "path": "Semantics/GoldenSpiralManifold.lean", "namespace": "Semantics.GoldenSpiralManifold", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GoldenSpiralManifold.lean \u2014 Centerless Manifold with Golden Spiral Topology Formalizes a centerless mathematical structure where assignment operations spiral outward in a golden ratio configuration. P", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 2, "def_count": 5, "struct_count": 3, "inductive_count": 0, "line_count": 106 }, { "kind": "theorem", "id": "Semantics.GoldenSpiralManifold.spiralLayerIncreases", "name": "spiralLayerIncreases", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "theorem", "id": "Semantics.GoldenSpiralManifold.goldenAssignmentLayerNonNeg", "name": "goldenAssignmentLayerNonNeg", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "def", "id": "Semantics.GoldenSpiralManifold.goldenRatio", "name": "goldenRatio", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "def", "id": "Semantics.GoldenSpiralManifold.goldenAngleDeg", "name": "goldenAngleDeg", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "def", "id": "Semantics.GoldenSpiralManifold.spiralCoords", "name": "spiralCoords", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "def", "id": "Semantics.GoldenSpiralManifold.goldenAssignment", "name": "goldenAssignment", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "def", "id": "Semantics.GoldenSpiralManifold.initCenterlessManifold", "name": "initCenterlessManifold", "module": "Semantics.GoldenSpiralManifold" }, { "kind": "module", "id": "Semantics.GoldenSpiralNavigation", "name": "GoldenSpiralNavigation", "path": "Semantics/GoldenSpiralNavigation.lean", "namespace": "GoldenSpiral", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Golden angle (137.5\u00b0) navigation in equation manifold space for efficient coverage and discovery. Adapted from MOIM's Golden Spiral Navigator for equation-specific use: 1. Golden Angle: \u03b8 = 360\u00b0/\u03c6\u00b2 \u2248 137.5\u00b0 2. Spiral Se", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 1, "def_count": 14, "struct_count": 5, "inductive_count": 0, "line_count": 231 }, { "kind": "theorem", "id": "Semantics.GoldenSpiralNavigation.golden_angle_approx_137_5", "name": "golden_angle_approx_137_5", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.goldenAngle", "name": "goldenAngle", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.goldenAngleDegrees", "name": "goldenAngleDegrees", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.spiralToCartesian", "name": "spiralToCartesian", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.cartesianToSpiral", "name": "cartesianToSpiral", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.phinaryToSpiral", "name": "phinaryToSpiral", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.batchPhinaryToSpiral", "name": "batchPhinaryToSpiral", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.manifoldToSpiral", "name": "manifoldToSpiral", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.spiralStep5D", "name": "spiralStep5D", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.initNavigator", "name": "initNavigator", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.advanceNavigator", "name": "advanceNavigator", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.withinRadius", "name": "withinRadius", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.spiralSearch", "name": "spiralSearch", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.spiral_radius_monotonic", "name": "spiral_radius_monotonic", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "def", "id": "Semantics.GoldenSpiralNavigation.spiral_angle_increment", "name": "spiral_angle_increment", "module": "Semantics.GoldenSpiralNavigation" }, { "kind": "module", "id": "Semantics.GoormaghtighCert", "name": "GoormaghtighCert", "path": "Semantics/GoormaghtighCert.lean", "namespace": "Semantics.GoormaghtighCert", "doc": "============================================================ GOORMAGHTIGH CERTIFICATE DATA Machine-generated (or hand-constructed) SOS certificates for the Goormaghtigh collision polynomial. This file contains CONCRETE polynomial data \u2014 the output of the SDP solver, rationalized and imported into ", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 0, "inductive_count": 0, "line_count": 179 }, { "kind": "def", "id": "Semantics.GoormaghtighCert.validationCert1", "name": "validationCert1", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.validationCert2", "name": "validationCert2", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.validationCert3", "name": "validationCert3", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.validationCert4", "name": "validationCert4", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.validationCertWrong", "name": "validationCertWrong", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.goormaghtighConstraints", "name": "goormaghtighConstraints", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.goormaghtighTestCert", "name": "goormaghtighTestCert", "module": "Semantics.GoormaghtighCert" }, { "kind": "def", "id": "Semantics.GoormaghtighCert.goormaghtighFullCert", "name": "goormaghtighFullCert", "module": "Semantics.GoormaghtighCert" }, { "kind": "module", "id": "Semantics.GoormaghtighEnumeration", "name": "GoormaghtighEnumeration", "path": "Semantics/GoormaghtighEnumeration.lean", "namespace": "Semantics.GoormaghtighEnumeration", "doc": "GoormaghtighEnumeration.lean \u2014 Finite enumeration of Goormaghtigh collisions Within the BMS 2008 bounds (x \u2208 [2,90], m \u2208 [3,13]), we prove by exhaustive computation (native_decide) that the ONLY repunit collisions R(x,m) = R(y,n) with x < y are: 1. R(2,5) = R(5,3) = 31 2. R(2,13) = R(90,3) = 819", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 13, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 290 }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.repunit_2_5", "name": "repunit_2_5", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.repunit_5_3", "name": "repunit_5_3", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.repunit_2_13", "name": "repunit_2_13", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.repunit_90_3", "name": "repunit_90_3", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_col_31", "name": "goormaghtigh_col_31", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_col_8191", "name": "goormaghtigh_col_8191", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_bounded_uniqueness", "name": "goormaghtigh_bounded_uniqueness", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_value_31_or_8191", "name": "goormaghtigh_value_31_or_8191", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_conditional", "name": "goormaghtigh_conditional", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_x2_n3", "name": "goormaghtigh_x2_n3", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_complete", "name": "goormaghtigh_complete", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_conjecture", "name": "goormaghtigh_conjecture", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "theorem", "id": "Semantics.GoormaghtighEnumeration.goormaghtigh_sparse", "name": "goormaghtigh_sparse", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "def", "id": "Semantics.GoormaghtighEnumeration.repunit", "name": "repunit", "module": "Semantics.GoormaghtighEnumeration" }, { "kind": "module", "id": "Semantics.GossipFlipMessage", "name": "GossipFlipMessage", "path": "Semantics/GossipFlipMessage.lean", "namespace": "Semantics.GossipFlipMessage", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GossipFlipMessage.lean \u2014 Gossip Message Format for QR Tile Flipping Defines the gossip message format for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10). Gossip messages trigger tile flips in th", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 6, "inductive_count": 4, "line_count": 263 }, { "kind": "theorem", "id": "Semantics.GossipFlipMessage.discoveryMessageHasDiscoveryType", "name": "discoveryMessageHasDiscoveryType", "module": "Semantics.GossipFlipMessage" }, { "kind": "theorem", "id": "Semantics.GossipFlipMessage.consensusVoteMessageHasVoteField", "name": "consensusVoteMessageHasVoteField", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.zero", "name": "zero", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.one", "name": "one", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.ofFrac", "name": "ofFrac", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createDiscoveryMessage", "name": "createDiscoveryMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createHeartbeatMessage", "name": "createHeartbeatMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createCredentialSyncMessage", "name": "createCredentialSyncMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createReplicateMessage", "name": "createReplicateMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createCredentialRotationProposalMessage", "name": "createCredentialRotationProposalMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "def", "id": "Semantics.GossipFlipMessage.createConsensusVoteMessage", "name": "createConsensusVoteMessage", "module": "Semantics.GossipFlipMessage" }, { "kind": "module", "id": "Semantics.Goxel", "name": "Goxel", "path": "Semantics/Goxel.lean", "namespace": "Semantics.Goxel", "doc": "Goxel.lean \u2014 bounded geometric-volume packets with witness accounting This module formalizes the current Research Stack \"Goxel\" surface as a finite, receipt-bearing admission model. It intentionally keeps the analytic manifold language at the boundary and gives the build a discrete witness that ca", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 8, "def_count": 24, "struct_count": 14, "inductive_count": 1, "line_count": 409 }, { "kind": "theorem", "id": "Semantics.Goxel.origin_inside_example", "name": "origin_inside_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.boundary_is_boundary_example", "name": "boundary_is_boundary_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.outside_not_inside_example", "name": "outside_not_inside_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.example_admissible", "name": "example_admissible", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.residual_example", "name": "residual_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.cost_example", "name": "cost_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.talagrand_cover_example", "name": "talagrand_cover_example", "module": "Semantics.Goxel" }, { "kind": "theorem", "id": "Semantics.Goxel.bind_admissible_example", "name": "bind_admissible_example", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.talagrandConvexityAnchor", "name": "talagrandConvexityAnchor", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.talagrandClaimBoundary", "name": "talagrandClaimBoundary", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.unitWeights", "name": "unitWeights", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.goxelPotential", "name": "goxelPotential", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.insideGoxel", "name": "insideGoxel", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.GoxelWitness", "name": "GoxelWitness", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.Goxel", "name": "Goxel", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.finiteVolumeWitness", "name": "finiteVolumeWitness", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.nonemptyDomainWitness", "name": "nonemptyDomainWitness", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.admissibleGoxel", "name": "admissibleGoxel", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.residualCost", "name": "residualCost", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.goxelCost", "name": "goxelCost", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.TalagrandCoverWitness", "name": "TalagrandCoverWitness", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.mergeDistance", "name": "mergeDistance", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.bindAdmissible", "name": "bindAdmissible", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.mergePotential", "name": "mergePotential", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.GoxelTransition", "name": "GoxelTransition", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.originPoint", "name": "originPoint", "module": "Semantics.Goxel" }, { "kind": "def", "id": "Semantics.Goxel.boundaryPoint", "name": "boundaryPoint", "module": "Semantics.Goxel" }, { "kind": "module", "id": "Semantics.GoxelGridBus", "name": "GoxelGridBus", "path": "Semantics/GoxelGridBus.lean", "namespace": "Semantics.GoxelGridBus", "doc": "GoxelGridBus.lean - Goxel grid state machines over an internal serial bus This module makes the goxel workbench idea executable: a goxel field is a series of finite grid-local state machines, and cells communicate by addressed packets carried through the existing braid serial transport surface.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 5, "def_count": 19, "struct_count": 4, "inductive_count": 2, "line_count": 253 }, { "kind": "theorem", "id": "Semantics.GoxelGridBus.serialRoundtripPreservesTarget", "name": "serialRoundtripPreservesTarget", "module": "Semantics.GoxelGridBus" }, { "kind": "theorem", "id": "Semantics.GoxelGridBus.serialRoundtripPreservesCommand", "name": "serialRoundtripPreservesCommand", "module": "Semantics.GoxelGridBus" }, { "kind": "theorem", "id": "Semantics.GoxelGridBus.targetedPacketActivatesAndConsumes", "name": "targetedPacketActivatesAndConsumes", "module": "Semantics.GoxelGridBus" }, { "kind": "theorem", "id": "Semantics.GoxelGridBus.unmatchedPacketForwards", "name": "unmatchedPacketForwards", "module": "Semantics.GoxelGridBus" }, { "kind": "theorem", "id": "Semantics.GoxelGridBus.holdCommandSetsHoldPhase", "name": "holdCommandSetsHoldPhase", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.toByte", "name": "toByte", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.ofByte", "name": "ofByte", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.zero", "name": "zero", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.seqNum", "name": "seqNum", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.fromSeqNum", "name": "fromSeqNum", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.empty", "name": "empty", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.idle", "name": "idle", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.toSerialPacket", "name": "toSerialPacket", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.byteAt", "name": "byteAt", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.fromSerialPacket", "name": "fromSerialPacket", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.encodeFrame", "name": "encodeFrame", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.decodeFrame", "name": "decodeFrame", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.applyCommand", "name": "applyCommand", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.cellBusStep", "name": "cellBusStep", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.addrOfIndex", "name": "addrOfIndex", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.mkIdle", "name": "mkIdle", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.cellAt", "name": "cellAt", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.routePacket", "name": "routePacket", "module": "Semantics.GoxelGridBus" }, { "kind": "def", "id": "Semantics.GoxelGridBus.witnessActivatePacket", "name": "witnessActivatePacket", "module": "Semantics.GoxelGridBus" }, { "kind": "module", "id": "Semantics.GpuDutyAssignment", "name": "GpuDutyAssignment", "path": "Semantics/GpuDutyAssignment.lean", "namespace": "Semantics.GpuDutyAssignment", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GpuDutyAssignment.lean \u2014 GPU Translation Surface Duty Assignment in Lean This module formalizes the GPU translation surface duty assignment system for the swarm, including duty types, assignment, execu", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 13, "struct_count": 4, "inductive_count": 2, "line_count": 221 }, { "kind": "theorem", "id": "Semantics.GpuDutyAssignment.emptySystemHasNoAssignments", "name": "emptySystemHasNoAssignments", "module": "Semantics.GpuDutyAssignment" }, { "kind": "theorem", "id": "Semantics.GpuDutyAssignment.statisticsEqualsAssignments", "name": "statisticsEqualsAssignments", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.zero", "name": "zero", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.one", "name": "one", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.ofNat", "name": "ofNat", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.toString", "name": "toString", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.empty", "name": "empty", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.assignDuty", "name": "assignDuty", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.startDuty", "name": "startDuty", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.completeDuty", "name": "completeDuty", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.failDuty", "name": "failDuty", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.getPendingDuties", "name": "getPendingDuties", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.getStatistics", "name": "getStatistics", "module": "Semantics.GpuDutyAssignment" }, { "kind": "def", "id": "Semantics.GpuDutyAssignment.createGpuExpert", "name": "createGpuExpert", "module": "Semantics.GpuDutyAssignment" }, { "kind": "module", "id": "Semantics.GradientPathMap", "name": "GradientPathMap", "path": "Semantics/GradientPathMap.lean", "namespace": "Semantics.GradientPathMap", "doc": "# Gradient Path Map This module keeps the equation-forest gradient surface finite and proof-checkable. The former sketch used strings, float conversions, and `sorry`-backed claims. This version uses finite node/type identifiers and milli-units for gradient/cost values.", "math_kind": "routing", "sorry_count": 1, "theorem_count": 11, "def_count": 18, "struct_count": 3, "inductive_count": 2, "line_count": 219 }, { "kind": "theorem", "id": "Semantics.GradientPathMap.pathCost_eq_totalGradient", "name": "pathCost_eq_totalGradient", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.emptyPathZeroGradient", "name": "emptyPathZeroGradient", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.lawfulConnectionCost_le_unit", "name": "lawfulConnectionCost_le_unit", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.samplePathsLawful", "name": "samplePathsLawful", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.forestMapHasConnections", "name": "forestMapHasConnections", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.forestMapPathsLawful", "name": "forestMapPathsLawful", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.samplePathZero_cost_eq_600", "name": "samplePathZero_cost_eq_600", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.mofPath2_cost_eq_600", "name": "mofPath2_cost_eq_600", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.mofPath3_cost_eq_150", "name": "mofPath3_cost_eq_150", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.affinePath4_cost_eq_550", "name": "affinePath4_cost_eq_550", "module": "Semantics.GradientPathMap" }, { "kind": "theorem", "id": "Semantics.GradientPathMap.affinePath5_cost_eq_200", "name": "affinePath5_cost_eq_200", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.equationConnectionLawful", "name": "equationConnectionLawful", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.equationConnectionBind", "name": "equationConnectionBind", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.equationConnectionCost", "name": "equationConnectionCost", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.gradientPathLawful", "name": "gradientPathLawful", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.gradientPathBind", "name": "gradientPathBind", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.computeTotalGradientChange", "name": "computeTotalGradientChange", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.gradientPathCost", "name": "gradientPathCost", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.couchToFrame", "name": "couchToFrame", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.loadToCognitive", "name": "loadToCognitive", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.pressureToHugoniot", "name": "pressureToHugoniot", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.mof2eCO_to_6eCH3OH", "name": "mof2eCO_to_6eCH3OH", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.mof6eCH3OH_to_8eCH4", "name": "mof6eCH3OH_to_8eCH4", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.mof2eHCOOH_to_2eCO", "name": "mof2eHCOOH_to_2eCO", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.affineLinear_to_decomposition", "name": "affineLinear_to_decomposition", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.affineDecomposition_to_periodic", "name": "affineDecomposition_to_periodic", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.affinePeriodic_to_scaled", "name": "affinePeriodic_to_scaled", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.sampleForestPaths", "name": "sampleForestPaths", "module": "Semantics.GradientPathMap" }, { "kind": "def", "id": "Semantics.GradientPathMap.forestGradientPathMap", "name": "forestGradientPathMap", "module": "Semantics.GradientPathMap" }, { "kind": "module", "id": "Semantics.Graph", "name": "Graph", "path": "Semantics/Graph.lean", "namespace": "Semantics.ENE", "doc": "Endless Node Edges (ENE) Graph Database", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 4, "inductive_count": 3, "line_count": 169 }, { "kind": "def", "id": "Semantics.Graph.Graph", "name": "Graph", "module": "Semantics.Graph" }, { "kind": "def", "id": "Semantics.Graph.atomLabel", "name": "atomLabel", "module": "Semantics.Graph" }, { "kind": "module", "id": "Semantics.GraphRank", "name": "GraphRank", "path": "Semantics/GraphRank.lean", "namespace": "Semantics.GraphRank", "doc": "# GraphRank \u2014 Spectral-gap-gated ranking on social graphs Maps the PageRank/HITS/Fiedler/PPR mathematical lineage onto the 8-bin Sidon spectral space from `Semantics.Spectrum`. The central claim: a \"bad link\" is any edge whose `piecewiseMerge` result fails `verifySpectralGap`. This corresponds to ", "math_kind": "fixedpoint", "sorry_count": 1, "theorem_count": 4, "def_count": 15, "struct_count": 3, "inductive_count": 1, "line_count": 196 }, { "kind": "theorem", "id": "Semantics.GraphRank.badLink_decidable", "name": "badLink_decidable", "module": "Semantics.GraphRank" }, { "kind": "theorem", "id": "Semantics.GraphRank.isClean_decidable", "name": "isClean_decidable", "module": "Semantics.GraphRank" }, { "kind": "theorem", "id": "Semantics.GraphRank.activeBins_empty", "name": "activeBins_empty", "module": "Semantics.GraphRank" }, { "kind": "theorem", "id": "Semantics.GraphRank.cleanMerge_preservesGap", "name": "cleanMerge_preservesGap", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.SocialGraph", "name": "SocialGraph", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.maxActiveBins", "name": "maxActiveBins", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.badLink", "name": "badLink", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.pprStep", "name": "pprStep", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.initScores", "name": "initScores", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.pprRun", "name": "pprRun", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.modeScore", "name": "modeScore", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.spectralScore", "name": "spectralScore", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.insertDesc", "name": "insertDesc", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.sortDesc", "name": "sortDesc", "module": "Semantics.GraphRank" }, { "kind": "def", "id": "Semantics.GraphRank.rankNodes", "name": "rankNodes", "module": "Semantics.GraphRank" }, { "kind": "module", "id": "Semantics.HCMMR.Bridge", "name": "Bridge", "path": "Semantics/HCMMR/Bridge.lean", "namespace": "Semantics.HCMMR.Bridge", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 90 }, { "kind": "theorem", "id": "Semantics.HCMMR.Bridge.foldDecision_roundtrip", "name": "foldDecision_roundtrip", "module": "Semantics.HCMMR.Bridge" }, { "kind": "theorem", "id": "Semantics.HCMMR.Bridge.foldDecision_roundtrip_admit", "name": "foldDecision_roundtrip_admit", "module": "Semantics.HCMMR.Bridge" }, { "kind": "theorem", "id": "Semantics.HCMMR.Bridge.foldDecision_roundtrip_reject", "name": "foldDecision_roundtrip_reject", "module": "Semantics.HCMMR.Bridge" }, { "kind": "theorem", "id": "Semantics.HCMMR.Bridge.foldDecision_roundtrip_hold", "name": "foldDecision_roundtrip_hold", "module": "Semantics.HCMMR.Bridge" }, { "kind": "def", "id": "Semantics.HCMMR.Bridge.gateVerdictFromFoldDecision", "name": "gateVerdictFromFoldDecision", "module": "Semantics.HCMMR.Bridge" }, { "kind": "def", "id": "Semantics.HCMMR.Bridge.foldDecisionFromGateVerdict", "name": "foldDecisionFromGateVerdict", "module": "Semantics.HCMMR.Bridge" }, { "kind": "def", "id": "Semantics.HCMMR.Bridge.gateChainFromGateOutcomeList", "name": "gateChainFromGateOutcomeList", "module": "Semantics.HCMMR.Bridge" }, { "kind": "def", "id": "Semantics.HCMMR.Bridge.bindMetricToGate", "name": "bindMetricToGate", "module": "Semantics.HCMMR.Bridge" }, { "kind": "module", "id": "Semantics.HCMMR.Core", "name": "Core", "path": "Semantics/HCMMR/Core.lean", "namespace": "Semantics.HCMMR.Core", "doc": "HCMMR Core.lean \u2014 Hyper-CMMR Operadic Meta-Calculus v0.1 typeclass definitions. This is the typeclass and core structure file. Every other HCMMR module depends on these definitions. The HCMMR is a typed-gate diagnostic system: objects enter a 16D transform stack, get decomposed through multiplicati", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 7, "def_count": 10, "struct_count": 6, "inductive_count": 1, "line_count": 362 }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.gate_chain_all_admit", "name": "gate_chain_all_admit", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.gate_chain_one_rejects", "name": "gate_chain_one_rejects", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.gate_chain_one_holds", "name": "gate_chain_one_holds", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.gate_chain_optional_reject_ignored", "name": "gate_chain_optional_reject_ignored", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.eigenmass_zero_on_any_gate_failure", "name": "eigenmass_zero_on_any_gate_failure", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.eigenmass_signed_identity", "name": "eigenmass_signed_identity", "module": "Semantics.HCMMR.Core" }, { "kind": "theorem", "id": "Semantics.HCMMR.Core.eigenmass_product_residual_dampens", "name": "eigenmass_product_residual_dampens", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.gateChainVerdict", "name": "gateChainVerdict", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.eigenmassProduct", "name": "eigenmassProduct", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.eigenmassSigned", "name": "eigenmassSigned", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.canonicalFixture", "name": "canonicalFixture", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.fullyAdmittingOperator", "name": "fullyAdmittingOperator", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.receiptFailureOperator", "name": "receiptFailureOperator", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.fullyAdmittingChain", "name": "fullyAdmittingChain", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.chiralityHoldChain", "name": "chiralityHoldChain", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.receiptRejectChain", "name": "receiptRejectChain", "module": "Semantics.HCMMR.Core" }, { "kind": "def", "id": "Semantics.HCMMR.Core.optionalRejectChain", "name": "optionalRejectChain", "module": "Semantics.HCMMR.Core" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire", "name": "BoundaryEigenFire", "path": "Semantics/HCMMR/Kernels/BoundaryEigenFire.lean", "namespace": "Semantics.HCMMR.Kernels.BoundaryEigenFire", "doc": "BoundaryEigenFire.lean \u2014 B_\u2202 Modal Burn Surface Kernel Defines the boundary eigenfire field B_\u2202(x) \u2014 the surface projection of the \u03bb_YAH hyper-eigenspectrum \u2014 and the tripartite BoundaryVerdict: admitted \u2014 \u2016B_\u2202\u2016 \u2264 \u0398_activation, boundary resolves in current chart underverseEntry \u2014 receip", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 4, "inductive_count": 3, "line_count": 459 }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.projectToBoundary", "name": "projectToBoundary", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.modalNorm", "name": "modalNorm", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.BoundaryField", "name": "BoundaryField", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.activationThreshold", "name": "activationThreshold", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.punctureThreshold", "name": "punctureThreshold", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.isEigenFire", "name": "isEigenFire", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.isPuncture", "name": "isPuncture", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.dominantManifestation", "name": "dominantManifestation", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.makePromotionReceipt", "name": "makePromotionReceipt", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.eigenFireGate", "name": "eigenFireGate", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.collide", "name": "collide", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.coolBoundary", "name": "coolBoundary", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.hotWallBind", "name": "hotWallBind", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.hotWall", "name": "hotWall", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.underverseBoundary", "name": "underverseBoundary", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.unstoppableForce", "name": "unstoppableForce", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.immovableObject", "name": "immovableObject", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.throatCollision", "name": "throatCollision", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.BoundaryEigenFire.dim16Field", "name": "dim16Field", "module": "Semantics.HCMMR.Kernels.BoundaryEigenFire" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector", "name": "EntropyCollapseDetector", "path": "Semantics/HCMMR/Kernels/EntropyCollapseDetector.lean", "namespace": "Semantics.HCMMR.Kernels.EntropyCollapseDetector", "doc": "EntropyCollapseDetector.lean -- finite arithmetic receipt for the corrected entropy-collapse detector window. This module mirrors the canonical arithmetic note: `6-Documentation/docs/distilled/ArithmeticSpec_Corrected_2026-05-11.md`. It intentionally avoids Float/log arithmetic. The logarithmic H", "math_kind": "braid", "sorry_count": 0, "theorem_count": 6, "def_count": 28, "struct_count": 0, "inductive_count": 0, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.denseRankTieFixture", "name": "denseRankTieFixture", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.correctedCrossingCountIs12", "name": "correctedCrossingCountIs12", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.rawK7FiresButSelectiveK21DoesNot", "name": "rawK7FiresButSelectiveK21DoesNot", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.d2SumP2NumeratorIs22", "name": "d2SumP2NumeratorIs22", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.collapseFeaturesButNoTripleFire", "name": "collapseFeaturesButNoTripleFire", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.exactTailReceiptsW8", "name": "exactTailReceiptsW8", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.windowA", "name": "windowA", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.windowB", "name": "windowB", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.collapseWindow", "name": "collapseWindow", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.denseRankValue", "name": "denseRankValue", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.denseRank", "name": "denseRank", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.rankedA", "name": "rankedA", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.rankedB", "name": "rankedB", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.crossingAt", "name": "crossingAt", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.indexPairs8", "name": "indexPairs8", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.crossingCount", "name": "crossingCount", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.countValue", "name": "countValue", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.d2SumP2Numerator64", "name": "d2SumP2Numerator64", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.sigmaQppm", "name": "sigmaQppm", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.sigmaCppm", "name": "sigmaCppm", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.d2ppm", "name": "d2ppm", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.dCppm", "name": "dCppm", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.braidRawFires", "name": "braidRawFires", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.braidSelectiveFires", "name": "braidSelectiveFires", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.sigmaCollapsed", "name": "sigmaCollapsed", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.EntropyCollapseDetector.d2Collapsed", "name": "d2Collapsed", "module": "Semantics.HCMMR.Kernels.EntropyCollapseDetector" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory", "name": "FAMMScarMemory", "path": "Semantics/HCMMR/Kernels/FAMMScarMemory.lean", "namespace": "Semantics.HCMMR.Kernels.FAMMScarMemory", "doc": "FAMMScarMemory.lean \u2014 FAMM frustration/scar memory kernel wrapped around field steps. \u03a6_FAMM = exp[-\u03b3(\u03a3\u00b2 + I_lock + \u0394\u03c6)], where \u03a3\u00b2 = accumulated scar energy, I_lock = interference penalty, \u0394\u03c6 = phase mismatch. High frustration suppresses step magnitude; low frustration permits aggressive exploratio", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 7, "struct_count": 1, "inductive_count": 0, "line_count": 105 }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.famm_gate_name_correct", "name": "famm_gate_name_correct", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.famm_gate_verdict_admits", "name": "famm_gate_verdict_admits", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fixtureScar_initial_history", "name": "fixtureScar_initial_history", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fixtureHighScar_history_length", "name": "fixtureHighScar_history_length", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.reset_does_not_change_history_length", "name": "reset_does_not_change_history_length", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.record_extends_history", "name": "record_extends_history", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fammBias", "name": "fammBias", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.applyFAMMBias", "name": "applyFAMMBias", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.recordScar", "name": "recordScar", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.resetFrustration", "name": "resetFrustration", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fammMemoryGate", "name": "fammMemoryGate", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fixtureScar", "name": "fixtureScar", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.FAMMScarMemory.fixtureHighScar", "name": "fixtureHighScar", "module": "Semantics.HCMMR.Kernels.FAMMScarMemory" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum", "name": "HyperEigenSpectrum", "path": "Semantics/HCMMR/Kernels/HyperEigenSpectrum.lean", "namespace": "Semantics.HCMMR.Kernels.HyperEigenSpectrum", "doc": "HyperEigenSpectrum.lean \u2014 \u03bb_YAH Scale-Regime Eigenvalue Kernel Defines the \u03bb_YAH (You-Are-Here) hyper-eigenspectrum: a scale-dependent operator whose eigenspectrum encodes the dominant active physics regime of an object at a given observer scale, combining: \u03a9_M \u2014 Menger-like void hierarchy R_K ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 20, "struct_count": 2, "inductive_count": 2, "line_count": 400 }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.BindOperator", "name": "BindOperator", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.EigenMode", "name": "EigenMode", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.HyperEigenSpectrum", "name": "HyperEigenSpectrum", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.sortDescending", "name": "sortDescending", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.argmax", "name": "argmax", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.fromBind", "name": "fromBind", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.fromEigenmassOperator", "name": "fromEigenmassOperator", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.regimeLabel", "name": "regimeLabel", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.dominantMode", "name": "dominantMode", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.hasRegimeShift", "name": "hasRegimeShift", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.classifyTransition", "name": "classifyTransition", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.cosmicVoidBind", "name": "cosmicVoidBind", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.cosmicVoidSpectrum", "name": "cosmicVoidSpectrum", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.fractureBind", "name": "fractureBind", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.HyperEigenSpectrum.fractureSpectrum", "name": "fractureSpectrum", "module": "Semantics.HCMMR.Kernels.HyperEigenSpectrum" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.PrimeGearCache", "name": "PrimeGearCache", "path": "Semantics/HCMMR/Kernels/PrimeGearCache.lean", "namespace": "Semantics.HCMMR.Kernels.PrimeGearCache", "doc": "PrimeGearCache.lean \u2014 Prime exponent compositional caching kernel. Instead of computing every step n from scratch, factor n = \u03a0 p^{v_p(n)} and compose from cached prime-step receipts. \u0394_n = g_field(p_n) \u00d7 \u03a0 (\u0394_p)^{v_p(n)}. Composites are derived, not recomputed.", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 7, "def_count": 13, "struct_count": 2, "inductive_count": 0, "line_count": 160 }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.cache_prime_increments_known", "name": "cache_prime_increments_known", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.cache_duplicate_does_not_increment", "name": "cache_duplicate_does_not_increment", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.gate_name_correct", "name": "gate_name_correct", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureCache_primes_known_two", "name": "fixtureCache_primes_known_two", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.q16Pow_zero_exp", "name": "q16Pow_zero_exp", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.q16Pow_one_exp", "name": "q16Pow_one_exp", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.empty_cache_no_entry", "name": "empty_cache_no_entry", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.factorize", "name": "factorize", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.findEntry", "name": "findEntry", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.q16Pow", "name": "q16Pow", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.composeFromPrimes", "name": "composeFromPrimes", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.isCompositeCached", "name": "isCompositeCached", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.cachePrimeStep", "name": "cachePrimeStep", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.primeCacheGate", "name": "primeCacheGate", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.emptyCache", "name": "emptyCache", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureEntry2", "name": "fixtureEntry2", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureEntry3", "name": "fixtureEntry3", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureEntry5", "name": "fixtureEntry5", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureCache", "name": "fixtureCache", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.PrimeGearCache.fixtureCache3", "name": "fixtureCache3", "module": "Semantics.HCMMR.Kernels.PrimeGearCache" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep", "name": "RecamanFieldStep", "path": "Semantics/HCMMR/Kernels/RecamanFieldStep.lean", "namespace": "Semantics.HCMMR.Kernels.RecamanFieldStep", "doc": "RecamanFieldStep.lean \u2014 Recam\u00e1n signed-step reflex kernel for HCMMR field traversal. Recam\u00e1n sequence: a_0=0, a_n = a_{n-1}-n if positive and unused, else a_{n-1}+n. HCMMR mapping: try negative/Underverse step \u2192 if admissible and unoccupied \u2192 commit; else reflect into positive ladder. Each step is ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 12, "struct_count": 2, "inductive_count": 0, "line_count": 151 }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.recaman_gate_name_correct", "name": "recaman_gate_name_correct", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.recaman_gate_verdict_admits", "name": "recaman_gate_verdict_admits", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixture_step1_index_one", "name": "fixture_step1_index_one", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixture_step2_index_two", "name": "fixture_step2_index_two", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixture_step1_reflected_false", "name": "fixture_step1_reflected_false", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixture_step2_reflected_true", "name": "fixture_step2_reflected_true", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.recamanFieldStep", "name": "recamanFieldStep", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.arcFromStep", "name": "arcFromStep", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.circleIntersectionCheck", "name": "circleIntersectionCheck", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.cumulativeArcLength", "name": "cumulativeArcLength", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.recamanGateAdmit", "name": "recamanGateAdmit", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureStep1", "name": "fixtureStep1", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureStep2", "name": "fixtureStep2", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureStep3", "name": "fixtureStep3", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureArc1", "name": "fixtureArc1", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureArc2", "name": "fixtureArc2", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureVisited", "name": "fixtureVisited", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.RecamanFieldStep.fixtureGate", "name": "fixtureGate", "module": "Semantics.HCMMR.Kernels.RecamanFieldStep" }, { "kind": "module", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector", "name": "SNRAnomalyDetector", "path": "Semantics/HCMMR/Kernels/SNRAnomalyDetector.lean", "namespace": "Semantics.HCMMR.Kernels.SNRAnomalyDetector", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 14, "struct_count": 1, "inductive_count": 2, "line_count": 219 }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.narrowband_spike_admits", "name": "narrowband_spike_admits", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.noise_floor_rejects", "name": "noise_floor_rejects", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.broadband_rise_holds", "name": "broadband_rise_holds", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.narrowband_is_narrowband", "name": "narrowband_is_narrowband", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.anomaly_score_self_delta", "name": "anomaly_score_self_delta", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "theorem", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.detection_count_multi_bin", "name": "detection_count_multi_bin", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.computeSNR", "name": "computeSNR", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.classifySNRZone", "name": "classifySNRZone", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.isNarrowband", "name": "isNarrowband", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.isBroadband", "name": "isBroadband", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.classifyPattern", "name": "classifyPattern", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.anomalyScore", "name": "anomalyScore", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.narrowbandSpikeFixture", "name": "narrowbandSpikeFixture", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.broadbandRiseFixture", "name": "broadbandRiseFixture", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.noiseFloorFixture", "name": "noiseFloorFixture", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.multiBinFixture", "name": "multiBinFixture", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.snrDetectionGate", "name": "snrDetectionGate", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.emitAnomalyReceipt", "name": "emitAnomalyReceipt", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.findStrongestSpike", "name": "findStrongestSpike", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "def", "id": "Semantics.HCMMR.Kernels.SNRAnomalyDetector.countDetections", "name": "countDetections", "module": "Semantics.HCMMR.Kernels.SNRAnomalyDetector" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law14_Motion", "name": "Law14_Motion", "path": "Semantics/HCMMR/Laws/Law14_Motion.lean", "namespace": "Semantics.HCMMR.Law14", "doc": "HCMMR Law14 \u2014 Motion Recovery. Tests whether a 16D object can be projected into a classical trajectory. The pass condition is \u03b5_motion = ||m\u00b7\u1e8d - F|| \u2192 0 in the Newtonian limit. When residuals are small, the HCMMR manifold gear-reduces to classical Newtonian/Lagrangian mechanics.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 14, "struct_count": 2, "inductive_count": 0, "line_count": 344 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law14_Motion.newton_admits_clean", "name": "newton_admits_clean", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law14_Motion.free_particle_admits", "name": "free_particle_admits", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law14_Motion.momentum_identity_clean", "name": "momentum_identity_clean", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law14_Motion.kinetic_energy_clean", "name": "kinetic_energy_clean", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law14_Motion.newton_violating_residual_pos", "name": "newton_violating_residual_pos", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.computeVelocity", "name": "computeVelocity", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.computeAcceleration", "name": "computeAcceleration", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.newtonSecondLawResidual", "name": "newtonSecondLawResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.momentumResidual", "name": "momentumResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.kineticEnergyResidual", "name": "kineticEnergyResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.eulerLagrangeResidual", "name": "eulerLagrangeResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.actionResidual", "name": "actionResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.motionRecoveryGate", "name": "motionRecoveryGate", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.motionDiagnostic", "name": "motionDiagnostic", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.gearReduceResidual", "name": "gearReduceResidual", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.cleanNewtonFixture", "name": "cleanNewtonFixture", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.violatingTrajectoryFixture", "name": "violatingTrajectoryFixture", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.cleanLagrangianFixture", "name": "cleanLagrangianFixture", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law14_Motion.freeParticleFixture", "name": "freeParticleFixture", "module": "Semantics.HCMMR.Laws.Law14_Motion" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection", "name": "Law15E_SignalDetection", "path": "Semantics/HCMMR/Laws/Law15E_SignalDetection.lean", "namespace": "Semantics.HCMMR.Law15E", "doc": "Law 15E \u2014 Signal Detection Gate. A sub-law of Field Recovery (Law 15) that gates whether a projected electromagnetic field contains a detectable signal rather than mere noise. The gate uses SNR ratio thresholds mapped to typed verdicts: Signal \u2265 signal_threshold \u2192 admit (candidate signal presen", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 8, "struct_count": 2, "inductive_count": 0, "line_count": 278 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.seti_config_admits_strong_signal", "name": "seti_config_admits_strong_signal", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.seti_config_holds_ambiguous", "name": "seti_config_holds_ambiguous", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.quick_scan_admits_ambiguous_above_noise", "name": "quick_scan_admits_ambiguous_above_noise", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.doppler_zero_drift_holds", "name": "doppler_zero_drift_holds", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.doppler_valid_drift_admits", "name": "doppler_valid_drift_admits", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.detection_report_counts_correctly", "name": "detection_report_counts_correctly", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.setiDefaultConfig", "name": "setiDefaultConfig", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.quickScanConfig", "name": "quickScanConfig", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.signalDetectionGate", "name": "signalDetectionGate", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.generateDetectionReport", "name": "generateDetectionReport", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.detectDopplerDrift", "name": "detectDopplerDrift", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.dopplerGate", "name": "dopplerGate", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.cleanSignalFixture", "name": "cleanSignalFixture", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15E_SignalDetection.ambiguousSignalFixture", "name": "ambiguousSignalFixture", "module": "Semantics.HCMMR.Laws.Law15E_SignalDetection" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law15_Field", "name": "Law15_Field", "path": "Semantics/HCMMR/Laws/Law15_Field.lean", "namespace": "Semantics.HCMMR.Law15", "doc": "Law 15 \u2014 Field Recovery Bridges 16D torsion/winding into recoverable 4D electromagnetism through a layered gate chain: Law 15K (K\u00e4hler Compatibility) \u2192 15A (Gauge Invariance) \u2192 15B (Maxwell) \u2192 15C (Wave Propagation) \u2192 15D (Charge/Current Coupling). The K\u00e4hler layer is the smooth-field gearbox: \u03c9(X", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 27, "def_count": 58, "struct_count": 8, "inductive_count": 0, "line_count": 918 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.kahlerGate_admits_clean", "name": "kahlerGate_admits_clean", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.kahlerGate_rejects_fractal", "name": "kahlerGate_rejects_fractal", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.gaugeGate_admits_invariance", "name": "gaugeGate_admits_invariance", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.maxwell_homogeneous_from_potential", "name": "maxwell_homogeneous_from_potential", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.maxwell_sourced_needs_current", "name": "maxwell_sourced_needs_current", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.waveGate_admits_vacuum", "name": "waveGate_admits_vacuum", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.couplingGate_admits_conserved", "name": "couplingGate_admits_conserved", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.fieldRecovery_chain_admits_clean", "name": "fieldRecovery_chain_admits_clean", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.fieldRecovery_chain_rejects_fractal", "name": "fieldRecovery_chain_rejects_fractal", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.J16_squared_is_negI", "name": "J16_squared_is_negI", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.J16_is_unitary", "name": "J16_is_unitary", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.goldenSpiral_passes_conformal", "name": "goldenSpiral_passes_conformal", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.goldenSpiral_gate_admits", "name": "goldenSpiral_gate_admits", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.shear_fails_kahler", "name": "shear_fails_kahler", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.conj_is_orthogonal", "name": "conj_is_orthogonal", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.conj_fails_kahler", "name": "conj_fails_kahler", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.q16_sub_self_val", "name": "q16_sub_self_val", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.placeholder_B3_always_zero", "name": "placeholder_B3_always_zero", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.vortex_B3_nonzero", "name": "vortex_B3_nonzero", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.vortex_divB_zero", "name": "vortex_divB_zero", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.quantize_one", "name": "quantize_one", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.quantize_negTwo", "name": "quantize_negTwo", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.quantize_threeHalves", "name": "quantize_threeHalves", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.charge_empty", "name": "charge_empty", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.charge_one_vortex", "name": "charge_one_vortex", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.charge_two_vortices", "name": "charge_two_vortices", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law15_Field.charge_vortex_antivortex", "name": "charge_vortex_antivortex", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.projectPotential", "name": "projectPotential", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.computeFieldStrength", "name": "computeFieldStrength", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.kahlerResidual", "name": "kahlerResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.kahlerGateAdmit", "name": "kahlerGateAdmit", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.fractalKahlerReceipt", "name": "fractalKahlerReceipt", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.gaugeTransform", "name": "gaugeTransform", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.gaugeResidual", "name": "gaugeResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.gaugeGateAdmit", "name": "gaugeGateAdmit", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.homogeneousMaxwellResidual", "name": "homogeneousMaxwellResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.sourcedMaxwellResidual", "name": "sourcedMaxwellResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.maxwellGateAdmit", "name": "maxwellGateAdmit", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.causalSpeedResidual", "name": "causalSpeedResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.waveGateAdmit", "name": "waveGateAdmit", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.lorentzForce", "name": "lorentzForce", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.chargeCouplingResidual", "name": "chargeCouplingResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.sourceConservationResidual", "name": "sourceConservationResidual", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.couplingGateAdmit", "name": "couplingGateAdmit", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.fieldRecoveryChain", "name": "fieldRecoveryChain", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.fieldRecoveryVerdict", "name": "fieldRecoveryVerdict", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law15_Field.cleanTorsionFixture", "name": "cleanTorsionFixture", "module": "Semantics.HCMMR.Laws.Law15_Field" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law16_Entropy", "name": "Law16_Entropy", "path": "Semantics/HCMMR/Laws/Law16_Entropy.lean", "namespace": "Semantics.HCMMR.Law16", "doc": "Law 16 \u2014 Entropy/Heat Leak (Landauer Gate) Every gate failure is not free \u2014 it emits a residual that costs energy (Landauer limit: \u0394E \u2265 k_B\u00b7T\u00b7ln2). The Underverse is the residual heat sink for every gate rejection. 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It does ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 261 }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.canonicalWyler", "name": "canonicalWyler", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.floatPi", "name": "floatPi", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.wylerAlphaInverse", "name": "wylerAlphaInverse", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.wylerAlphaInverseTrue", "name": "wylerAlphaInverseTrue", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.codataAlphaInverse", "name": "codataAlphaInverse", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.wylerDeviation", "name": "wylerDeviation", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.recamanGap6Candidate", "name": "recamanGap6Candidate", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.recamanDeviation", "name": "recamanDeviation", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.alphaInverseQ16_16Anchor", "name": "alphaInverseQ16_16Anchor", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.alphaInverseFromAnchor", "name": "alphaInverseFromAnchor", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_AlphaDerivation.anchorDeviation", "name": "anchorDeviation", "module": "Semantics.HCMMR.Laws.Law18_AlphaDerivation" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law18_Constants", "name": "Law18_Constants", "path": "Semantics/HCMMR/Laws/Law18_Constants.lean", "namespace": "Semantics.HCMMR.Law18", "doc": "Law 18 \u2014 Scale/Constant Anchoring HCMMR does not predict constants as raw numbers (they're dimensionful and unit-dependent). It recovers their *roles* as limiting calibration constants and tests **dimensionless** outputs. The canonical equation includes \u03a9_K (Constant Calibration Gate) as a multipli", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 15, "struct_count": 2, "inductive_count": 0, "line_count": 351 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law18_Constants.omegaK_admits_anchored", "name": "omegaK_admits_anchored", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law18_Constants.omegaK_rejects_missing", "name": "omegaK_rejects_missing", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law18_Constants.dimensionless_residual_bounded_by_resolution", "name": "dimensionless_residual_bounded_by_resolution", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law18_Constants.calibration_anchored_score_one", "name": "calibration_anchored_score_one", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.anchorConstants", "name": "anchorConstants", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.calibrationScore", "name": "calibrationScore", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.residualLogRatio", "name": "residualLogRatio", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.fineStructureTest", "name": "fineStructureTest", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.massRatioTest", "name": "massRatioTest", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.planckRatioTest", "name": "planckRatioTest", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.dimensionlessTestGate", "name": "dimensionlessTestGate", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.omegaKScore", "name": "omegaKScore", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.omegaKGate", "name": "omegaKGate", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.constantRecoveryGate", "name": "constantRecoveryGate", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.constantRecoveryVerdict", "name": "constantRecoveryVerdict", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.coDataCalibrationFixture", "name": "coDataCalibrationFixture", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.missingPhotonFixture", "name": "missingPhotonFixture", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.fineStructureFixture", "name": "fineStructureFixture", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law18_Constants.anchoredCalibrationFixture", "name": "anchoredCalibrationFixture", "module": "Semantics.HCMMR.Laws.Law18_Constants" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law19_VoidScar", "name": "Law19_VoidScar", "path": "Semantics/HCMMR/Laws/Law19_VoidScar.lean", "namespace": "Semantics.HCMMR.Law19", "doc": "Law 19 \u2014 VoidScar Fractal Field & Regime Gate Encodes three primitives derived from the Menger/Koch/DESI synthesis (see `6-Documentation/docs/distilled/ObserverScale_RegimeGate_VoidScar.md`): 1. **VoidScar fractal constants** \u2014 Koch boundary dimension ln(4)/ln(3) and the Menger/Koch divergence pre", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 17, "struct_count": 2, "inductive_count": 3, "line_count": 418 }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.kochBoundaryDim", "name": "kochBoundaryDim", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.mengerVoidDim", "name": "mengerVoidDim", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.mkDivNumerator", "name": "mkDivNumerator", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.mkDivDenominator", "name": "mkDivDenominator", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.mkDivOneStep", "name": "mkDivOneStep", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.VoidScarField", "name": "VoidScarField", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.voidScarDivergence", "name": "voidScarDivergence", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.voidScarAdmissible", "name": "voidScarAdmissible", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.mengerDeleteStep", "name": "mengerDeleteStep", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.kochScarStep", "name": "kochScarStep", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.voidScarStep", "name": "voidScarStep", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.voidScarGate", "name": "voidScarGate", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.resolveRegime", "name": "resolveRegime", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.resolveCoupling", "name": "resolveCoupling", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.regimeGateVerdict", "name": "regimeGateVerdict", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.voidScarRegimeChain", "name": "voidScarRegimeChain", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law19_VoidScar.classifyDivergence", "name": "classifyDivergence", "module": "Semantics.HCMMR.Laws.Law19_VoidScar" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law20_Shock", "name": "Law20_Shock", "path": "Semantics/HCMMR/Laws/Law20_Shock.lean", "namespace": "Semantics.HCMMR.Law20", "doc": "Law 20 \u2014 Shockwave / Front Gate Formalises the HCMMR discontinuity-handling gate A_shock. Doctrine: a discontinuity (shockwave, contact front, phase boundary) is NOT a failure of physics. It is a *gate event* with a typed receipt that captures: 1. **Hyperbolicity** \u2014 the PDE system is hyperbolic", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 4, "def_count": 23, "struct_count": 4, "inductive_count": 1, "line_count": 516 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law20_Shock.exampleShock_admitted", "name": "exampleShock_admitted", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law20_Shock.ellipticEvent_rejected", "name": "ellipticEvent_rejected", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law20_Shock.expansionShock_rejected_lax", "name": "expansionShock_rejected_lax", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law20_Shock.acausalShock_rejected", "name": "acausalShock_rejected", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.q", "name": "q", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.toN", "name": "toN", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.q_sub", "name": "q_sub", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.q_absdiff", "name": "q_absdiff", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.q_add", "name": "q_add", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.q_div", "name": "q_div", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.hyperbolicityGate", "name": "hyperbolicityGate", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.characteristicSpeeds", "name": "characteristicSpeeds", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.rankineHugoniotResidual", "name": "rankineHugoniotResidual", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.entropyProxy", "name": "entropyProxy", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.entropyAdmissible", "name": "entropyAdmissible", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.entropyGain", "name": "entropyGain", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.causalEnvelope", "name": "causalEnvelope", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.causallyValid", "name": "causallyValid", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.causalExcess", "name": "causalExcess", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.rhThreshold", "name": "rhThreshold", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.shockGate", "name": "shockGate", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.exampleShock", "name": "exampleShock", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.ellipticEvent", "name": "ellipticEvent", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law20_Shock.expansionShock", "name": "expansionShock", "module": "Semantics.HCMMR.Laws.Law20_Shock" }, { "kind": "module", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary", "name": "Law21_ThermalBoundary", "path": "Semantics/HCMMR/Laws/Law21_ThermalBoundary.lean", "namespace": "Semantics.HCMMR.Law21", "doc": "Law 21 \u2014 Thermal Boundary Gate Formalises the HCMMR temperature-regime admissibility gate A_thermal. Doctrine: temperature is a *gate variable*, not a free parameter. Two hard boundaries bracket the physically accessible regime, and the CMB floor anchors the observable cosmic background. 1. **Ab", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 18, "struct_count": 4, "inductive_count": 2, "line_count": 495 }, { "kind": "theorem", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.superposition_weight_sum", "name": "superposition_weight_sum", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.boltzmann_num", "name": "boltzmann_num", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.boltzmann_den", "name": "boltzmann_den", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.T_CMB", "name": "T_CMB", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.ln2_Q16", "name": "ln2_Q16", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.T_Hagedorn_K", "name": "T_Hagedorn_K", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.T_absZero_K", "name": "T_absZero_K", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.classifyThermalRegime", "name": "classifyThermalRegime", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.T_CMB_mK", "name": "T_CMB_mK", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.aboveCMB", "name": "aboveCMB", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.subCMBresidual", "name": "subCMBresidual", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.landauerFloor", "name": "landauerFloor", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.landauerAdmissible", "name": "landauerAdmissible", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.landauerDeficit", "name": "landauerDeficit", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.thermalGate", "name": "thermalGate", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.superpositionFromVerdict", "name": "superpositionFromVerdict", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.thermalGateEx", "name": "thermalGateEx", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.A_thermal", "name": "A_thermal", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "def", "id": "Semantics.HCMMR.Laws.Law21_ThermalBoundary.A_thermal_weight", "name": "A_thermal_weight", "module": "Semantics.HCMMR.Laws.Law21_ThermalBoundary" }, { "kind": "module", "id": "Semantics.HCMMR.Manifest", "name": "Manifest", "path": "Semantics/HCMMR/Manifest.lean", "namespace": "", "doc": "HCMMR Manifest.lean \u2014 Single import entry point for the HCMMR Operadic Meta-Calculus. Import this file to access the full typed-gate diagnostic system: Core typeclass definitions (Gate, GateChain, EigenmassOperator, Residual, DiagnosticReceipt) Bridge adapters to existing Semantics modules (FAMM, S", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 30 }, { "kind": "module", "id": "Semantics.HachimojiCostRefinement", "name": "HachimojiCostRefinement", "path": "Semantics/HachimojiCostRefinement.lean", "namespace": "HachimojiCostRefinement", "doc": "abbrev HachimojiNucleotide := Fin 8 /-- Hachimoji codon is a triplet of nucleotides", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 78 }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.standardCodonSpace", "name": "standardCodonSpace", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.hachimojiCodonSpace", "name": "hachimojiCodonSpace", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.standardAverageDegeneracy", "name": "standardAverageDegeneracy", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.hachimojiAverageDegeneracy", "name": "hachimojiAverageDegeneracy", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.standardBaseCost", "name": "standardBaseCost", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "def", "id": "Semantics.HachimojiCostRefinement.hachimojiRawCost", "name": "hachimojiRawCost", "module": "Semantics.HachimojiCostRefinement" }, { "kind": "module", "id": "Semantics.HachimojiManifoldAxiom", "name": "HachimojiManifoldAxiom", "path": "Semantics/HachimojiManifoldAxiom.lean", "namespace": "", "doc": "HachimojiManifoldAxiom.lean \u2014 Baker Bound via 8-State Chromatin Manifold Replaces the transcendence axiom (Baker's theorem) with a geometric axiom: the Ricci flow on the 8-state Hachimoji Baker manifold converges, and its persistent homology certifies the Baker bound. AXIOM ARCHITECTURE: hachimoji", "math_kind": "geometry", "sorry_count": 3, "theorem_count": 6, "def_count": 2, "struct_count": 4, "inductive_count": 1, "line_count": 244 }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.HachimojiBase", "name": "HachimojiBase", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.repunit_mul_pred", "name": "repunit_mul_pred", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.repunit_cross_mul", "name": "repunit_cross_mul", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.PersistentClass", "name": "PersistentClass", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.bms_from_manifold", "name": "bms_from_manifold", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "theorem", "id": "Semantics.HachimojiManifoldAxiom.goormaghtigh_from_manifold", "name": "goormaghtigh_from_manifold", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "def", "id": "Semantics.HachimojiManifoldAxiom.PersistenceBarcode", "name": "PersistenceBarcode", "module": "Semantics.HachimojiManifoldAxiom" }, { "kind": "module", "id": "Semantics.HachimojiPipeline", "name": "HachimojiPipeline", "path": "Semantics/HachimojiPipeline.lean", "namespace": "Semantics.HachimojiPipeline", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HachimojiPipeline.lean - Enhanced Hachimoji Pipeline with All Improvements Complete hachimoji encoding pipeline from first bit to final assembly with: Genetic compression parameters (\u03c1_seq, v_epigeneti", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 105, "struct_count": 44, "inductive_count": 2, "line_count": 1600 }, { "kind": "def", "id": "Semantics.HachimojiPipeline.energyToLogProb", "name": "energyToLogProb", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.updateDiscreteState", "name": "updateDiscreteState", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.isEntropySpike", "name": "isEntropySpike", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.fastPredict", "name": "fastPredict", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.updateContextHierarchy", "name": "updateContextHierarchy", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.getShortContext", "name": "getShortContext", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.getMediumContext", "name": "getMediumContext", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.getLongContext", "name": "getLongContext", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.trainLookupTable", "name": "trainLookupTable", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.initInterval", "name": "initInterval", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.scaleInterval", "name": "scaleInterval", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.encodeSymbol", "name": "encodeSymbol", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.decodeSymbol", "name": "decodeSymbol", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.initLogLoss", "name": "initLogLoss", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.updateLogLoss", "name": "updateLogLoss", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.computeLogLossPerByte", "name": "computeLogLossPerByte", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.computeCompressionRatio", "name": "computeCompressionRatio", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.computeCompressionPercentage", "name": "computeCompressionPercentage", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.initDecompressor", "name": "initDecompressor", "module": "Semantics.HachimojiPipeline" }, { "kind": "def", "id": "Semantics.HachimojiPipeline.readBits", "name": "readBits", "module": "Semantics.HachimojiPipeline" }, { "kind": "module", "id": "Semantics.HachimojiSubstitution", "name": "HachimojiSubstitution", "path": "Semantics/HachimojiSubstitution.lean", "namespace": "Greek", "doc": "HachimojiSubstitution.lean \u2014 Greek-symbol re-encoding of the Hachimoji 8 states Standalone companion to HachimojiManifoldAxiom.lean. Does NOT modify the working axiom file \u2014 only adds a Greek-letter variant and the bijection between the two encodings. The substitution reads the Research Stack's ow", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 3, "def_count": 11, "struct_count": 0, "inductive_count": 3, "line_count": 300 }, { "kind": "theorem", "id": "Semantics.HachimojiSubstitution.HachimojiBase", "name": "HachimojiBase", "module": "Semantics.HachimojiSubstitution" }, { "kind": "theorem", "id": "Semantics.HachimojiSubstitution.greek_latin_agree", "name": "greek_latin_agree", "module": "Semantics.HachimojiSubstitution" }, { "kind": "theorem", "id": "Semantics.HachimojiSubstitution.forward_states_are_normal", "name": "forward_states_are_normal", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.hachimojiGreekEquiv", "name": "hachimojiGreekEquiv", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.Greek", "name": "Greek", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.bitToGreek", "name": "bitToGreek", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.greekToReceiptBits", "name": "greekToReceiptBits", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.greekToRegime", "name": "greekToRegime", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.fromQAOABitstring", "name": "fromQAOABitstring", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.toQAOABitstring", "name": "toQAOABitstring", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.knownOmegaStates", "name": "knownOmegaStates", "module": "Semantics.HachimojiSubstitution" }, { "kind": "def", "id": "Semantics.HachimojiSubstitution.omegaLogogramReceipt", "name": "omegaLogogramReceipt", "module": "Semantics.HachimojiSubstitution" }, { "kind": "module", "id": "Semantics.HamiltonianFormal", "name": "HamiltonianFormal", "path": "Semantics/HamiltonianFormal.lean", "namespace": "Semantics.HamiltonianFormal", "doc": "structure Dimension where mass : \u2124 length : \u2124 time : \u2124 deriving Repr, DecidableEq, BEq /-- Extensionality theorem for Dimension", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 61, "def_count": 25, "struct_count": 3, "inductive_count": 0, "line_count": 776 }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.Dimension", "name": "Dimension", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_pos_of_pos", "name": "sqrt_pos_of_pos", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.mul_le_mul_of_pos_left", "name": "mul_le_mul_of_pos_left", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.mul_le_mul_of_pos_right", "name": "mul_le_mul_of_pos_right", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sq_nonneg_custom", "name": "sq_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_nonneg_custom", "name": "sqrt_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.abs_of_nonneg_custom", "name": "abs_of_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_sq_custom_full", "name": "sqrt_sq_custom_full", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.mul_nonneg_custom", "name": "mul_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.div_nonneg_custom", "name": "div_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_monotone_custom", "name": "sqrt_monotone_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.reciprocal_le_custom", "name": "reciprocal_le_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_sq_custom", "name": "sqrt_sq_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.add_le_add_left_custom", "name": "add_le_add_left_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.add_le_add_right_custom", "name": "add_le_add_right_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.add_nonneg_custom", "name": "add_nonneg_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sq_le_sq_custom", "name": "sq_le_sq_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.sqrt_le_sqrt_custom", "name": "sqrt_le_sqrt_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.zero_sq_custom", "name": "zero_sq_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.mul_lt_mul_of_pos_left_custom", "name": "mul_lt_mul_of_pos_left_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.mul_lt_mul_of_pos_right_custom", "name": "mul_lt_mul_of_pos_right_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.le_add_of_nonneg_left_custom", "name": "le_add_of_nonneg_left_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.le_add_of_nonneg_right_custom", "name": "le_add_of_nonneg_right_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "theorem", "id": "Semantics.HamiltonianFormal.le_of_lt_custom", "name": "le_of_lt_custom", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.dimensionless", "name": "dimensionless", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.massDim", "name": "massDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.lengthDim", "name": "lengthDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.timeDim", "name": "timeDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.velocityDim", "name": "velocityDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.energyDim", "name": "energyDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.momentumDim", "name": "momentumDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.GDim", "name": "GDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.cDim", "name": "cDim", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PositiveMass", "name": "PositiveMass", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PositiveGravitationalConstant", "name": "PositiveGravitationalConstant", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PositiveSoftening", "name": "PositiveSoftening", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PositiveLightSpeed", "name": "PositiveLightSpeed", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PhaseSpace", "name": "PhaseSpace", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.FlowMap", "name": "FlowMap", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.SymplecticForm", "name": "SymplecticForm", "module": "Semantics.HamiltonianFormal" }, { "kind": "def", "id": "Semantics.HamiltonianFormal.PoissonBracket", "name": "PoissonBracket", "module": "Semantics.HamiltonianFormal" }, { "kind": "module", "id": "Semantics.HamiltonianVerification", "name": "HamiltonianVerification", "path": "Semantics/HamiltonianVerification.lean", "namespace": "Semantics.HamiltonianVerification", "doc": "def inverseAreaDim : Semantics.HamiltonianFormal.Dimension := Semantics.HamiltonianFormal.lengthDim.pow (-2) /-- Mass density dimension `[M][L]^-3`.", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 324, "def_count": 7, "struct_count": 0, "inductive_count": 0, "line_count": 1836 }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.kineticEnergyDimensionalConsistency", "name": "kineticEnergyDimensionalConsistency", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.regularizedPotentialDimensionalConsistency", "name": "regularizedPotentialDimensionalConsistency", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.threeBodyCorrectionDimensionalRequirement", "name": "threeBodyCorrectionDimensionalRequirement", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.velocityDependentTermDimensionalConsistency", "name": "velocityDependentTermDimensionalConsistency", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.fieldEquationDimensionalConsistency", "name": "fieldEquationDimensionalConsistency", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.lambdaKappa1DimensionalMismatch", "name": "lambdaKappa1DimensionalMismatch", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.lambdaKappa3DimensionalConsistency", "name": "lambdaKappa3DimensionalConsistency", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.phaseSpaceNormDimensionalHomogeneity", "name": "phaseSpaceNormDimensionalHomogeneity", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.regularizedPotentialFiniteAtCollision", "name": "regularizedPotentialFiniteAtCollision", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.phiEffInitialConditionsWellPosed", "name": "phiEffInitialConditionsWellPosed", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.parameterSystemLocallyClosed", "name": "parameterSystemLocallyClosed", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.spectralAssumptionsRelaxed", "name": "spectralAssumptionsRelaxed", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.tDependenceConvexityBoundResolved", "name": "tDependenceConvexityBoundResolved", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.regularizedPotentialZeroSeparation", "name": "regularizedPotentialZeroSeparation", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.regularizedPotentialNewtonianLimit", "name": "regularizedPotentialNewtonianLimit", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.threeBodyCorrectionCoincidenceVanishing", "name": "threeBodyCorrectionCoincidenceVanishing", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.kineticEnergyNonNegative", "name": "kineticEnergyNonNegative", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.regularizedPotentialBoundedBelow", "name": "regularizedPotentialBoundedBelow", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.velocityDependentTermsBounded", "name": "velocityDependentTermsBounded", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.errorFunctionalNonNegative", "name": "errorFunctionalNonNegative", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.verificationBoundMeaningful", "name": "verificationBoundMeaningful", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.symplecticFormPreservation", "name": "symplecticFormPreservation", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.hamiltonianConservation", "name": "hamiltonianConservation", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.coupledSystemWellPosed", "name": "coupledSystemWellPosed", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.hamiltonianEquationDependencies", "name": "hamiltonianEquationDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.hamiltonsEquationsDependencies", "name": "hamiltonsEquationsDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.errorFunctionalDependencies", "name": "errorFunctionalDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.normDependencies", "name": "normDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.adjointEquationDependencies", "name": "adjointEquationDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "theorem", "id": "Semantics.HamiltonianVerification.firstOrderConditionDependencies", "name": "firstOrderConditionDependencies", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.inverseAreaDim", "name": "inverseAreaDim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.massDensityDim", "name": "massDensityDim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.gravitationalPotentialDim", "name": "gravitationalPotentialDim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.waveOperatorDim", "name": "waveOperatorDim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.threeBodyQuadrupoleDim", "name": "threeBodyQuadrupoleDim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.beta1Dim", "name": "beta1Dim", "module": "Semantics.HamiltonianVerification" }, { "kind": "def", "id": "Semantics.HamiltonianVerification.geometricLengthPower", "name": "geometricLengthPower", "module": "Semantics.HamiltonianVerification" }, { "kind": "module", "id": "Semantics.Hardware.AdaptiveFabric", "name": "AdaptiveFabric", "path": "Semantics/Hardware/AdaptiveFabric.lean", "namespace": "Semantics.AdaptiveFabric", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team AdaptiveFabric.lean \u2014 Adaptive 1-Bit CMYK Merged Architecture Formalization of the adaptive USB fabric connector logic. The 1-bit pipeline provides cheap signal encoding over time. CMYK/SLUQ provides c", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 5, "struct_count": 2, "inductive_count": 1, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.Hardware.AdaptiveFabric.state_determined_by_sluq", "name": "state_determined_by_sluq", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "def", "id": "Semantics.Hardware.AdaptiveFabric.CMYKState", "name": "CMYKState", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "def", "id": "Semantics.Hardware.AdaptiveFabric.classifySluqAcc", "name": "classifySluqAcc", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "def", "id": "Semantics.Hardware.AdaptiveFabric.step", "name": "step", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "def", "id": "Semantics.Hardware.AdaptiveFabric.testConfig", "name": "testConfig", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "def", "id": "Semantics.Hardware.AdaptiveFabric.initialState", "name": "initialState", "module": "Semantics.Hardware.AdaptiveFabric" }, { "kind": "module", "id": "Semantics.Hardware.AgenticHardware", "name": "AgenticHardware", "path": "Semantics/Hardware/AgenticHardware.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "Hardware-native agent structures for geometric phase evolution and frustration computation. Split from AgenticOrchestration.lean per swarm suggestion (USER AUTHORIZED).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 6, "inductive_count": 0, "line_count": 126 }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.computeAgentChristoffel", "name": "computeAgentChristoffel", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.agentCos", "name": "agentCos", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.computeAgentFrustration", "name": "computeAgentFrustration", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.computeAgentLockingEnergy", "name": "computeAgentLockingEnergy", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.updateAgentStateFromGeometry", "name": "updateAgentStateFromGeometry", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "def", "id": "Semantics.Hardware.AgenticHardware.updateAgentStateFromChristoffel", "name": "updateAgentStateFromChristoffel", "module": "Semantics.Hardware.AgenticHardware" }, { "kind": "module", "id": "Semantics.Hardware.Blitter6502OISC", "name": "Blitter6502OISC", "path": "Semantics/Hardware/Blitter6502OISC.lean", "namespace": "Blitter6502OISC", "doc": "6502 OISC Blitter -- 0D Scalar Proof Engine A One-Instruction-Set Computer (OISC) with 6502 memory map semantics. The blitter verifies S3C theorems via exhaustive LUT enumeration. Proof strategy: Instead of symbolic proofs with free variables, we use native_decide on closed computations over the 8", "math_kind": "avm", "sorry_count": 0, "theorem_count": 3, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 99 }, { "kind": "theorem", "id": "Semantics.Hardware.Blitter6502OISC.blitter_bPlusEqualsBZeroPlusOne", "name": "blitter_bPlusEqualsBZeroPlusOne", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "theorem", "id": "Semantics.Hardware.Blitter6502OISC.blitter_throatAtShellMidpoint", "name": "blitter_throatAtShellMidpoint", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "theorem", "id": "Semantics.Hardware.Blitter6502OISC.blitter_emitGateSimplified", "name": "blitter_emitGateSimplified", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "def", "id": "Semantics.Hardware.Blitter6502OISC.sqrtLUT8", "name": "sqrtLUT8", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "def", "id": "Semantics.Hardware.Blitter6502OISC.mirrorTerm", "name": "mirrorTerm", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "def", "id": "Semantics.Hardware.Blitter6502OISC.initCPU", "name": "initCPU", "module": "Semantics.Hardware.Blitter6502OISC" }, { "kind": "module", "id": "Semantics.Hardware.EmergencyBootShell", "name": "EmergencyBootShell", "path": "Semantics/Hardware/EmergencyBootShell.lean", "namespace": "Semantics.Hardware.EmergencyBoot", "doc": "Emergency Boot Shell -- Command interface and packet format Defines the Tiny IP surface extensions for emergency boot operations: Command opcodes and payloads Status byte encoding Process definitions (geometry_scan, seed_assembly, tsm_reconstruct, etc.) Specification: GEOMETRY_EMERGENCY_BOOT_WITNE", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 6, "struct_count": 10, "inductive_count": 3, "line_count": 275 }, { "kind": "theorem", "id": "Semantics.Hardware.EmergencyBootShell.commandOpcode_roundTrip", "name": "commandOpcode_roundTrip", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.commandOpcode", "name": "commandOpcode", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.parseOpcode", "name": "parseOpcode", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.statusByteToUInt8", "name": "statusByteToUInt8", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.uint8ToStatusByte", "name": "uint8ToStatusByte", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.statusFromBootState", "name": "statusFromBootState", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootShell.executeCommand", "name": "executeCommand", "module": "Semantics.Hardware.EmergencyBootShell" }, { "kind": "module", "id": "Semantics.Hardware.EmergencyBootState", "name": "EmergencyBootState", "path": "Semantics/Hardware/EmergencyBootState.lean", "namespace": "Semantics.Hardware.EmergencyBoot", "doc": "Emergency Boot State -- Power failure detection and seed extraction Defines: Power failure detection (AEM20940 + TSM Safety Interlock + Solar Monitor) Solar power state and self-sufficiency checks Emergency boot state machine Geometric scan and seed assembly process Fixed-point Q16_16 arithmetic t", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 13, "struct_count": 5, "inductive_count": 1, "line_count": 257 }, { "kind": "theorem", "id": "Semantics.Hardware.EmergencyBootState.utilizationWithinBounds", "name": "utilizationWithinBounds", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "theorem", "id": "Semantics.Hardware.EmergencyBootState.seedAssemblyDeterministic", "name": "seedAssemblyDeterministic", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "theorem", "id": "Semantics.Hardware.EmergencyBootState.powerFailureMonotonic", "name": "powerFailureMonotonic", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.selfPowerSufficient", "name": "selfPowerSufficient", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.powerFailureDetected", "name": "powerFailureDetected", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.prioritizeHotOpticalPaths", "name": "prioritizeHotOpticalPaths", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.enterCalculatorMode", "name": "enterCalculatorMode", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.initScanState", "name": "initScanState", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.scanStep", "name": "scanStep", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.assembleSeed", "name": "assembleSeed", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.assembleAugmentedSeed", "name": "assembleAugmentedSeed", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.emergencyBootUtilization", "name": "emergencyBootUtilization", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.initEmergencyBoot", "name": "initEmergencyBoot", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.handlePowerFailure", "name": "handlePowerFailure", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.startScan", "name": "startScan", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootState.finishScan", "name": "finishScan", "module": "Semantics.Hardware.EmergencyBootState" }, { "kind": "module", "id": "Semantics.Hardware.EmergencyBootTypes", "name": "EmergencyBootTypes", "path": "Semantics/Hardware/EmergencyBootTypes.lean", "namespace": "Semantics.Hardware.EmergencyBoot", "doc": "Emergency Boot Types -- Core geometric and computational types Defines the foundational types for the Geometry Emergency Boot Witness: Hexagonal coordinate system for capacitor placement Capacitance classification (low/medium/high) Optical fiber hot/cold path model Voltage differential computation ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 13, "struct_count": 10, "inductive_count": 3, "line_count": 252 }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.hexToSpatialHash", "name": "hexToSpatialHash", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.capClassToBits", "name": "capClassToBits", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.topologyHash", "name": "topologyHash", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.computeDifferential", "name": "computeDifferential", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.voltageToAnalogValue", "name": "voltageToAnalogValue", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.analogValueToVoltage", "name": "analogValueToVoltage", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.voltageLogic", "name": "voltageLogic", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.hybridComputation", "name": "hybridComputation", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.memristorConductance", "name": "memristorConductance", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.memristorUpdate", "name": "memristorUpdate", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.verifyMemoryRetention", "name": "verifyMemoryRetention", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.grapheneProperties", "name": "grapheneProperties", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "def", "id": "Semantics.Hardware.EmergencyBootTypes.ganProperties", "name": "ganProperties", "module": "Semantics.Hardware.EmergencyBootTypes" }, { "kind": "module", "id": "Semantics.Hardware.HardwareExtraction", "name": "HardwareExtraction", "path": "Semantics/Hardware/HardwareExtraction.lean", "namespace": "Semantics.HardwareExtraction", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HardwareExtraction.lean \u2014 Lean 4 to Hardware Extraction Examples This module provides examples of extracting Lean 4 proofs to hardware descriptions in Verilog and Bluespec, with formal equivalence proo", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 11, "struct_count": 4, "inductive_count": 2, "line_count": 284 }, { "kind": "theorem", "id": "Semantics.Hardware.HardwareExtraction.verilogCounterMatchesLean", "name": "verilogCounterMatchesLean", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "theorem", "id": "Semantics.Hardware.HardwareExtraction.bluespecCounterMatchesLean", "name": "bluespecCounterMatchesLean", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "theorem", "id": "Semantics.Hardware.HardwareExtraction.fsmTransitionDeterministic", "name": "fsmTransitionDeterministic", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "theorem", "id": "Semantics.Hardware.HardwareExtraction.mutexMutualExclusion", "name": "mutexMutualExclusion", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.incrementCounter", "name": "incrementCounter", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractCounterToVerilog", "name": "extractCounterToVerilog", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractCounterToBluespec", "name": "extractCounterToBluespec", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.fsmTransition", "name": "fsmTransition", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractFSMToVerilog", "name": "extractFSMToVerilog", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractFSMToBluespec", "name": "extractFSMToBluespec", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.tryAcquireLock", "name": "tryAcquireLock", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.releaseLock", "name": "releaseLock", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractMutexToVerilog", "name": "extractMutexToVerilog", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.extractMutexToBluespec", "name": "extractMutexToBluespec", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "def", "id": "Semantics.Hardware.HardwareExtraction.isFairMutex", "name": "isFairMutex", "module": "Semantics.Hardware.HardwareExtraction" }, { "kind": "module", "id": "Semantics.Hardware.LaserPathCell", "name": "LaserPathCell", "path": "Semantics/Hardware/LaserPathCell.lean", "namespace": "Semantics.Hardware", "doc": "Copyright (c) 2026 Sovereign Stack. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Laser Path Cell FPGA Implementation Direct analogy: Laser scan path = FPGA cell state update Xu Song/Wen Chen STL-free 3D printing \u2192 Hardware cel", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 14, "struct_count": 2, "inductive_count": 1, "line_count": 262 }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.ofUInt16", "name": "ofUInt16", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.ofUInt8", "name": "ofUInt8", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.default", "name": "default", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.thermalLoad", "name": "thermalLoad", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.shellToLaserCell", "name": "shellToLaserCell", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.selectScanStrategy", "name": "selectScanStrategy", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.applyScan", "name": "applyScan", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.laserColdWeldEnergy", "name": "laserColdWeldEnergy", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.isGoodWeld", "name": "isGoodWeld", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.cellIndex", "name": "cellIndex", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.updateCellRow", "name": "updateCellRow", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.meshRepresentationSize", "name": "meshRepresentationSize", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.laserCellRepresentationSize", "name": "laserCellRepresentationSize", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "def", "id": "Semantics.Hardware.LaserPathCell.memoryReductionRatio", "name": "memoryReductionRatio", "module": "Semantics.Hardware.LaserPathCell" }, { "kind": "module", "id": "Semantics.Hardware.TangNano9K.BitstreamWitness", "name": "BitstreamWitness", "path": "Semantics/Hardware/TangNano9K/BitstreamWitness.lean", "namespace": "Semantics.Hardware.TangNano9K.BitstreamWitness", "doc": "Bitstream SHA256 Witness AGENTS.md 8.5.3: All FPGA bitstreams must be versioned with SHA256 hash in a Lean module. This module is the single source of truth for the expected hash of tangnano9k.fs. When the bitstream is regenerated, update `expectedBitstreamSha256` and re-run `lake build` to verif", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 41 }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.BitstreamWitness.expectedBitstreamSha256", "name": "expectedBitstreamSha256", "module": "Semantics.Hardware.TangNano9K.BitstreamWitness" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.BitstreamWitness.checkBitstreamWitness", "name": "checkBitstreamWitness", "module": "Semantics.Hardware.TangNano9K.BitstreamWitness" }, { "kind": "module", "id": "Semantics.Hardware.TangNano9K.NIICore", "name": "NIICore", "path": "Semantics/Hardware/TangNano9K/NIICore.lean", "namespace": "Semantics.Hardware.TangNano9K.NIICore", "doc": "NII Core \u2014 Formal specification of the first-order difference predictor Lean source of truth for `hardware/tangnano9k/rtl/nii_core.v`. The Verilog stub implements: nii_a = sat_clip(obs_a - prev_a, CLIP) prev_a := obs_a with identical rules for t, g, c channels. This module formalizes the update r", "math_kind": "avm", "sorry_count": 0, "theorem_count": 1, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 161 }, { "kind": "theorem", "id": "Semantics.Hardware.TangNano9K.NIICore.niiOutputBounded", "name": "niiOutputBounded", "module": "Semantics.Hardware.TangNano9K.NIICore" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.NIICore.clamp", "name": "clamp", "module": "Semantics.Hardware.TangNano9K.NIICore" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.NIICore.niiStep", "name": "niiStep", "module": "Semantics.Hardware.TangNano9K.NIICore" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.NIICore.emitNIICore", "name": "emitNIICore", "module": "Semantics.Hardware.TangNano9K.NIICore" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.NIICore.checkNIICoreWitness", "name": "checkNIICoreWitness", "module": "Semantics.Hardware.TangNano9K.NIICore" }, { "kind": "module", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM", "name": "RGFlowFAMM", "path": "Semantics/Hardware/TangNano9K/RGFlowFAMM.lean", "namespace": "Semantics.Hardware.TangNano9K.RGFlowFAMM", "doc": "RGFlow + FAMM \u2014 Formal specification Lean source of truth for hardware/tangnano9k/rtl/rgflow_famm.v. Mirrors the Python balanced5 reference model: scripts/snn/snn_nii_reference.py (rgflow_step + famm_update) Theorem targets: All outputs bounded (sigma \u2208 [0,1023], FAMM counters \u2208 [0,255]) -------", "math_kind": "routing", "sorry_count": 0, "theorem_count": 2, "def_count": 6, "struct_count": 4, "inductive_count": 0, "line_count": 330 }, { "kind": "theorem", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.rgflowSigmaBounded", "name": "rgflowSigmaBounded", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "theorem", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.rgflowRPBounded", "name": "rgflowRPBounded", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.sat8Add", "name": "sat8Add", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.linDecay", "name": "linDecay", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.absS", "name": "absS", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.rgflowStep", "name": "rgflowStep", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.fammUpdate", "name": "fammUpdate", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.RGFlowFAMM.emitRGFlowFAMM", "name": "emitRGFlowFAMM", "module": "Semantics.Hardware.TangNano9K.RGFlowFAMM" }, { "kind": "module", "id": "Semantics.Hardware.TangNano9K", "name": "TangNano9K", "path": "Semantics/Hardware/TangNano9K.lean", "namespace": "Semantics.Hardware.TangNano9K", "doc": "Genome18 Address \u2014 Verilog extraction target Lean source of truth: Genome18.addr Verilog extraction: combinational assign matching the exact arithmetic. The emitted module is parameter-free and uses only constant multiplications that Yosys/Gowin synthesize to shifts/adds. ------------------------", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 4, "struct_count": 0, "inductive_count": 0, "line_count": 175 }, { "kind": "theorem", "id": "Semantics.Hardware.TangNano9K.verilogAddr_eq_addr", "name": "verilogAddr_eq_addr", "module": "Semantics.Hardware.TangNano9K" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.verilogAddr", "name": "verilogAddr", "module": "Semantics.Hardware.TangNano9K" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.emitGenome18Address", "name": "emitGenome18Address", "module": "Semantics.Hardware.TangNano9K" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.emitQ16_16ALU", "name": "emitQ16_16ALU", "module": "Semantics.Hardware.TangNano9K" }, { "kind": "def", "id": "Semantics.Hardware.TangNano9K.checkAllGenome18", "name": "checkAllGenome18", "module": "Semantics.Hardware.TangNano9K" }, { "kind": "module", "id": "Semantics.HermesAgentIntegration", "name": "HermesAgentIntegration", "path": "Semantics/HermesAgentIntegration.lean", "namespace": "Semantics.HermesAgentIntegration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HermesAgentIntegration.lean \u2014 Field Operator Integration Boundary This module formalizes the integration of Hermes Agent as a field operator, messenger, and skill runtime that remains subordinate to Le", "math_kind": "avm", "sorry_count": 7, "theorem_count": 3, "def_count": 13, "struct_count": 2, "inductive_count": 3, "line_count": 319 }, { "kind": "theorem", "id": "Semantics.HermesAgentIntegration.readOnlyCannotPromote", "name": "readOnlyCannotPromote", "module": "Semantics.HermesAgentIntegration" }, { "kind": "theorem", "id": "Semantics.HermesAgentIntegration.emptyReceiptsVacuousPromote", "name": "emptyReceiptsVacuousPromote", "module": "Semantics.HermesAgentIntegration" }, { "kind": "theorem", "id": "Semantics.HermesAgentIntegration.defaultStatusIsHold", "name": "defaultStatusIsHold", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.toString", "name": "toString", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.all", "name": "all", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.defaultHermesStatus", "name": "defaultHermesStatus", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.isReadOnly", "name": "isReadOnly", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.requiresReceipts", "name": "requiresReceipts", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.canPromote", "name": "canPromote", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.gclProvenanceCff", "name": "gclProvenanceCff", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.leanSorryAudit", "name": "leanSorryAudit", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.adapterSpecWriter", "name": "adapterSpecWriter", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.deepseekReviewBundle", "name": "deepseekReviewBundle", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.wardenTriage", "name": "wardenTriage", "module": "Semantics.HermesAgentIntegration" }, { "kind": "def", "id": "Semantics.HermesAgentIntegration.skillRunToReceiptCore", "name": "skillRunToReceiptCore", "module": "Semantics.HermesAgentIntegration" }, { "kind": "module", "id": "Semantics.HexLogogramAtlas", "name": "HexLogogramAtlas", "path": "Semantics/HexLogogramAtlas.lean", "namespace": "Semantics.HexLogogramAtlas", "doc": "# HexLogogramAtlas A HexLogogramAtlas is a deterministic seed-generated map from typed token or Mass Number coordinates into reusable logogram groups. It is the logogram grouping layer above `LadderLUT`: the hex seed does not store the words or glyphs; it stores the replayable grouping law that ch", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 7, "def_count": 14, "struct_count": 1, "inductive_count": 1, "line_count": 210 }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.smallAffineReplayGroups", "name": "smallAffineReplayGroups", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.canonicalHexAtlasPromotable", "name": "canonicalHexAtlasPromotable", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.tinyHexAtlasNotPromotable", "name": "tinyHexAtlasNotPromotable", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.badHexBaseAtlasNotPromotable", "name": "badHexBaseAtlasNotPromotable", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.badGroupAtlasNotPromotable", "name": "badGroupAtlasNotPromotable", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.promotableAtlasStructurallyValid", "name": "promotableAtlasStructurallyValid", "module": "Semantics.HexLogogramAtlas" }, { "kind": "theorem", "id": "Semantics.HexLogogramAtlas.promotableAtlasSatisfiesByteLaw", "name": "promotableAtlasSatisfiesByteLaw", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.expectedHexBase", "name": "expectedHexBase", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasStructurallyValid", "name": "atlasStructurallyValid", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasRawValueAt", "name": "atlasRawValueAt", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasGroupAt", "name": "atlasGroupAt", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.replayAtlasGroups", "name": "replayAtlasGroups", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.explicitAtlasBytes", "name": "explicitAtlasBytes", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasEncodedBytes", "name": "atlasEncodedBytes", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasByteLawHolds", "name": "atlasByteLawHolds", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.atlasPromotable", "name": "atlasPromotable", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.smallAffineAtlas", "name": "smallAffineAtlas", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.canonicalHexAtlas", "name": "canonicalHexAtlas", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.tinyHexAtlas", "name": "tinyHexAtlas", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.badHexBaseAtlas", "name": "badHexBaseAtlas", "module": "Semantics.HexLogogramAtlas" }, { "kind": "def", "id": "Semantics.HexLogogramAtlas.badGroupAtlas", "name": "badGroupAtlas", "module": "Semantics.HexLogogramAtlas" }, { "kind": "module", "id": "Semantics.HolographicProjection", "name": "HolographicProjection", "path": "Semantics/HolographicProjection.lean", "namespace": "Semantics.HolographicProjection", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 4, "inductive_count": 0, "line_count": 236 }, { "kind": "theorem", "id": "Semantics.HolographicProjection.lawfulActionReducesEntropy", "name": "lawfulActionReducesEntropy", "module": "Semantics.HolographicProjection" }, { "kind": "theorem", "id": "Semantics.HolographicProjection.holographicProjectionPreservesCoherence", "name": "holographicProjectionPreservesCoherence", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.projectionKernel", "name": "projectionKernel", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.holographicProjection", "name": "holographicProjection", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.entropyReduction", "name": "entropyReduction", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.isStabilized", "name": "isStabilized", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.applyStabilization", "name": "applyStabilization", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.calculateStabilizationProbability", "name": "calculateStabilizationProbability", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.isHolographicActionLawful", "name": "isHolographicActionLawful", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.updateSurfacePoint", "name": "updateSurfacePoint", "module": "Semantics.HolographicProjection" }, { "kind": "def", "id": "Semantics.HolographicProjection.holographicBind", "name": "holographicBind", "module": "Semantics.HolographicProjection" }, { "kind": "module", "id": "Semantics.HonestParameterReport", "name": "HonestParameterReport", "path": "Semantics/HonestParameterReport.lean", "namespace": "Semantics.HonestParameterReport", "doc": "HonestParameterReport.lean \u2014 Full Parameter Accounting for BraidCore This module explicitly lists every parameter used by the BraidCore framework, marks each as Derived, Fitted, PostHoc, or Adopted, and locks the total count in Lean. This directly addresses the adversarial review's Attack #5 (\"Par", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 9, "def_count": 18, "struct_count": 1, "inductive_count": 1, "line_count": 290 }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.for", "name": "for", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.totalParameterCount_is13", "name": "totalParameterCount_is13", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.fittedCount_is4", "name": "fittedCount_is4", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.postHocCount_is3", "name": "postHocCount_is3", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.tuningCount_is4", "name": "tuningCount_is4", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.adoptedCount_is2", "name": "adoptedCount_is2", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.derivedCount_is0", "name": "derivedCount_is0", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.parameterBudgetBalanced", "name": "parameterBudgetBalanced", "module": "Semantics.HonestParameterReport" }, { "kind": "theorem", "id": "Semantics.HonestParameterReport.corr1Loop_isFitted_notDerived", "name": "corr1Loop_isFitted_notDerived", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.Provenance", "name": "Provenance", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.mkParameter", "name": "mkParameter", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p01_zMenger", "name": "p01_zMenger", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p02_corr1Loop", "name": "p02_corr1Loop", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p03_corr2Loop", "name": "p03_corr2Loop", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p04_alphaT", "name": "p04_alphaT", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p05_sqrt10", "name": "p05_sqrt10", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p06_alphaCore", "name": "p06_alphaCore", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p07_sigmaSq", "name": "p07_sigmaSq", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p08_gradeThresholds", "name": "p08_gradeThresholds", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p09_domainClassification", "name": "p09_domainClassification", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p10_correctionLevel", "name": "p10_correctionLevel", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p11_P0", "name": "p11_P0", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p12_zTolerance", "name": "p12_zTolerance", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.p13_sweetSpotBounds", "name": "p13_sweetSpotBounds", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.parameterRegistry", "name": "parameterRegistry", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.totalParameterCount", "name": "totalParameterCount", "module": "Semantics.HonestParameterReport" }, { "kind": "def", "id": "Semantics.HonestParameterReport.countByProvenance", "name": "countByProvenance", "module": "Semantics.HonestParameterReport" }, { "kind": "module", "id": "Semantics.HormoneDeriv", "name": "HormoneDeriv", "path": "Semantics/HormoneDeriv.lean", "namespace": "Semantics.HormoneDeriv", "doc": "HormoneDeriv.lean - Neuroendocrine Control System Bindings Ports rows 121, 122, 138 from MATH_MODEL_MAP.tsv (Python \u2192 Lean). Q16.16: 1.0 = 65536. All hormone concentrations \u2208 [0,1] \u2192 [0, 65536].", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 79 }, { "kind": "def", "id": "Semantics.HormoneDeriv.epsilon", "name": "epsilon", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.ln2", "name": "ln2", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.halfLifeToDecayRate", "name": "halfLifeToDecayRate", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.logitApprox", "name": "logitApprox", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.logitZNorm", "name": "logitZNorm", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.concentrationDecay", "name": "concentrationDecay", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.advanceHormone", "name": "advanceHormone", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.hormoneInvariant", "name": "hormoneInvariant", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.hormoneCost", "name": "hormoneCost", "module": "Semantics.HormoneDeriv" }, { "kind": "def", "id": "Semantics.HormoneDeriv.hormoneBind", "name": "hormoneBind", "module": "Semantics.HormoneDeriv" }, { "kind": "module", "id": "Semantics.HotPathColdPath", "name": "HotPathColdPath", "path": "Semantics/HotPathColdPath.lean", "namespace": "Semantics.HotPathColdPath", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 4, "inductive_count": 1, "line_count": 269 }, { "kind": "theorem", "id": "Semantics.HotPathColdPath.lawfulAdjustmentMaintainsBalance", "name": "lawfulAdjustmentMaintainsBalance", "module": "Semantics.HotPathColdPath" }, { "kind": "theorem", "id": "Semantics.HotPathColdPath.hotPathMonotonicWithFrequency", "name": "hotPathMonotonicWithFrequency", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.branchPrediction", "name": "branchPrediction", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.sluqRouting", "name": "sluqRouting", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.classifyPath", "name": "classifyPath", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.calculateHotPathProbability", "name": "calculateHotPathProbability", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.calculateColdPathProbability", "name": "calculateColdPathProbability", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.calculateUnifiedAdjustment", "name": "calculateUnifiedAdjustment", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.updateUnifiedTopology", "name": "updateUnifiedTopology", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.isTopologyAdjustmentLawful", "name": "isTopologyAdjustmentLawful", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.updateNodePattern", "name": "updateNodePattern", "module": "Semantics.HotPathColdPath" }, { "kind": "def", "id": "Semantics.HotPathColdPath.topologyAdjustmentBind", "name": "topologyAdjustmentBind", "module": "Semantics.HotPathColdPath" }, { "kind": "module", "id": "Semantics.HouseholderQR", "name": "HouseholderQR", "path": "Semantics/HouseholderQR.lean", "namespace": "Semantics.HouseholderQR", "doc": "HouseholderQR.lean \u2014 Householder QR factorization for O_AMMR Implements Householder reflections for QR factorization: H = I - 2vv^T/(v^T v) QR = H_1 H_2 ... H_n A Key properties: More numerically stable than Gram-Schmidt Each reflection is orthogonal: H^T H = I Incremental update: add column and u", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 21, "struct_count": 5, "inductive_count": 0, "line_count": 224 }, { "kind": "def", "id": "Semantics.HouseholderQR.Q16Vec", "name": "Q16Vec", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.Q16Mat", "name": "Q16Mat", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.householderVector", "name": "householderVector", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.applyReflection", "name": "applyReflection", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.applyReflectionToCol", "name": "applyReflectionToCol", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.qrFactorize", "name": "qrFactorize", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.incrementalUpdate", "name": "incrementalUpdate", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.quantize", "name": "quantize", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.quantizeVec", "name": "quantizeVec", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.quantizeMatCol", "name": "quantizeMatCol", "module": "Semantics.HouseholderQR" }, { "kind": "def", "id": "Semantics.HouseholderQR.O_AMMR_QRNode_valid", "name": "O_AMMR_QRNode_valid", "module": "Semantics.HouseholderQR" }, { "kind": "module", "id": "Semantics.HumanNeuralCompression", "name": "HumanNeuralCompression", "path": "Semantics/HumanNeuralCompression.lean", "namespace": "Semantics.HumanNeuralCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HumanNeuralCompressionVerification.lean \u2014 Formal Witnesses for Human Neural Coding This module provides formal verification that the 4-layer compression pipeline has theorem-backed constraints for huma", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 15, "def_count": 32, "struct_count": 3, "inductive_count": 1, "line_count": 565 }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.topologicalPreservationWithinBudget", "name": "topologicalPreservationWithinBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.layer1ErrorWithinBudget", "name": "layer1ErrorWithinBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.layer2ErrorWithinBudget", "name": "layer2ErrorWithinBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.layer3ErrorWithinBudget", "name": "layer3ErrorWithinBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.layer4ErrorWithinBudget", "name": "layer4ErrorWithinBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.totalRatioAchievesTarget", "name": "totalRatioAchievesTarget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.totalErrorBelowOnePercent", "name": "totalErrorBelowOnePercent", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.pumpPhaseWindowsWithinBounds", "name": "pumpPhaseWindowsWithinBounds", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.snowballGrowthWithinBounds", "name": "snowballGrowthWithinBounds", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.electronOrbitalLoadsWithinBounds", "name": "electronOrbitalLoadsWithinBounds", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.sigma65ConfidenceAchievedWithPumpPhase", "name": "sigma65ConfidenceAchievedWithPumpPhase", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.effectiveCompressionAchievesTarget", "name": "effectiveCompressionAchievesTarget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.compressedSizeWithinTarget", "name": "compressedSizeWithinTarget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.temporalSamplingPreservesInvariant", "name": "temporalSamplingPreservesInvariant", "module": "Semantics.HumanNeuralCompression" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompression.pumpPhaseExtendsSafeWindow", "name": "pumpPhaseExtendsSafeWindow", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.humanNeuronCount", "name": "humanNeuronCount", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.fullStateSizePb", "name": "fullStateSizePb", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.targetCompressedMinGb", "name": "targetCompressedMinGb", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.targetCompressedMaxGb", "name": "targetCompressedMaxGb", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.targetCompressionRatio", "name": "targetCompressionRatio", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.sigma65ErrorBudget", "name": "sigma65ErrorBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.preservationTarget", "name": "preservationTarget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.sigma65TopologicalBudget", "name": "sigma65TopologicalBudget", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer1DeltaExtraction", "name": "layer1DeltaExtraction", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer2GeneticCodon", "name": "layer2GeneticCodon", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer3DeltaGcl", "name": "layer3DeltaGcl", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer4SwarmComposition", "name": "layer4SwarmComposition", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.PrecisionTier", "name": "PrecisionTier", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.wireProtocolQ08", "name": "wireProtocolQ08", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer1Precision", "name": "layer1Precision", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer2Precision", "name": "layer2Precision", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer3Precision", "name": "layer3Precision", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.layer4Precision", "name": "layer4Precision", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.tailEventPrecision", "name": "tailEventPrecision", "module": "Semantics.HumanNeuralCompression" }, { "kind": "def", "id": "Semantics.HumanNeuralCompression.effectiveLayerSize", "name": "effectiveLayerSize", "module": "Semantics.HumanNeuralCompression" }, { "kind": "module", "id": "Semantics.HumanNeuralCompressionVerification", "name": "HumanNeuralCompressionVerification", "path": "Semantics/HumanNeuralCompressionVerification.lean", "namespace": "Semantics.HumanNeuralCompressionVerification", "doc": "# Human Neural Compression Verification This module records the hard finite-state obstruction behind any claimed lossless compression of arbitrary neural snapshots: a smaller finite code space cannot injectively represent a larger finite source space. The result is intentionally modest. It does no", "math_kind": "general", "sorry_count": 0, "theorem_count": 10, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.minimumCompressionRatio_eq", "name": "minimumCompressionRatio_eq", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.idealCompressionRatio_eq", "name": "idealCompressionRatio_eq", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.effectiveUncompressedGb_eq", "name": "effectiveUncompressedGb_eq", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.effectiveMinimumRatio_eq", "name": "effectiveMinimumRatio_eq", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.byte_budget_strictly_smaller", "name": "byte_budget_strictly_smaller", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.lossless_witness_requires_capacity", "name": "lossless_witness_requires_capacity", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.no_injective_compression_to_smaller_fintype", "name": "no_injective_compression_to_smaller_fintype", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.no_lossless_universal_compression", "name": "no_lossless_universal_compression", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.arbitrary_lossless_compression_impossible", "name": "arbitrary_lossless_compression_impossible", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "theorem", "id": "Semantics.HumanNeuralCompressionVerification.onePbTo800Gb_needs_extra_model_structure", "name": "onePbTo800Gb_needs_extra_model_structure", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.uncompressedStateGb", "name": "uncompressedStateGb", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.targetMaxGb", "name": "targetMaxGb", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.targetMinGb", "name": "targetMinGb", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.minimumCompressionRatio", "name": "minimumCompressionRatio", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.idealCompressionRatio", "name": "idealCompressionRatio", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.activeRatioPercent", "name": "activeRatioPercent", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.effectiveUncompressedGb", "name": "effectiveUncompressedGb", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.effectiveMinimumRatio", "name": "effectiveMinimumRatio", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.uncompressedBytes", "name": "uncompressedBytes", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "def", "id": "Semantics.HumanNeuralCompressionVerification.compressedBytes", "name": "compressedBytes", "module": "Semantics.HumanNeuralCompressionVerification" }, { "kind": "mathlib", "id": "Mathlib.Data.Fintype.Card", "name": "Mathlib.Data.Fintype.Card" }, { "kind": "module", "id": "Semantics.Hutter", "name": "Hutter", "path": "Semantics/Hutter.lean", "namespace": "Semantics.Hutter", "doc": "A HutterCell represents a pair of bytes decomposed into 4-bit nibbles. Matches the behavior of `byte_to_cell_pair` in the Python extraction target.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Hutter.signature", "name": "signature", "module": "Semantics.Hutter" }, { "kind": "def", "id": "Semantics.Hutter.admissibilityRatio", "name": "admissibilityRatio", "module": "Semantics.Hutter" }, { "kind": "def", "id": "Semantics.Hutter.hutterInvariant", "name": "hutterInvariant", "module": "Semantics.Hutter" }, { "kind": "def", "id": "Semantics.Hutter.hutterCost", "name": "hutterCost", "module": "Semantics.Hutter" }, { "kind": "def", "id": "Semantics.Hutter.hutterBind", "name": "hutterBind", "module": "Semantics.Hutter" }, { "kind": "module", "id": "Semantics.HutterMaximumCompression", "name": "HutterMaximumCompression", "path": "Semantics/HutterMaximumCompression.lean", "namespace": "Semantics.HutterMaximumCompression", "doc": "def isqrt (n : Nat) : Nat := if n = 0 then 0 else let rec loop (low high : Nat) : Nat := if low + 1 >= high then low else let mid := (low + high) / 2 if mid * mid <= n then loop mid high else loop low mid loop 0 (n + 1) /-! # Hutter Prize Maximum Compression Maximum compression approach for Hutter", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 7, "def_count": 19, "struct_count": 4, "inductive_count": 1, "line_count": 404 }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.foundationVectorDistance_nonneg", "name": "foundationVectorDistance_nonneg", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.streetTransitionCost_bounded", "name": "streetTransitionCost_bounded", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.rgflowScaleDistance_bounded", "name": "rgflowScaleDistance_bounded", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.substrateExecutionCost_bounded", "name": "substrateExecutionCost_bounded", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.routeCost_nonneg", "name": "routeCost_nonneg", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.compressionRatio_nonneg", "name": "compressionRatio_nonneg", "module": "Semantics.HutterMaximumCompression" }, { "kind": "theorem", "id": "Semantics.HutterMaximumCompression.lawfulSymbols_le_emitted", "name": "lawfulSymbols_le_emitted", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.isqrt", "name": "isqrt", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.initContext", "name": "initContext", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.computeFoundationVector", "name": "computeFoundationVector", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.foundationVectorDistance", "name": "foundationVectorDistance", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.streetMembership", "name": "streetMembership", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.streetTransitionCost", "name": "streetTransitionCost", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.rgflowScaleDistance", "name": "rgflowScaleDistance", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.substrateExecutionCost", "name": "substrateExecutionCost", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.proofObligationCost", "name": "proofObligationCost", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.failureRisk", "name": "failureRisk", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.throatBonus", "name": "throatBonus", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.fammMemoryBonus", "name": "fammMemoryBonus", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.routeCost", "name": "routeCost", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.shouldEmit", "name": "shouldEmit", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.emitSymbol", "name": "emitSymbol", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.computeMetrics", "name": "computeMetrics", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.compressionInvariant", "name": "compressionInvariant", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.compressionCost", "name": "compressionCost", "module": "Semantics.HutterMaximumCompression" }, { "kind": "def", "id": "Semantics.HutterMaximumCompression.hutterMaximumCompressionBind", "name": "hutterMaximumCompressionBind", "module": "Semantics.HutterMaximumCompression" }, { "kind": "module", "id": "Semantics.HutterPrizeCompression", "name": "HutterPrizeCompression", "path": "Semantics/HutterPrizeCompression.lean", "namespace": "Semantics.HutterPrizeCompression", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HutterPrizeCompression.lean \u2014 Formalization of Winning Hutter Prize Equation Implements the winning equation from WGSL parallel hypothesis generation: C = (0.4*C_comp + 0.35*C_phys + 0.25*C_geom) \u00d7 (S ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 6, "def_count": 23, "struct_count": 6, "inductive_count": 0, "line_count": 420 }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.weightedLeSelf", "name": "weightedLeSelf", "module": "Semantics.HutterPrizeCompression" }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.unifiedFieldBounded", "name": "unifiedFieldBounded", "module": "Semantics.HutterPrizeCompression" }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.manifoldScalingBounded", "name": "manifoldScalingBounded", "module": "Semantics.HutterPrizeCompression" }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.hutterPrizeCompressionBounded", "name": "hutterPrizeCompressionBounded", "module": "Semantics.HutterPrizeCompression" }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.compressionRatioBounded", "name": "compressionRatioBounded", "module": "Semantics.HutterPrizeCompression" }, { "kind": "theorem", "id": "Semantics.HutterPrizeCompression.targetLessThanRecord", "name": "targetLessThanRecord", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.computeUnifiedField", "name": "computeUnifiedField", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.assignMassIndex", "name": "assignMassIndex", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.unifiedFieldBoundedMassIndex", "name": "unifiedFieldBoundedMassIndex", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.manifoldScalingBoundedMassIndex", "name": "manifoldScalingBoundedMassIndex", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.hutterPrizeCompressionBoundedMassIndex", "name": "hutterPrizeCompressionBoundedMassIndex", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.compressionRatioBoundedMassIndex", "name": "compressionRatioBoundedMassIndex", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.searchSpace", "name": "searchSpace", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.currentSearchPosition", "name": "currentSearchPosition", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.initGpuSearch", "name": "initGpuSearch", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.assignProofSearchDuty", "name": "assignProofSearchDuty", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.gpuAcceleratedUnifiedFieldSearch", "name": "gpuAcceleratedUnifiedFieldSearch", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.computeManifoldScaling", "name": "computeManifoldScaling", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.computeHutterPrizeCompression", "name": "computeHutterPrizeCompression", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.compressionRatioSI", "name": "compressionRatioSI", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.compressionPercentage", "name": "compressionPercentage", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.compressionRatioFromPercentage", "name": "compressionRatioFromPercentage", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.hutterPrizeFormat", "name": "hutterPrizeFormat", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.hutterRecordRatio", "name": "hutterRecordRatio", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.hutterTargetRatio", "name": "hutterTargetRatio", "module": "Semantics.HutterPrizeCompression" }, { "kind": "def", "id": "Semantics.HutterPrizeCompression.beatsHutterTarget", "name": "beatsHutterTarget", "module": "Semantics.HutterPrizeCompression" }, { "kind": "module", "id": "Semantics.HutterPrizeFlow", "name": "HutterPrizeFlow", "path": "Semantics/HutterPrizeFlow.lean", "namespace": "Semantics.HutterPrizeFlow", "doc": "HutterPrizeFlow.lean A Hutter-Prize-oriented reduced flow model. This file specializes the earlier unified conviction/flow machinery to an objective shaped like the real compression target: total score \u2248 archive size + decoder complexity + resource penalties in a reduced finite-dimensional state", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 14, "def_count": 30, "struct_count": 1, "inductive_count": 0, "line_count": 397 }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.numerator_nonneg", "name": "numerator_nonneg", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.geometry_pos", "name": "geometry_pos", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.energy_pos", "name": "energy_pos", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.phi_nonneg", "name": "phi_nonneg", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.decoderTerm_nonneg", "name": "decoderTerm_nonneg", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.resourceTerm_nonneg", "name": "resourceTerm_nonneg", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.phiHP_lower_bound", "name": "phiHP_lower_bound", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.phiHP_ge_phi_minus_comp", "name": "phiHP_ge_phi_minus_comp", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.phiHP_ge_phi_of_zeroComp", "name": "phiHP_ge_phi_of_zeroComp", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.increasing_decoder_cost_increases_phiHP", "name": "increasing_decoder_cost_increases_phiHP", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.increasing_resource_cost_increases_phiHP", "name": "increasing_resource_cost_increases_phiHP", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.sufficient_compression_gain_can_offset_penalties", "name": "sufficient_compression_gain_can_offset_penalties", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.flowHP_differs_from_base_on_tau", "name": "flowHP_differs_from_base_on_tau", "module": "Semantics.HutterPrizeFlow" }, { "kind": "theorem", "id": "Semantics.HutterPrizeFlow.flowHP_differs_from_base_on_sigma", "name": "flowHP_differs_from_base_on_sigma", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.rho", "name": "rho", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.v", "name": "v", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.tau", "name": "tau", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.sigma", "name": "sigma", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.q", "name": "q", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.kappa", "name": "kappa", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.eps", "name": "eps", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.mk", "name": "mk", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.neg", "name": "neg", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.add", "name": "add", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.smul", "name": "smul", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.WellFormed", "name": "WellFormed", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.numerator", "name": "numerator", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.geometry", "name": "geometry", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.energy", "name": "energy", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.phi", "name": "phi", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.gradPhi", "name": "gradPhi", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.flow", "name": "flow", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.compressionTerm", "name": "compressionTerm", "module": "Semantics.HutterPrizeFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeFlow.decoderTerm", "name": "decoderTerm", "module": "Semantics.HutterPrizeFlow" }, { "kind": "module", "id": "Semantics.HutterPrizeISA", "name": "HutterPrizeISA", "path": "Semantics/HutterPrizeISA.lean", "namespace": "Semantics.HutterPrizeISA", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HutterPrizeISA.lean - Hutter Prize Optimized ISA Specification Designs an entirely new ISA specifically optimized for Hutter Prize compression: Maximum compression efficiency targeting < 112.86MB for 1", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 9, "struct_count": 4, "inductive_count": 1, "line_count": 295 }, { "kind": "theorem", "id": "Semantics.HutterPrizeISA.hutterPiWitness", "name": "hutterPiWitness", "module": "Semantics.HutterPrizeISA" }, { "kind": "theorem", "id": "Semantics.HutterPrizeISA.opcodeUtilizationBounded", "name": "opcodeUtilizationBounded", "module": "Semantics.HutterPrizeISA" }, { "kind": "theorem", "id": "Semantics.HutterPrizeISA.registerEfficiencyBounded", "name": "registerEfficiencyBounded", "module": "Semantics.HutterPrizeISA" }, { "kind": "theorem", "id": "Semantics.HutterPrizeISA.overallScoreBounded", "name": "overallScoreBounded", "module": "Semantics.HutterPrizeISA" }, { "kind": "theorem", "id": "Semantics.HutterPrizeISA.targetLessThanRecord", "name": "targetLessThanRecord", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.hutterRecordRatio", "name": "hutterRecordRatio", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.hutterTargetRatio", "name": "hutterTargetRatio", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.hutterPi", "name": "hutterPi", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.hutterPhi", "name": "hutterPhi", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.circularCompressionRatio", "name": "circularCompressionRatio", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.analyzeHutterOpcodeUtilization", "name": "analyzeHutterOpcodeUtilization", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.analyzeHutterRegisterEfficiency", "name": "analyzeHutterRegisterEfficiency", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.runHutterSwarmAnalysis", "name": "runHutterSwarmAnalysis", "module": "Semantics.HutterPrizeISA" }, { "kind": "def", "id": "Semantics.HutterPrizeISA.exampleHutterParams", "name": "exampleHutterParams", "module": "Semantics.HutterPrizeISA" }, { "kind": "module", "id": "Semantics.HutterPrizeRGFlow", "name": "HutterPrizeRGFlow", "path": "Semantics/HutterPrizeRGFlow.lean", "namespace": "Semantics.HutterPrizeRGFlow", "doc": "def floatToQ16_16 (f : Float) : Semantics.Q16_16.Q16_16 := let scaled := f * 65536.0 let int := scaled.toUInt32.toNat Semantics.Q16_16.Q16_16.ofNat int /-! # Hutter Prize RGFlow Filter RGFlow-based filtering for Hutter Prize text compression (enwik8). Maps text to DNA, then to amino acids, then ap", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 3, "inductive_count": 2, "line_count": 191 }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.floatToQ16_16", "name": "floatToQ16_16", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.bitsToDNANucleotide", "name": "bitsToDNANucleotide", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.charToDNA", "name": "charToDNA", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.codonToAminoAcid", "name": "codonToAminoAcid", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.dnaToAminoAcids", "name": "dnaToAminoAcids", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.textToAminoAcids", "name": "textToAminoAcids", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.countUniqueAminoAcids", "name": "countUniqueAminoAcids", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.spectralDensity", "name": "spectralDensity", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.countTransitions", "name": "countTransitions", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.calculateMuQ", "name": "calculateMuQ", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.aminoAcidCounts", "name": "aminoAcidCounts", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.aminoAcidEntropy", "name": "aminoAcidEntropy", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.calculateSigmaQ", "name": "calculateSigmaQ", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.calculateTextRGFlowState", "name": "calculateTextRGFlowState", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "def", "id": "Semantics.HutterPrizeRGFlow.isTextLawful", "name": "isTextLawful", "module": "Semantics.HutterPrizeRGFlow" }, { "kind": "module", "id": "Semantics.HybridConvergence", "name": "HybridConvergence", "path": "Semantics/HybridConvergence.lean", "namespace": "Semantics.HybridConvergence", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HybridConvergence.lean \u2014 Cross-Domain Emergent Convergence This module proves a novel theorem bridging: ExperienceCompression (L0-L3 knowledge hierarchy) OrderedFieldTokens (test-time search with phase", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 17, "struct_count": 4, "inductive_count": 3, "line_count": 278 }, { "kind": "theorem", "id": "Semantics.HybridConvergence.adaptiveSpatialTokenConvergence", "name": "adaptiveSpatialTokenConvergence", "module": "Semantics.HybridConvergence" }, { "kind": "theorem", "id": "Semantics.HybridConvergence.compressionSearchEquivalence", "name": "compressionSearchEquivalence", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.zero", "name": "zero", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.one", "name": "one", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.ofNat", "name": "ofNat", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.add", "name": "add", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.sub", "name": "sub", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.mul", "name": "mul", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.div", "name": "div", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.le", "name": "le", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.tokenCountForLevel", "name": "tokenCountForLevel", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.wellFormedLength", "name": "wellFormedLength", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.validateTokenSequence", "name": "validateTokenSequence", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.baseTokenScore", "name": "baseTokenScore", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.compressionMultiplier", "name": "compressionMultiplier", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.verifierScore", "name": "verifierScore", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.sigmaThreshold", "name": "sigmaThreshold", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.metaAccumulate", "name": "metaAccumulate", "module": "Semantics.HybridConvergence" }, { "kind": "def", "id": "Semantics.HybridConvergence.isPromotable", "name": "isPromotable", "module": "Semantics.HybridConvergence" }, { "kind": "module", "id": "Semantics.HybridTSMPISTTorus", "name": "HybridTSMPISTTorus", "path": "Semantics/HybridTSMPISTTorus.lean", "namespace": "Semantics.HybridTSMPISTTorus", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 19, "struct_count": 3, "inductive_count": 1, "line_count": 280 }, { "kind": "theorem", "id": "Semantics.HybridTSMPISTTorus.geneticScoreBounded", "name": "geneticScoreBounded", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.geneticOptimizationScore", "name": "geneticOptimizationScore", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.informationDensity", "name": "informationDensity", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.normalizedTensionRatio", "name": "normalizedTensionRatio", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.classifyPhase", "name": "classifyPhase", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.lyapunovFunctional", "name": "lyapunovFunctional", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.mirrorInvolution", "name": "mirrorInvolution", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.isResonant", "name": "isResonant", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.applyPistBlitter", "name": "applyPistBlitter", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.applyResonanceJump", "name": "applyResonanceJump", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.applyTorusRouting", "name": "applyTorusRouting", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.updateGeneticScore", "name": "updateGeneticScore", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.updatePhase", "name": "updatePhase", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.lawfulProjection", "name": "lawfulProjection", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.lyapunovDescentCheck", "name": "lyapunovDescentCheck", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.isHybridActionLawful", "name": "isHybridActionLawful", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.hybridTSMBind", "name": "hybridTSMBind", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.examplePistState", "name": "examplePistState", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.exampleTorusState", "name": "exampleTorusState", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "def", "id": "Semantics.HybridTSMPISTTorus.exampleHybridState", "name": "exampleHybridState", "module": "Semantics.HybridTSMPISTTorus" }, { "kind": "module", "id": "Semantics.HydrogenicPhiTorsionBraid", "name": "HydrogenicPhiTorsionBraid", "path": "Semantics/HydrogenicPhiTorsionBraid.lean", "namespace": "Semantics.HydrogenicPhiTorsionBraid", "doc": "Fixed-point hard-math gate for the hydrogenic Phi-torsion braid. The browser/Python braid emits a generation trace. This Lean module owns the routing decision: hard mathematical states are reduced to finite event-cell fields, then compared against a braid sample. The module does not claim to solve ", "math_kind": "routing", "sorry_count": 0, "theorem_count": 5, "def_count": 28, "struct_count": 4, "inductive_count": 4, "line_count": 332 }, { "kind": "theorem", "id": "Semantics.HydrogenicPhiTorsionBraid.navierNoCfdRoutes", "name": "navierNoCfdRoutes", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "theorem", "id": "Semantics.HydrogenicPhiTorsionBraid.zeroConstraintQuarantinesYangMills", "name": "zeroConstraintQuarantinesYangMills", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "theorem", "id": "Semantics.HydrogenicPhiTorsionBraid.navierGateCostPositive", "name": "navierGateCostPositive", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "theorem", "id": "Semantics.HydrogenicPhiTorsionBraid.yangMillsToyRemainsResidue", "name": "yangMillsToyRemainsResidue", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "theorem", "id": "Semantics.HydrogenicPhiTorsionBraid.defaultTensegrityHasSixEdges", "name": "defaultTensegrityHasSixEdges", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.q0Max", "name": "q0Max", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.q0Half", "name": "q0Half", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.satQ0", "name": "satQ0", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.addQ0", "name": "addQ0", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.avgQ0", "name": "avgQ0", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.nominalBraidSample", "name": "nominalBraidSample", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.BraidSample", "name": "BraidSample", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.residualPressure", "name": "residualPressure", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.promotionPressure", "name": "promotionPressure", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.colorRope", "name": "colorRope", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.ColorRope", "name": "ColorRope", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.natAbsDiff", "name": "natAbsDiff", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.partLoad", "name": "partLoad", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.edgeStrain", "name": "edgeStrain", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.defaultTensegrity", "name": "defaultTensegrity", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.totalTensegrityStrain", "name": "totalTensegrityStrain", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.tensegrityCoherent", "name": "tensegrityCoherent", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "def", "id": "Semantics.HydrogenicPhiTorsionBraid.shouldRouteNoCfd", "name": "shouldRouteNoCfd", "module": "Semantics.HydrogenicPhiTorsionBraid" }, { "kind": "module", "id": "Semantics.HyperFlow", "name": "HyperFlow", "path": "Semantics/HyperFlow.lean", "namespace": "Semantics.HyperFlow", "doc": "HyperFlow.lean - Fixed-Point Hyperbolic Flow Dynamics", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 3, "line_count": 78 }, { "kind": "def", "id": "Semantics.HyperFlow.hyperFlowSignature", "name": "hyperFlowSignature", "module": "Semantics.HyperFlow" }, { "kind": "def", "id": "Semantics.HyperFlow.classifyHyperFlow", "name": "classifyHyperFlow", "module": "Semantics.HyperFlow" }, { "kind": "module", "id": "Semantics.HyperbolicEncoding", "name": "HyperbolicEncoding", "path": "Semantics/HyperbolicEncoding.lean", "namespace": "Semantics.HyperbolicEncoding", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HyperbolicEncoding.lean \u2014 Hyperbolic Manifold Coordinate Encoding Replaces infra/hyperbolic_encoding.py with a formal Lean module. Defines Poincar\u00e9 disk coordinates and M\u00f6bius transformations for seman", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 11, "struct_count": 3, "inductive_count": 0, "line_count": 233 }, { "kind": "theorem", "id": "Semantics.HyperbolicEncoding.dimensionWeightsLength", "name": "dimensionWeightsLength", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.zero", "name": "zero", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.one", "name": "one", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.ofFrac", "name": "ofFrac", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.toNat", "name": "toNat", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.dimensionWeights", "name": "dimensionWeights", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.encodeToPoincare", "name": "encodeToPoincare", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.decodeFromPoincare", "name": "decodeFromPoincare", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.mobiusTransform", "name": "mobiusTransform", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.hyperbolicDistance", "name": "hyperbolicDistance", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.initHyperbolicCache", "name": "initHyperbolicCache", "module": "Semantics.HyperbolicEncoding" }, { "kind": "def", "id": "Semantics.HyperbolicEncoding.getOrEncode", "name": "getOrEncode", "module": "Semantics.HyperbolicEncoding" }, { "kind": "module", "id": "Semantics.HypercubeTopology", "name": "HypercubeTopology", "path": "Semantics/HypercubeTopology.lean", "namespace": "Semantics.HypercubeTopology", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 10, "struct_count": 4, "inductive_count": 0, "line_count": 221 }, { "kind": "theorem", "id": "Semantics.HypercubeTopology.lawfulActionPreservesNeighborCount", "name": "lawfulActionPreservesNeighborCount", "module": "Semantics.HypercubeTopology" }, { "kind": "theorem", "id": "Semantics.HypercubeTopology.hypercubeDistanceSymmetric", "name": "hypercubeDistanceSymmetric", "module": "Semantics.HypercubeTopology" }, { "kind": "theorem", "id": "Semantics.HypercubeTopology.hypercubeDiameterEqualsDimensions", "name": "hypercubeDiameterEqualsDimensions", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.hypercubeDistance", "name": "hypercubeDistance", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.areNeighbors", "name": "areNeighbors", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.getNeighbors", "name": "getNeighbors", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.neighborCount", "name": "neighborCount", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.connectivity", "name": "connectivity", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.hypercubeDiameter", "name": "hypercubeDiameter", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.bisectionBandwidth", "name": "bisectionBandwidth", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.isHypercubeActionLawful", "name": "isHypercubeActionLawful", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.toggleCoordinate", "name": "toggleCoordinate", "module": "Semantics.HypercubeTopology" }, { "kind": "def", "id": "Semantics.HypercubeTopology.hypercubeBind", "name": "hypercubeBind", "module": "Semantics.HypercubeTopology" }, { "kind": "module", "id": "Semantics.Hyperfluid", "name": "Hyperfluid", "path": "Semantics/Hyperfluid.lean", "namespace": "Semantics.Hyperfluid", "doc": "", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 1, "inductive_count": 0, "line_count": 21 }, { "kind": "def", "id": "Semantics.Hyperfluid.propagateStress", "name": "propagateStress", "module": "Semantics.Hyperfluid" }, { "kind": "module", "id": "Semantics.ImaginarySemanticTime", "name": "ImaginarySemanticTime", "path": "Semantics/ImaginarySemanticTime.lean", "namespace": "Semantics.ImaginarySemanticTime", "doc": "ImaginarySemanticTime.lean -- Semantic Time as a Dimensionless Complex Quantity The user proposes: unify imaginary numbers (i as dimensionless unit) with semantic mass to create \"Imaginary Semantic Time\" (IST). Core insight: ALL measurement is fundamentally information. The imaginary unit i repres", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 19, "def_count": 16, "struct_count": 3, "inductive_count": 0, "line_count": 464 }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.for", "name": "for", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.iUnitSemanticOne", "name": "iUnitSemanticOne", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.mengerSemanticTimeK0", "name": "mengerSemanticTimeK0", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.p04SemanticTimeCorrect", "name": "p04SemanticTimeCorrect", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.p04SemanticTimeMagnitude", "name": "p04SemanticTimeMagnitude", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatioIs3_k0", "name": "semanticPeriodRatioIs3_k0", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatioIs3_k1", "name": "semanticPeriodRatioIs3_k1", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatioIs3_k2", "name": "semanticPeriodRatioIs3_k2", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatioIs3_k5", "name": "semanticPeriodRatioIs3_k5", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatioIs3_k10", "name": "semanticPeriodRatioIs3_k10", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.observerProjectionPreservesSemantic", "name": "observerProjectionPreservesSemantic", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.p04ProjectedPhysicalMagnitude", "name": "p04ProjectedPhysicalMagnitude", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.p04ProjectedPhysicalGreaterThan60", "name": "p04ProjectedPhysicalGreaterThan60", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.trivial_observer_sees_zero", "name": "trivial_observer_sees_zero", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.sieve_independent_of_P0", "name": "sieve_independent_of_P0", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.reconcileObservers_correct_mod_\u21131", "name": "reconcileObservers_correct_mod_\u21131", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.reconcileObservers_correct_mod_\u21132", "name": "reconcileObservers_correct_mod_\u21132", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.sieveProject_lt_sieveModulus", "name": "sieveProject_lt_sieveModulus", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "theorem", "id": "Semantics.ImaginarySemanticTime.reconcileObservers_recovers_coordinate", "name": "reconcileObservers_recovers_coordinate", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.iUnit", "name": "iUnit", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.semanticScale", "name": "semanticScale", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.observerProject", "name": "observerProject", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.mengerSemanticTime", "name": "mengerSemanticTime", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.p04SemanticTime", "name": "p04SemanticTime", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.semanticPeriodRatio", "name": "semanticPeriodRatio", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.p0EarthObserverYears", "name": "p0EarthObserverYears", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.p04ProjectedPhysical", "name": "p04ProjectedPhysical", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.sieveProject", "name": "sieveProject", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.reconcileObservers", "name": "reconcileObservers", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.humanObserver", "name": "humanObserver", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.dolphinObserver", "name": "dolphinObserver", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.sharedCoordinate", "name": "sharedCoordinate", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.humanShadow", "name": "humanShadow", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.dolphinShadow", "name": "dolphinShadow", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "def", "id": "Semantics.ImaginarySemanticTime.reconciledShadow", "name": "reconciledShadow", "module": "Semantics.ImaginarySemanticTime" }, { "kind": "module", "id": "Semantics.InformationConservation", "name": "InformationConservation", "path": "Semantics/InformationConservation.lean", "namespace": "Semantics.InformationConservation", "doc": "inductive InformationPhase where | bulk : InformationPhase -- Kinetic matter active in 3D manifold | horizon : InformationPhase -- Bits trapped on holographic surface | vacuum : InformationPhase -- Ambient radiation in dark matter pool /-- Information state with discrete microstate tracking (Iro", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 8, "def_count": 5, "struct_count": 1, "inductive_count": 1, "line_count": 106 }, { "kind": "theorem", "id": "Semantics.InformationConservation.bandyopadhyayCycleConservation", "name": "bandyopadhyayCycleConservation", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.transferPreservesTotalInformation", "name": "transferPreservesTotalInformation", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.lawfulTransferPreservesNonNegativity", "name": "lawfulTransferPreservesNonNegativity", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.informationAdditivity", "name": "informationAdditivity", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.transferBulkToHorizonPreservesTotal", "name": "transferBulkToHorizonPreservesTotal", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.transferHorizonToVacuumPreservesTotal", "name": "transferHorizonToVacuumPreservesTotal", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.informationNonNegative", "name": "informationNonNegative", "module": "Semantics.InformationConservation" }, { "kind": "theorem", "id": "Semantics.InformationConservation.totalDominatesEachPhase", "name": "totalDominatesEachPhase", "module": "Semantics.InformationConservation" }, { "kind": "def", "id": "Semantics.InformationConservation.totalInformation", "name": "totalInformation", "module": "Semantics.InformationConservation" }, { "kind": "def", "id": "Semantics.InformationConservation.transferInformation", "name": "transferInformation", "module": "Semantics.InformationConservation" }, { "kind": "def", "id": "Semantics.InformationConservation.isLawfulTransfer", "name": "isLawfulTransfer", "module": "Semantics.InformationConservation" }, { "kind": "def", "id": "Semantics.InformationConservation.transferCost", "name": "transferCost", "module": "Semantics.InformationConservation" }, { "kind": "def", "id": "Semantics.InformationConservation.informationInvariant", "name": "informationInvariant", "module": "Semantics.InformationConservation" }, { "kind": "module", "id": "Semantics.Ingestion", "name": "Ingestion", "path": "Semantics/Ingestion.lean", "namespace": "Semantics.Ingestion", "doc": "Master Ingestion Mapping: Decomposes IA metadata into the 6D Sovereign Genome.", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Ingestion.mapToGenome", "name": "mapToGenome", "module": "Semantics.Ingestion" }, { "kind": "def", "id": "Semantics.Ingestion.isRecordLawful", "name": "isRecordLawful", "module": "Semantics.Ingestion" }, { "kind": "module", "id": "Semantics.InteractionGraphSidon", "name": "InteractionGraphSidon", "path": "Semantics/InteractionGraphSidon.lean", "namespace": "Semantics.InteractionGraphSidon", "doc": "InteractionGraphSidon.lean \u2014 RRC weak-axis reconstruction via interaction-graph freeness The atproto/Mastodon observation (and the RRC \"weak axis\" problem) are the same abstract structure: an object's full identity/classification is hidden from any single partial view. Multiple independent weak pr", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 3, "def_count": 15, "struct_count": 2, "inductive_count": 0, "line_count": 191 }, { "kind": "theorem", "id": "Semantics.InteractionGraphSidon.reconstructWeakAxes_mod_a", "name": "reconstructWeakAxes_mod_a", "module": "Semantics.InteractionGraphSidon" }, { "kind": "theorem", "id": "Semantics.InteractionGraphSidon.reconstructWeakAxes_mod_b", "name": "reconstructWeakAxes_mod_b", "module": "Semantics.InteractionGraphSidon" }, { "kind": "theorem", "id": "Semantics.InteractionGraphSidon.weakAxis_coprime_intersect", "name": "weakAxis_coprime_intersect", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.wordProduct", "name": "wordProduct", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.isSidonWitness", "name": "isSidonWitness", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.project", "name": "project", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.independentAxes", "name": "independentAxes", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.reconstructWeakAxes", "name": "reconstructWeakAxes", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.identityAxis", "name": "identityAxis", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.hostingAxis", "name": "hostingAxis", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.appAxis", "name": "appAxis", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.toyClass", "name": "toyClass", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.idShadow", "name": "idShadow", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.hostShadow", "name": "hostShadow", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.appShadow", "name": "appShadow", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.reconstructedTwo", "name": "reconstructedTwo", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.reconstructedThree", "name": "reconstructedThree", "module": "Semantics.InteractionGraphSidon" }, { "kind": "def", "id": "Semantics.InteractionGraphSidon.toyGraph", "name": "toyGraph", "module": "Semantics.InteractionGraphSidon" }, { "kind": "module", "id": "Semantics.InteratomicPotential", "name": "InteratomicPotential", "path": "Semantics/InteratomicPotential.lean", "namespace": "Semantics", "doc": "structure AtomicState where manifold : Array Q16_16 entropy : Q16_16 phiGate : Q16_16 deriving Repr, Inhabited /-- The Landauer Limit threshold for thermodynamic stability.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 54 }, { "kind": "theorem", "id": "Semantics.InteratomicPotential.lawful_resonance_of_stable_atoms", "name": "lawful_resonance_of_stable_atoms", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.landauerThreshold", "name": "landauerThreshold", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.goldenRatio", "name": "goldenRatio", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.isStable", "name": "isStable", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.atomicInvariant", "name": "atomicInvariant", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.interatomicCost", "name": "interatomicCost", "module": "Semantics.InteratomicPotential" }, { "kind": "def", "id": "Semantics.InteratomicPotential.interatomicBind", "name": "interatomicBind", "module": "Semantics.InteratomicPotential" }, { "kind": "module", "id": "Semantics.IntrinsicGeometry", "name": "IntrinsicGeometry", "path": "Semantics/IntrinsicGeometry.lean", "namespace": "Semantics.IntrinsicGeometry", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team IntrinsicGeometry.lean \u2014 Computing the Actual Shape of the Codebase Manifold This module formalizes intrinsic geometric properties extracted from the import dependency graph: Geodesic distance (shorte", "math_kind": "geometry", "sorry_count": 1, "theorem_count": 0, "def_count": 25, "struct_count": 3, "inductive_count": 0, "line_count": 292 }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.listBind", "name": "listBind", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.listFilterMap", "name": "listFilterMap", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.extractSomes", "name": "extractSomes", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.Graph", "name": "Graph", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.outNeighbors", "name": "outNeighbors", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.inNeighbors", "name": "inNeighbors", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.degree", "name": "degree", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.elem", "name": "elem", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.List", "name": "List", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.bfsStep", "name": "bfsStep", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.bfsDistancesFuel", "name": "bfsDistancesFuel", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.geodesicDistance", "name": "geodesicDistance", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.curvature", "name": "curvature", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.pathCountThrough", "name": "pathCountThrough", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.betweennessCentrality", "name": "betweennessCentrality", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.find2Cycles", "name": "find2Cycles", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.isSource", "name": "isSource", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.isSink", "name": "isSink", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.isIsolated", "name": "isIsolated", "module": "Semantics.IntrinsicGeometry" }, { "kind": "def", "id": "Semantics.IntrinsicGeometry.diameter", "name": "diameter", "module": "Semantics.IntrinsicGeometry" }, { "kind": "module", "id": "Semantics.InvariantReceipt.All", "name": "All", "path": "Semantics/InvariantReceipt/All.lean", "namespace": "", "doc": "Invariant Receipt Protocol: Top-level aggregator", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 14 }, { "kind": "module", "id": "Semantics.InvariantReceipt.Core", "name": "Core", "path": "Semantics/InvariantReceipt/Core.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Core ModelUpgrade structure and predicates", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 30 }, { "kind": "def", "id": "Semantics.InvariantReceipt.Core.computable", "name": "computable", "module": "Semantics.InvariantReceipt.Core" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Core.Hostable", "name": "Hostable", "module": "Semantics.InvariantReceipt.Core" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Core.lawfulStep", "name": "lawfulStep", "module": "Semantics.InvariantReceipt.Core" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Core.lawful", "name": "lawful", "module": "Semantics.InvariantReceipt.Core" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Instances.AVM", "name": "AVM", "path": "Semantics/InvariantReceipt/Instances/AVM.lean", "namespace": "InvariantReceipt.AVM", "doc": "AVM Instance for Invariant Receipt Protocol", "math_kind": "avm", "sorry_count": 0, "theorem_count": 1, "def_count": 8, "struct_count": 1, "inductive_count": 1, "line_count": 89 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.AVM.Th3_avm_closure", "name": "Th3_avm_closure", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmInvariant", "name": "avmInvariant", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmStep", "name": "avmStep", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmTransform", "name": "avmTransform", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmCost", "name": "avmCost", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmResidual", "name": "avmResidual", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmProject", "name": "avmProject", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmValidAtScale", "name": "avmValidAtScale", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.AVM.avmModel", "name": "avmModel", "module": "Semantics.InvariantReceipt.Instances.AVM" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda", "name": "DeltaPhiGammaKLambda", "path": "Semantics/InvariantReceipt/Instances/DeltaPhiGammaKLambda.lean", "namespace": "InvariantReceipt.DPG", "doc": "Delta-Phi-Gamma-K-Lambda Instance for Invariant Receipt Protocol", "math_kind": "avm", "sorry_count": 0, "theorem_count": 1, "def_count": 12, "struct_count": 1, "inductive_count": 1, "line_count": 140 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.Th4_compression_admissibility_skeleton", "name": "Th4_compression_admissibility_skeleton", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgInvariant", "name": "dpgInvariant", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.hashBytes", "name": "hashBytes", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.hashInts", "name": "hashInts", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.MixHash", "name": "MixHash", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.computeDelta", "name": "computeDelta", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgTransform", "name": "dpgTransform", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgCost", "name": "dpgCost", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgResidual", "name": "dpgResidual", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgProject", "name": "dpgProject", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgValidAtScale", "name": "dpgValidAtScale", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.dpgModel", "name": "dpgModel", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda.DoctrineAdmissible", "name": "DoctrineAdmissible", "module": "Semantics.InvariantReceipt.Instances.DeltaPhiGammaKLambda" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Instances.GRW", "name": "GRW", "path": "Semantics/InvariantReceipt/Instances/GRW.lean", "namespace": "InvariantReceipt.GRW", "doc": "GRW Instance for Invariant Receipt Protocol", "math_kind": "avm", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 2, "inductive_count": 1, "line_count": 120 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.GRW.grwRoundTrip", "name": "grwRoundTrip", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.GRW.Th5_grw_receipt_soundness", "name": "Th5_grw_receipt_soundness", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwInvariant", "name": "grwInvariant", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwTransform", "name": "grwTransform", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwCost", "name": "grwCost", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwResidual", "name": "grwResidual", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwProject", "name": "grwProject", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwValidAtScale", "name": "grwValidAtScale", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwModel", "name": "grwModel", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwToWire", "name": "grwToWire", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwFromWire", "name": "grwFromWire", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.GRW.grwAdapter", "name": "grwAdapter", "module": "Semantics.InvariantReceipt.Instances.GRW" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Instances.NUVMAP", "name": "NUVMAP", "path": "Semantics/InvariantReceipt/Instances/NUVMAP.lean", "namespace": "InvariantReceipt.NUVMAP", "doc": "NUVMAP Instance for Invariant Receipt Protocol", "math_kind": "avm", "sorry_count": 0, "theorem_count": 3, "def_count": 7, "struct_count": 5, "inductive_count": 3, "line_count": 213 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.Th6_nuvmap_invariant_preservation", "name": "Th6_nuvmap_invariant_preservation", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.Th7_nuvmap_projection_deterministic", "name": "Th7_nuvmap_projection_deterministic", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.Th8_nuvmap_partition_complete", "name": "Th8_nuvmap_partition_complete", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.invariant", "name": "invariant", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.transform", "name": "transform", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.project", "name": "project", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.validAtScale", "name": "validAtScale", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.residual", "name": "residual", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.cost", "name": "cost", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.NUVMAP.nuvmapModel", "name": "nuvmapModel", "module": "Semantics.InvariantReceipt.Instances.NUVMAP" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Instances.TMARP", "name": "TMARP", "path": "Semantics/InvariantReceipt/Instances/TMARP.lean", "namespace": "InvariantReceipt.TMARP", "doc": "TMARP Instance for Invariant Receipt Protocol", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 11, "struct_count": 2, "inductive_count": 1, "line_count": 164 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarp_dpg_refinement", "name": "tmarp_dpg_refinement", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpInvariant", "name": "tmarpInvariant", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpAtomize", "name": "tmarpAtomize", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpTransform", "name": "tmarpTransform", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpCost", "name": "tmarpCost", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpResidual", "name": "tmarpResidual", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpProject", "name": "tmarpProject", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpValidAtScale", "name": "tmarpValidAtScale", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpModel", "name": "tmarpModel", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.u32Bytes", "name": "u32Bytes", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.u64Bytes", "name": "u64Bytes", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Instances.TMARP.tmarpToDPG", "name": "tmarpToDPG", "module": "Semantics.InvariantReceipt.Instances.TMARP" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Ledger", "name": "Ledger", "path": "Semantics/InvariantReceipt/Ledger.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Cost ledger and deterministic tracking", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 0, "line_count": 16 }, { "kind": "def", "id": "Semantics.InvariantReceipt.Ledger.Ledger", "name": "Ledger", "module": "Semantics.InvariantReceipt.Ledger" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Ledger.deterministic", "name": "deterministic", "module": "Semantics.InvariantReceipt.Ledger" }, { "kind": "module", "id": "Semantics.InvariantReceipt.Receipt", "name": "Receipt", "path": "Semantics/InvariantReceipt/Receipt.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Receipt and Outcome types", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 1, "line_count": 17 }, { "kind": "module", "id": "Semantics.InvariantReceipt.Status", "name": "Status", "path": "Semantics/InvariantReceipt/Status.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Model promotion status and registry", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 1, "line_count": 28 }, { "kind": "module", "id": "Semantics.InvariantReceipt.SubstrateAdapter", "name": "SubstrateAdapter", "path": "Semantics/InvariantReceipt/SubstrateAdapter.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Substrate adapter with round-trip law", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 0, "line_count": 15 }, { "kind": "module", "id": "Semantics.InvariantReceipt.Theorems", "name": "Theorems", "path": "Semantics/InvariantReceipt/Theorems.lean", "namespace": "InvariantReceipt", "doc": "Invariant Receipt Protocol: Core theorems", "math_kind": "avm", "sorry_count": 0, "theorem_count": 3, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 47 }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Theorems.Th1_admissibility_soundness", "name": "Th1_admissibility_soundness", "module": "Semantics.InvariantReceipt.Theorems" }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Theorems.Th2_adapter_round_trip", "name": "Th2_adapter_round_trip", "module": "Semantics.InvariantReceipt.Theorems" }, { "kind": "theorem", "id": "Semantics.InvariantReceipt.Theorems.Th3_hostable_from_witness", "name": "Th3_hostable_from_witness", "module": "Semantics.InvariantReceipt.Theorems" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Theorems.Th4_compression_admissibility", "name": "Th4_compression_admissibility", "module": "Semantics.InvariantReceipt.Theorems" }, { "kind": "def", "id": "Semantics.InvariantReceipt.Theorems.Th5_grw_receipt_soundness", "name": "Th5_grw_receipt_soundness", "module": "Semantics.InvariantReceipt.Theorems" }, { "kind": "module", "id": "Semantics.JouleEnergy", "name": "JouleEnergy", "path": "Semantics/JouleEnergy.lean", "namespace": "Semantics.JouleEnergy", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 2, "def_count": 11, "struct_count": 3, "inductive_count": 0, "line_count": 200 }, { "kind": "theorem", "id": "Semantics.JouleEnergy.lawfulTransitionPreservesEnergyMonotonicity", "name": "lawfulTransitionPreservesEnergyMonotonicity", "module": "Semantics.JouleEnergy" }, { "kind": "theorem", "id": "Semantics.JouleEnergy.energyConservation", "name": "energyConservation", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.jouleEnergyChargeVoltage", "name": "jouleEnergyChargeVoltage", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.joulePowerVoltageCurrent", "name": "joulePowerVoltageCurrent", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.jouleEnergyPowerTime", "name": "jouleEnergyPowerTime", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.jouleCurrentChargeTime", "name": "jouleCurrentChargeTime", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.isEnergyTransitionLawful", "name": "isEnergyTransitionLawful", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.energyTransitionCost", "name": "energyTransitionCost", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.updateEnergyState", "name": "updateEnergyState", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.energyBind", "name": "energyBind", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.energyEfficiency", "name": "energyEfficiency", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.powerEfficiency", "name": "powerEfficiency", "module": "Semantics.JouleEnergy" }, { "kind": "def", "id": "Semantics.JouleEnergy.energyPerTask", "name": "energyPerTask", "module": "Semantics.JouleEnergy" }, { "kind": "module", "id": "Semantics.JsonLSurfaceConnector", "name": "JsonLSurfaceConnector", "path": "Semantics/JsonLSurfaceConnector.lean", "namespace": "Semantics.JsonLSurfaceConnector", "doc": "# JSON-L Surface Connector Lean-owned connector manifest for this instance. External MCP/surface shims may serialize these records, but source/op categories, genome routing, bind class, and connector lawfulness live here.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 22, "struct_count": 5, "inductive_count": 6, "line_count": 261 }, { "kind": "theorem", "id": "Semantics.JsonLSurfaceConnector.bindConnectorEventLawful", "name": "bindConnectorEventLawful", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "theorem", "id": "Semantics.JsonLSurfaceConnector.sourceTargetSwarmUnlawful", "name": "sourceTargetSwarmUnlawful", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.EventSource", "name": "EventSource", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.EventOperation", "name": "EventOperation", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.BindClass", "name": "BindClass", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.McpTool", "name": "McpTool", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.SurfaceTarget", "name": "SurfaceTarget", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.bin", "name": "bin", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.genomeAddress", "name": "genomeAddress", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.genomeBucket", "name": "genomeBucket", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.sourceTarget", "name": "sourceTarget", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.connectorInvariant", "name": "connectorInvariant", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.connectorCost", "name": "connectorCost", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.bindConnectorEvent", "name": "bindConnectorEvent", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.toJsonGenome", "name": "toJsonGenome", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.toJsonBindWitness", "name": "toJsonBindWitness", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.toJsonProvenance", "name": "toJsonProvenance", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.toJsonEvent", "name": "toJsonEvent", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.toJsonConnector", "name": "toJsonConnector", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.instanceConnector", "name": "instanceConnector", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.exampleGenome", "name": "exampleGenome", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "def", "id": "Semantics.JsonLSurfaceConnector.exampleBindWitness", "name": "exampleBindWitness", "module": "Semantics.JsonLSurfaceConnector" }, { "kind": "module", "id": "Semantics.KdVBurgersPDE", "name": "KdVBurgersPDE", "path": "Semantics/KdVBurgersPDE.lean", "namespace": "Semantics.KdVBurgersPDE", "doc": "KdVBurgersPDE.lean \u2014 Compound KdV-Burgers Equation in Q16_16 u_t + \u03b1\u00b7u\u00b7u_x + \u03b2\u00b7u_xx + \u03b3\u00b7u_xxx = 0 Combines nonlinear advection (\u03b1), viscous diffusion (\u03b2), and third-order dispersion (\u03b3). Captures both shock formation and wave-breaking phenomena. Reference: Wang 1996 (10.1016/0375-9601(96)00103-x)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 13, "struct_count": 1, "inductive_count": 0, "line_count": 163 }, { "kind": "theorem", "id": "Semantics.KdVBurgersPDE.kdv_energy_correspondence", "name": "kdv_energy_correspondence", "module": "Semantics.KdVBurgersPDE" }, { "kind": "theorem", "id": "Semantics.KdVBurgersPDE.kdv_mass_correspondence", "name": "kdv_mass_correspondence", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.thirdDiff", "name": "thirdDiff", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kdvBurgersRHS", "name": "kdvBurgersRHS", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.stepEuler", "name": "stepEuler", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.runSteps", "name": "runSteps", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kineticEnergy", "name": "kineticEnergy", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.maxVelocity", "name": "maxVelocity", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.totalMass", "name": "totalMass", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.dispersionRatio", "name": "dispersionRatio", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kdvBurgersInvariant", "name": "kdvBurgersInvariant", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.testKdVState", "name": "testKdVState", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kdvBurgersToBraidDef", "name": "kdvBurgersToBraidDef", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kdvBurgersToBraid", "name": "kdvBurgersToBraid", "module": "Semantics.KdVBurgersPDE" }, { "kind": "def", "id": "Semantics.KdVBurgersPDE.kdvTheoremReceipt", "name": "kdvTheoremReceipt", "module": "Semantics.KdVBurgersPDE" }, { "kind": "module", "id": "Semantics.KeplerianOrbit", "name": "KeplerianOrbit", "path": "Semantics/KeplerianOrbit.lean", "namespace": "Semantics.KeplerianOrbit", "doc": "The Minsky invariant E(x, y) = x^2 - \\epsilon x y + y^2 modeled as the discrete Hamiltonian (total energy) of the Keplerian orbit. The energy strictly limits the possible states the particle can occupy, partitioning the state space into discrete allowable resonant paths (orbit shells).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 12, "struct_count": 0, "inductive_count": 0, "line_count": 245 }, { "kind": "theorem", "id": "Semantics.KeplerianOrbit.oberth_positive_marching", "name": "oberth_positive_marching", "module": "Semantics.KeplerianOrbit" }, { "kind": "theorem", "id": "Semantics.KeplerianOrbit.oberth_amplification", "name": "oberth_amplification", "module": "Semantics.KeplerianOrbit" }, { "kind": "theorem", "id": "Semantics.KeplerianOrbit.ephemeris_energy_preserved", "name": "ephemeris_energy_preserved", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.minskyHamiltonian", "name": "minskyHamiltonian", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.inE8Lattice", "name": "inE8Lattice", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.inE16Lattice", "name": "inE16Lattice", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.isCohnElkiesCompliant", "name": "isCohnElkiesCompliant", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.q16ToInt", "name": "q16ToInt", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.getNextState", "name": "getNextState", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.ephemerisLUT", "name": "ephemerisLUT", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.applyOrbitalPerturbation", "name": "applyOrbitalPerturbation", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.energyChange", "name": "energyChange", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.linearEnergyChange", "name": "linearEnergyChange", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.quadraticEnergyChange", "name": "quadraticEnergyChange", "module": "Semantics.KeplerianOrbit" }, { "kind": "def", "id": "Semantics.KeplerianOrbit.oberthReceipt", "name": "oberthReceipt", "module": "Semantics.KeplerianOrbit" }, { "kind": "module", "id": "Semantics.Kernel.EigenGate", "name": "EigenGate", "path": "Semantics/Kernel/EigenGate.lean", "namespace": "Semantics.Kernel", "doc": "EigenGate.lean \u2014 The canonical eigengate type. Every physical law, every compression check, every routing decision is an eigenstate condition: \u2225G\u00b7s \u2212 s\u2225 \u2264 \u03c4, where G is the operator defining the expected invariant, and the residual is the fraction of deviation from identity. Residuals live in Q0_1", "math_kind": "routing", "sorry_count": 0, "theorem_count": 11, "def_count": 13, "struct_count": 1, "inductive_count": 2, "line_count": 180 }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.shore_is_zero", "name": "shore_is_zero", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.admit_verdict_on_zero_residual", "name": "admit_verdict_on_zero_residual", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.reject_verdict_on_high_residual", "name": "reject_verdict_on_high_residual", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.score_val_on_zero_residual", "name": "score_val_on_zero_residual", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.chain_all_admit_admits", "name": "chain_all_admit_admits", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.chain_one_rejects_rejects", "name": "chain_one_rejects_rejects", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.chain_optional_reject_no_effect", "name": "chain_optional_reject_no_effect", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.route_admit_zero_residual_is_eigenstate", "name": "route_admit_zero_residual_is_eigenstate", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.route_reject_no_receipt_is_error", "name": "route_reject_no_receipt_is_error", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.route_reject_with_receipt_is_underverse", "name": "route_reject_with_receipt_is_underverse", "module": "Semantics.Kernel.EigenGate" }, { "kind": "theorem", "id": "Semantics.Kernel.EigenGate.approach_bounded", "name": "approach_bounded", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.verdict", "name": "verdict", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.score", "name": "score", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.route", "name": "route", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.chainVerdict", "name": "chainVerdict", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.q0Ratio", "name": "q0Ratio", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.shore", "name": "shore", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.approach", "name": "approach", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.testGateAllAdmit", "name": "testGateAllAdmit", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.testGateAllReject", "name": "testGateAllReject", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.testGateResidualAtHalf", "name": "testGateResidualAtHalf", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.chainFixtureAllAdmit", "name": "chainFixtureAllAdmit", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.chainFixtureOneRejects", "name": "chainFixtureOneRejects", "module": "Semantics.Kernel.EigenGate" }, { "kind": "def", "id": "Semantics.Kernel.EigenGate.chainFixtureOptionalReject", "name": "chainFixtureOptionalReject", "module": "Semantics.Kernel.EigenGate" }, { "kind": "module", "id": "Semantics.Kernel.GateChain", "name": "GateChain", "path": "Semantics/Kernel/GateChain.lean", "namespace": "Semantics.Kernel", "doc": "GateChain.lean \u2014 Multiplicative eigengate composition. Imports EigenGate.lean for the canonical Eigengate, EigenVerdict, and score/verdict/route/chainVerdict primitives. Adds chain-level composition and product-score computation.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 56 }, { "kind": "theorem", "id": "Semantics.Kernel.GateChain.chainCompositionAllAdmit", "name": "chainCompositionAllAdmit", "module": "Semantics.Kernel.GateChain" }, { "kind": "theorem", "id": "Semantics.Kernel.GateChain.chain_optional_reject_preserves_admit", "name": "chain_optional_reject_preserves_admit", "module": "Semantics.Kernel.GateChain" }, { "kind": "theorem", "id": "Semantics.Kernel.GateChain.chainScore_all_admit_is_one", "name": "chainScore_all_admit_is_one", "module": "Semantics.Kernel.GateChain" }, { "kind": "def", "id": "Semantics.Kernel.GateChain.chainGatesToTuples", "name": "chainGatesToTuples", "module": "Semantics.Kernel.GateChain" }, { "kind": "def", "id": "Semantics.Kernel.GateChain.chainScore", "name": "chainScore", "module": "Semantics.Kernel.GateChain" }, { "kind": "def", "id": "Semantics.Kernel.GateChain.testChainAllAdmit", "name": "testChainAllAdmit", "module": "Semantics.Kernel.GateChain" }, { "kind": "def", "id": "Semantics.Kernel.GateChain.testChainOptionalOnly", "name": "testChainOptionalOnly", "module": "Semantics.Kernel.GateChain" }, { "kind": "module", "id": "Semantics.KillerCriterion", "name": "KillerCriterion", "path": "Semantics/KillerCriterion.lean", "namespace": "Semantics.Benchmarks.KillerCriterion", "doc": "# Killer Criterion: Rigid Formalization This module formalizes the benchmark claim: A planted lawful core is distinguishable from random noise and trivial repetition when and only when it satisfies the coincidence of: 1. exact spectral lawfulness, 2. RGFlow scale coherence, 3. verified payload id", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 11, "def_count": 7, "struct_count": 3, "inductive_count": 2, "line_count": 362 }, { "kind": "theorem", "id": "Semantics.KillerCriterion.noise_rejection_theorem", "name": "noise_rejection_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.repetition_rejection_theorem", "name": "repetition_rejection_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.chaos_rejection_theorem", "name": "chaos_rejection_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.incoherence_rejection_theorem", "name": "incoherence_rejection_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.blind_detection_theorem", "name": "blind_detection_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.core_admission_theorem", "name": "core_admission_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.noise_flanked_core_theorem", "name": "noise_flanked_core_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.repetition_flanked_core_theorem", "name": "repetition_flanked_core_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.admitted_core_not_sabotage", "name": "admitted_core_not_sabotage", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.unique_core_admission_theorem", "name": "unique_core_admission_theorem", "module": "Semantics.KillerCriterion" }, { "kind": "theorem", "id": "Semantics.KillerCriterion.canonical_pi_e_core_unique", "name": "canonical_pi_e_core_unique", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.entropyLower", "name": "entropyLower", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.entropyUpper", "name": "entropyUpper", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.densityUpper", "name": "densityUpper", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.IsSpectrallyLawful", "name": "IsSpectrallyLawful", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.IsKillerLawful", "name": "IsKillerLawful", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.RegionAdmitted", "name": "RegionAdmitted", "module": "Semantics.KillerCriterion" }, { "kind": "def", "id": "Semantics.KillerCriterion.KillerCriterionAdmission", "name": "KillerCriterionAdmission", "module": "Semantics.KillerCriterion" }, { "kind": "module", "id": "Semantics.LadderBraidAlgebra", "name": "LadderBraidAlgebra", "path": "Semantics/LadderBraidAlgebra.lean", "namespace": "Semantics.LadderBraidAlgebra", "doc": "LadderBraidAlgebra.lean \u2014 Ladder Operator Algebra on Braid Strand Phase Space This module establishes the isomorphism between quantum ladder operators (L\u208a/L\u208b) and braid crossing operations (crossStrands/crossStep). Key identifications (from arXiv:2507.16629, 2603.12392): \u2022 L\u208a/L\u208b = crossStrands on ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 19, "struct_count": 2, "inductive_count": 1, "line_count": 345 }, { "kind": "theorem", "id": "Semantics.LadderBraidAlgebra.commutator_antisymm", "name": "commutator_antisymm", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "theorem", "id": "Semantics.LadderBraidAlgebra.admissible_at_max_m_is_highest_weight", "name": "admissible_at_max_m_is_highest_weight", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "theorem", "id": "Semantics.LadderBraidAlgebra.ladder_raise_identity_test", "name": "ladder_raise_identity_test", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.zero", "name": "zero", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.fromPhaseVec", "name": "fromPhaseVec", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.commutatorRaw", "name": "commutatorRaw", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.ladderApplyPair", "name": "ladderApplyPair", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.ladderApplyState", "name": "ladderApplyState", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.ladderNormSq", "name": "ladderNormSq", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.fammEnforcesNormPositivity", "name": "fammEnforcesNormPositivity", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.raiseLowerCommutator", "name": "raiseLowerCommutator", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.lzRaiseCommutator", "name": "lzRaiseCommutator", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.IsHighestWeight", "name": "IsHighestWeight", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.liftToQ16", "name": "liftToQ16", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.ladderSpectralProfile", "name": "ladderSpectralProfile", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.treeNodeToLadderState", "name": "treeNodeToLadderState", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.ladderMatchesTreeDIAT", "name": "ladderMatchesTreeDIAT", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.eigensolidTestState", "name": "eigensolidTestState", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.computeCasimir", "name": "computeCasimir", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.spinOneM0", "name": "spinOneM0", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.spinOneM1", "name": "spinOneM1", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "def", "id": "Semantics.LadderBraidAlgebra.exampleTree", "name": "exampleTree", "module": "Semantics.LadderBraidAlgebra" }, { "kind": "module", "id": "Semantics.LadderLUT", "name": "LadderLUT", "path": "Semantics/LadderLUT.lean", "namespace": "Semantics.LadderLUT", "doc": "# LadderLUT A LadderLUT is a deterministic expansion packet for ordered fixed-width symbols. It replaces an explicit table such as ```text 000, 001, 002, 003, ... ``` with a compact generator rule plus residual and receipt accounting. The decimal identity `1 / 998001` is treated as a human-visi", "math_kind": "avm", "sorry_count": 0, "theorem_count": 8, "def_count": 13, "struct_count": 1, "inductive_count": 1, "line_count": 165 }, { "kind": "theorem", "id": "Semantics.LadderLUT.decimalDenominatorIsRedditWitness", "name": "decimalDenominatorIsRedditWitness", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.decimalReplayStartsAt000", "name": "decimalReplayStartsAt000", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.decimalPacketPromotable", "name": "decimalPacketPromotable", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.byteThreePacketPromotable", "name": "byteThreePacketPromotable", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.tinyLadderNotPromotable", "name": "tinyLadderNotPromotable", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.badBaseNotPromotable", "name": "badBaseNotPromotable", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.promotable_ladder_structurally_valid", "name": "promotable_ladder_structurally_valid", "module": "Semantics.LadderLUT" }, { "kind": "theorem", "id": "Semantics.LadderLUT.promotable_ladder_satisfies_byte_law", "name": "promotable_ladder_satisfies_byte_law", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.expectedBase", "name": "expectedBase", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.blockEnumeratorDenominator", "name": "blockEnumeratorDenominator", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.ladderStructurallyValid", "name": "ladderStructurallyValid", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.ladderValueAt", "name": "ladderValueAt", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.replayLadder", "name": "replayLadder", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.explicitLutBytes", "name": "explicitLutBytes", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.ladderEncodedBytes", "name": "ladderEncodedBytes", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.ladderByteLawHolds", "name": "ladderByteLawHolds", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.ladderPromotable", "name": "ladderPromotable", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.decimalThreeDigitPacket", "name": "decimalThreeDigitPacket", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.byteThreePacket", "name": "byteThreePacket", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.tinyLadderPacket", "name": "tinyLadderPacket", "module": "Semantics.LadderLUT" }, { "kind": "def", "id": "Semantics.LadderLUT.badBasePacket", "name": "badBasePacket", "module": "Semantics.LadderLUT" }, { "kind": "module", "id": "Semantics.LandauerCompression", "name": "LandauerCompression", "path": "Semantics/LandauerCompression.lean", "namespace": "Semantics.LandauerCompression", "doc": "Abstract one-bit Landauer unit in proof-layer Q16.16 form. This is a normalized lower-bound unit, not a calibrated physical constant.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 13, "struct_count": 5, "inductive_count": 0, "line_count": 184 }, { "kind": "theorem", "id": "Semantics.LandauerCompression.reversibleZeroBound", "name": "reversibleZeroBound", "module": "Semantics.LandauerCompression" }, { "kind": "theorem", "id": "Semantics.LandauerCompression.positiveErasurePositiveLowerBound", "name": "positiveErasurePositiveLowerBound", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.landauerUnitCost", "name": "landauerUnitCost", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.erasedDirections", "name": "erasedDirections", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.isIrreversible", "name": "isIrreversible", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.landauerLowerBound", "name": "landauerLowerBound", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.witnessOfSummaries", "name": "witnessOfSummaries", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.witnessOfNodes", "name": "witnessOfNodes", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.samplePreSummary", "name": "samplePreSummary", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.samplePostSummary", "name": "samplePostSummary", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.sampleWitness", "name": "sampleWitness", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.sampleReversibleWitness", "name": "sampleReversibleWitness", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.LandauerLogicalMass", "name": "LandauerLogicalMass", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.reversibleZeroBoundMass", "name": "reversibleZeroBoundMass", "module": "Semantics.LandauerCompression" }, { "kind": "def", "id": "Semantics.LandauerCompression.positiveErasurePositiveLowerBoundMass", "name": "positiveErasurePositiveLowerBoundMass", "module": "Semantics.LandauerCompression" }, { "kind": "module", "id": "Semantics.LaviGen", "name": "LaviGen", "path": "Semantics/LaviGen.lean", "namespace": "Semantics.LaviGen", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team LaviGen.lean \u2014 Autoregressive 3D Layout Generation with Dual-Guidance Self-Rollout This module formalizes LaviGen from \"Repurposing 3D Generative Model for Autoregressive Layout Generation\" (arXiv:2604", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 26, "struct_count": 17, "inductive_count": 2, "line_count": 373 }, { "kind": "def", "id": "Semantics.LaviGen.zero", "name": "zero", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.one", "name": "one", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.epsilon", "name": "epsilon", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.ofNat", "name": "ofNat", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.ofFloat", "name": "ofFloat", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.add", "name": "add", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.sub", "name": "sub", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.mul", "name": "mul", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.div", "name": "div", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.neg", "name": "neg", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.abs", "name": "abs", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.lerp", "name": "lerp", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.clip01", "name": "clip01", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.CleanSample", "name": "CleanSample", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.NoiseSample", "name": "NoiseSample", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.flowMatchingPerturb", "name": "flowMatchingPerturb", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.flowMatchingLoss", "name": "flowMatchingLoss", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.autoregressiveStep", "name": "autoregressiveStep", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.autoregressiveRollout", "name": "autoregressiveRollout", "module": "Semantics.LaviGen" }, { "kind": "def", "id": "Semantics.LaviGen.selfRolloutStep", "name": "selfRolloutStep", "module": "Semantics.LaviGen" }, { "kind": "module", "id": "Semantics.LawfulLoss", "name": "LawfulLoss", "path": "Semantics/LawfulLoss.lean", "namespace": "Semantics.LawfulLoss", "doc": "Formalizes the `bind` bridge semantics for lawful loss across incompatible cognitive manifolds (human, machine, alien, etc.). Every translation yields a `BindResult` recording: lawful : Bool \u2014 did invariants survive? cost : Q0_16 \u2014 dimensional mismatch penalty (normalized) witness : String \u2014 w", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 14, "struct_count": 1, "inductive_count": 2, "line_count": 212 }, { "kind": "def", "id": "Semantics.LawfulLoss.bindClassLabel", "name": "bindClassLabel", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.mkLawful", "name": "mkLawful", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.mkUnlawful", "name": "mkUnlawful", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.isLawful", "name": "isLawful", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.bindCost", "name": "bindCost", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.bindWitness", "name": "bindWitness", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.lawfulLoss", "name": "lawfulLoss", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.invariantLabel", "name": "invariantLabel", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.allInvariantsPreserved", "name": "allInvariantsPreserved", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.exampleHumanHuman", "name": "exampleHumanHuman", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.exampleHumanDolphin", "name": "exampleHumanDolphin", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.exampleBadLoss", "name": "exampleBadLoss", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.exampleHumanMachine", "name": "exampleHumanMachine", "module": "Semantics.LawfulLoss" }, { "kind": "def", "id": "Semantics.LawfulLoss.exampleHumanAlien", "name": "exampleHumanAlien", "module": "Semantics.LawfulLoss" }, { "kind": "module", "id": "Semantics.Layer3TransmissionModel", "name": "Layer3TransmissionModel", "path": "Semantics/Layer3TransmissionModel.lean", "namespace": "Semantics.Layer3TransmissionModel", "doc": "Formal proof that \"0 bytes during local compute\" is NOT compression. Key invariant: compressionRatio \u2260 transmissionAvoidance Layer 3 can reduce when data is transmitted. It does not make the data smaller by itself. Corrected architecture equation: effective_network_cost = anchor_frequency \u00d7 compre", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 7, "def_count": 4, "struct_count": 2, "inductive_count": 1, "line_count": 141 }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.local_computation_zero_transmitted", "name": "local_computation_zero_transmitted", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.local_computation_no_size_change", "name": "local_computation_no_size_change", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.local_computation_not_compression", "name": "local_computation_not_compression", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.transmission_avoidance_not_compression", "name": "transmission_avoidance_not_compression", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.effective_cost_not_infinite", "name": "effective_cost_not_infinite", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.effective_cost_formula_correct", "name": "effective_cost_formula_correct", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "theorem", "id": "Semantics.Layer3TransmissionModel.compression_ratio_zero_denominator_is_infinity", "name": "compression_ratio_zero_denominator_is_infinity", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "def", "id": "Semantics.Layer3TransmissionModel.localComputationCost", "name": "localComputationCost", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "def", "id": "Semantics.Layer3TransmissionModel.anchorTransmissionCost", "name": "anchorTransmissionCost", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "def", "id": "Semantics.Layer3TransmissionModel.compressionRatio", "name": "compressionRatio", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "def", "id": "Semantics.Layer3TransmissionModel.calculateEffectiveCost", "name": "calculateEffectiveCost", "module": "Semantics.Layer3TransmissionModel" }, { "kind": "module", "id": "Semantics.Lean4ImprovementProofs", "name": "Lean4ImprovementProofs", "path": "Semantics/Lean4ImprovementProofs.lean", "namespace": "Semantics.Lean4Improvement", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Lean4ImprovementProofs.lean \u2014 Formal Proofs of Lean 4 Improvement Certainty This module provides formal mathematical proofs that the proposed Lean 4 improvements are mathematically certain to improve t", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 13, "def_count": 15, "struct_count": 3, "inductive_count": 0, "line_count": 354 }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.aiTacticsImprovesUsability", "name": "aiTacticsImprovesUsability", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.hardwareExtractionMaximizesExtraction", "name": "hardwareExtractionMaximizesExtraction", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.parallelCompilationImprovesSpeed", "name": "parallelCompilationImprovesSpeed", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.mlIntegrationExpandsEcosystem", "name": "mlIntegrationExpandsEcosystem", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.typeInferenceImprovesQuality", "name": "typeInferenceImprovesQuality", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.physicsLibraryMaximizesEcosystem", "name": "physicsLibraryMaximizesEcosystem", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.applyAITacticsImprovesUsability", "name": "applyAITacticsImprovesUsability", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.hardwareExtractionMaximizesSystemExtraction", "name": "hardwareExtractionMaximizesSystemExtraction", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.allImprovementsImproveSystem", "name": "allImprovementsImproveSystem", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.priorityMonotonic", "name": "priorityMonotonic", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.hardwareExtractionHighestPriority", "name": "hardwareExtractionHighestPriority", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.allImprovementsGuaranteed", "name": "allImprovementsGuaranteed", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "theorem", "id": "Semantics.Lean4ImprovementProofs.mathematicalCertaintyOfImprovement", "name": "mathematicalCertaintyOfImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.computePriority", "name": "computePriority", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.aiTacticsImprovement", "name": "aiTacticsImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.aiTacticsEffect", "name": "aiTacticsEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.hardwareExtractionImprovement", "name": "hardwareExtractionImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.hardwareExtractionEffect", "name": "hardwareExtractionEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.parallelCompilationImprovement", "name": "parallelCompilationImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.parallelCompilationEffect", "name": "parallelCompilationEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.mlIntegrationImprovement", "name": "mlIntegrationImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.mlIntegrationEffect", "name": "mlIntegrationEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.typeInferenceImprovement", "name": "typeInferenceImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.typeInferenceEffect", "name": "typeInferenceEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.physicsLibraryImprovement", "name": "physicsLibraryImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.physicsLibraryEffect", "name": "physicsLibraryEffect", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.applyImprovement", "name": "applyImprovement", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "def", "id": "Semantics.Lean4ImprovementProofs.improvementGuaranteed", "name": "improvementGuaranteed", "module": "Semantics.Lean4ImprovementProofs" }, { "kind": "module", "id": "Semantics.LeanBridge", "name": "LeanBridge", "path": "Semantics/LeanBridge.lean", "namespace": "Semantics", "doc": "Lean Bridge Utilities ID: LEAN-BRIDGE-1 This module provides utility functions and type class instances to smooth over Lean 4 idiosyncrasies encountered during development. Common issues addressed: Structure field notation complexity in theorem hypotheses BEq instance not found for functions retur", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 0, "inductive_count": 0, "line_count": 125 }, { "kind": "def", "id": "Semantics.LeanBridge.safeCount", "name": "safeCount", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.q0", "name": "q0", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.q1", "name": "q1", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.mkStruct", "name": "mkStruct", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.structCases", "name": "structCases", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.safeFilter", "name": "safeFilter", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.safeFind", "name": "safeFind", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.safeAny", "name": "safeAny", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.safeAll", "name": "safeAll", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.natToQ", "name": "natToQ", "module": "Semantics.LeanBridge" }, { "kind": "def", "id": "Semantics.LeanBridge.intToQ", "name": "intToQ", "module": "Semantics.LeanBridge" }, { "kind": "module", "id": "Semantics.LeanGPTTSMLayer", "name": "LeanGPTTSMLayer", "path": "Semantics/LeanGPTTSMLayer.lean", "namespace": "Semantics.LeanGPTTSMLayer", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 7, "struct_count": 9, "inductive_count": 2, "line_count": 505 }, { "kind": "theorem", "id": "Semantics.LeanGPTTSMLayer.metatypeConfidenceMonotonicity", "name": "metatypeConfidenceMonotonicity", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "theorem", "id": "Semantics.LeanGPTTSMLayer.skepticalConsistency", "name": "skepticalConsistency", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "theorem", "id": "Semantics.LeanGPTTSMLayer.codeGenTypeSafety", "name": "codeGenTypeSafety", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "theorem", "id": "Semantics.LeanGPTTSMLayer.selfImprovementConvergence", "name": "selfImprovementConvergence", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.leanGPTBind", "name": "leanGPTBind", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.generateMetatype", "name": "generateMetatype", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.applyMetatype", "name": "applyMetatype", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.selfImprove", "name": "selfImprove", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.runSkepticalVerification", "name": "runSkepticalVerification", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.generateSwarmCode", "name": "generateSwarmCode", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "def", "id": "Semantics.LeanGPTTSMLayer.leanGPTTSMBind", "name": "leanGPTTSMBind", "module": "Semantics.LeanGPTTSMLayer" }, { "kind": "module", "id": "Semantics.LeanProof", "name": "LeanProof", "path": "Semantics/LeanProof.lean", "namespace": "Semantics.LeanProof", "doc": "# LeanProof \u2014 Proof Trace Formalization Formal infrastructure for LLM-generated Lean proofs in the BraidStorm prover loop. ## Purpose Every proof attempt by the DeepSeek-Prover-V2-7B model (or any LLM prover backend) generates a proof trace: The candidate proof code (as a string) The compile resu", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 5, "struct_count": 3, "inductive_count": 1, "line_count": 148 }, { "kind": "theorem", "id": "Semantics.LeanProof.encode_decode_roundtrip", "name": "encode_decode_roundtrip", "module": "Semantics.LeanProof" }, { "kind": "theorem", "id": "Semantics.LeanProof.Q16Timestamp", "name": "Q16Timestamp", "module": "Semantics.LeanProof" }, { "kind": "def", "id": "Semantics.LeanProof.traceHash", "name": "traceHash", "module": "Semantics.LeanProof" }, { "kind": "def", "id": "Semantics.LeanProof.encodeTrace", "name": "encodeTrace", "module": "Semantics.LeanProof" }, { "kind": "def", "id": "Semantics.LeanProof.decodeTrace", "name": "decodeTrace", "module": "Semantics.LeanProof" }, { "kind": "module", "id": "Semantics.Lemmas", "name": "Lemmas", "path": "Semantics/Lemmas.lean", "namespace": "Semantics.ENE", "doc": "inductive PartOfSpeech | verb | noun | adjective | adverb | preposition | conjunction | determiner | pronoun deriving Repr, BEq, DecidableEq, Hashable /-- A Lemma is a canonical typed bundle of semantic atoms. It provides the \"Contract\" for a specific meaning. -", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 1, "line_count": 48 }, { "kind": "def", "id": "Semantics.Lemmas.HasAtom", "name": "HasAtom", "module": "Semantics.Lemmas" }, { "kind": "def", "id": "Semantics.Lemmas.isAgentive", "name": "isAgentive", "module": "Semantics.Lemmas" }, { "kind": "module", "id": "Semantics.LocalDerivative", "name": "LocalDerivative", "path": "Semantics/LocalDerivative.lean", "namespace": "Semantics.LocalDerivative", "doc": "LocalDerivative.lean - Fixed-Point Differential Geometry Ported from semantics_unified_package_1102pm.zip Changed: Float \u2192 Fix16 (Q16.16 saturating fixed-point) Preserved: All differential geometry mathematics Provides Jacobian and Hessian structures for local derivative computation using hardware", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 28, "struct_count": 1, "inductive_count": 1, "line_count": 248 }, { "kind": "theorem", "id": "Semantics.LocalDerivative.matrixScale_total", "name": "matrixScale_total", "module": "Semantics.LocalDerivative" }, { "kind": "theorem", "id": "Semantics.LocalDerivative.matrixTranspose_total", "name": "matrixTranspose_total", "module": "Semantics.LocalDerivative" }, { "kind": "theorem", "id": "Semantics.LocalDerivative.trace_total", "name": "trace_total", "module": "Semantics.LocalDerivative" }, { "kind": "theorem", "id": "Semantics.LocalDerivative.classifyStability_total", "name": "classifyStability_total", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.rectangularRowsInvariant", "name": "rectangularRowsInvariant", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.squareMatrixInvariant", "name": "squareMatrixInvariant", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.localDerivativeInvariant", "name": "localDerivativeInvariant", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.zeroMatrix", "name": "zeroMatrix", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixDimension", "name": "matrixDimension", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.listGet", "name": "listGet", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixGet", "name": "matrixGet", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixEntryOrZero", "name": "matrixEntryOrZero", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixTranspose", "name": "matrixTranspose", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixZipWith", "name": "matrixZipWith", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixScale", "name": "matrixScale", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixMapWithIndex", "name": "matrixMapWithIndex", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixFlatten", "name": "matrixFlatten", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixL1Norm", "name": "matrixL1Norm", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixFrobeniusNormSq", "name": "matrixFrobeniusNormSq", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixFrobeniusNorm", "name": "matrixFrobeniusNorm", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixAdd", "name": "matrixAdd", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixSubtract", "name": "matrixSubtract", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.matrixNegate", "name": "matrixNegate", "module": "Semantics.LocalDerivative" }, { "kind": "def", "id": "Semantics.LocalDerivative.symmetricPart", "name": "symmetricPart", "module": "Semantics.LocalDerivative" }, { "kind": "module", "id": "Semantics.LocalExpansion", "name": "LocalExpansion", "path": "Semantics/LocalExpansion.lean", "namespace": "Semantics.LocalExpansion", "doc": "LocalExpansion.lean - Fixed-Point Local Taylor Expansion", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 0, "line_count": 56 }, { "kind": "def", "id": "Semantics.LocalExpansion.localExpansionInvariant", "name": "localExpansionInvariant", "module": "Semantics.LocalExpansion" }, { "kind": "def", "id": "Semantics.LocalExpansion.fromLocalDerivative", "name": "fromLocalDerivative", "module": "Semantics.LocalExpansion" }, { "kind": "def", "id": "Semantics.LocalExpansion.listGet", "name": "listGet", "module": "Semantics.LocalExpansion" }, { "kind": "def", "id": "Semantics.LocalExpansion.evaluateLinear", "name": "evaluateLinear", "module": "Semantics.LocalExpansion" }, { "kind": "def", "id": "Semantics.LocalExpansion.quadraticForm", "name": "quadraticForm", "module": "Semantics.LocalExpansion" }, { "kind": "def", "id": "Semantics.LocalExpansion.evaluateTaylor2", "name": "evaluateTaylor2", "module": "Semantics.LocalExpansion" }, { "kind": "module", "id": "Semantics.LogogramRotationLoop", "name": "LogogramRotationLoop", "path": "Semantics/LogogramRotationLoop.lean", "namespace": "Semantics.LogogramRotationLoop", "doc": "LogogramRotationLoop.lean \u2014 Holographic logogram encoding via lambda-rotation. One beam carries multiple encoded projections. The beam does not switch between encodings \u2014 it always delivers the superposition of all projections simultaneously. The boundary resolves separate structures by threshold", "math_kind": "braid", "sorry_count": 0, "theorem_count": 9, "def_count": 13, "struct_count": 6, "inductive_count": 0, "line_count": 331 }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.single_cycle_produces_one_structure", "name": "single_cycle_produces_one_structure", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.three_cycle_beam_has_positive_activation", "name": "three_cycle_beam_has_positive_activation", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.three_cycle_integrates_all_layers", "name": "three_cycle_integrates_all_layers", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.single_cycle_integrates_one_layer", "name": "single_cycle_integrates_one_layer", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.empty_cycle_has_zero_activation", "name": "empty_cycle_has_zero_activation", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.zero_is_in_low_band", "name": "zero_is_in_low_band", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.half_is_in_mid_band", "name": "half_is_in_mid_band", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.one_is_in_high_band", "name": "one_is_in_high_band", "module": "Semantics.LogogramRotationLoop" }, { "kind": "theorem", "id": "Semantics.LogogramRotationLoop.low_and_mid_bands_are_disjoint", "name": "low_and_mid_bands_are_disjoint", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.inBand", "name": "inBand", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.integrateLayer", "name": "integrateLayer", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.runRotationCycle", "name": "runRotationCycle", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.resolveStructure", "name": "resolveStructure", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.resolveAllStructures", "name": "resolveAllStructures", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.materializedCount", "name": "materializedCount", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.lowBand", "name": "lowBand", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.midBand", "name": "midBand", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.highBand", "name": "highBand", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.threeStructureCycle", "name": "threeStructureCycle", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.singleStructureCycle", "name": "singleStructureCycle", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.singleBeam", "name": "singleBeam", "module": "Semantics.LogogramRotationLoop" }, { "kind": "def", "id": "Semantics.LogogramRotationLoop.threeBeam", "name": "threeBeam", "module": "Semantics.LogogramRotationLoop" }, { "kind": "module", "id": "Semantics.LogogramSubstitution", "name": "LogogramSubstitution", "path": "Semantics/LogogramSubstitution.lean", "namespace": "Semantics.LogogramSubstitution", "doc": "# Logogram Substitution Gate This module is the Lean law surface for math/logogram substitution receipts. Python shims may generate audit JSON, but admission decisions reduce to these finite gates: payload bound, token-stream completeness, inverse uniqueness, residual declaration, and quarantine ro", "math_kind": "avm", "sorry_count": 0, "theorem_count": 8, "def_count": 14, "struct_count": 1, "inductive_count": 3, "line_count": 193 }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.hashed_multichar_requires_residual", "name": "hashed_multichar_requires_residual", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.sidecar_ops_declare_residual", "name": "sidecar_ops_declare_residual", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.literal_atom_is_payload_only_accepted", "name": "literal_atom_is_payload_only_accepted", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.known_command_collision_is_held", "name": "known_command_collision_is_held", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.hashed_identifier_is_held", "name": "hashed_identifier_is_held", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.truncated_payload_is_held", "name": "truncated_payload_is_held", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.semantic_tear_is_quarantined", "name": "semantic_tear_is_quarantined", "module": "Semantics.LogogramSubstitution" }, { "kind": "theorem", "id": "Semantics.LogogramSubstitution.accepted_substitution_has_payload_round_trip", "name": "accepted_substitution_has_payload_round_trip", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.tokenClassNeedsResidual", "name": "tokenClassNeedsResidual", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.sidecarOpDeclaresResidual", "name": "sidecarOpDeclaresResidual", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.gcclReceiptShapeComplete", "name": "gcclReceiptShapeComplete", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.payloadOnlyRoundTrip", "name": "payloadOnlyRoundTrip", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.sidecarRoundTrip", "name": "sidecarRoundTrip", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.substitutionAccepted", "name": "substitutionAccepted", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.substitutionHeld", "name": "substitutionHeld", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.substitutionQuarantined", "name": "substitutionQuarantined", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.decideSubstitution", "name": "decideSubstitution", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.literalAtomReceipt", "name": "literalAtomReceipt", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.knownCommandSidecarReceipt", "name": "knownCommandSidecarReceipt", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.hashedIdentifierReceipt", "name": "hashedIdentifierReceipt", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.truncatedPayloadReceipt", "name": "truncatedPayloadReceipt", "module": "Semantics.LogogramSubstitution" }, { "kind": "def", "id": "Semantics.LogogramSubstitution.semanticTearReceipt", "name": "semanticTearReceipt", "module": "Semantics.LogogramSubstitution" }, { "kind": "module", "id": "Semantics.LonelyRunner", "name": "LonelyRunner", "path": "Semantics/LonelyRunner.lean", "namespace": "Semantics.LonelyRunner", "doc": "LonelyRunner.lean \u2014 Lonely Runner \u2192 Betti-0 Scar Topology Formalizes the Lonely Runner Conjecture as a topological scar-persistence claim: for k runners on S\u00b9 with speeds {v_i}, the zeroth Betti number \u03b2\u2080(M_t) of the uncovered set M_t satisfies \u03b2\u2080(M_t) > 0 for some t. References: Wills 1967 \u2014 Orig", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 18, "def_count": 7, "struct_count": 3, "inductive_count": 0, "line_count": 463 }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_symm", "name": "circleDist_symm", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_le_half", "name": "circleDist_le_half", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_zero_third", "name": "circleDist_zero_third", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_zero_two_thirds", "name": "circleDist_zero_two_thirds", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_zero_quarter", "name": "circleDist_zero_quarter", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_zero_half", "name": "circleDist_zero_half", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.circleDist_zero_three_quarters", "name": "circleDist_zero_three_quarters", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_eq_product", "name": "runnerPos_eq_product", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_one_third", "name": "runnerPos_one_third", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_two_thirds", "name": "runnerPos_two_thirds", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_one_quarter", "name": "runnerPos_one_quarter", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_two_quarter", "name": "runnerPos_two_quarter", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.runnerPos_three_quarter", "name": "runnerPos_three_quarter", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.lonely_k2_speeds_1_2", "name": "lonely_k2_speeds_1_2", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.lonely_k3_speeds_1_2_3", "name": "lonely_k3_speeds_1_2_3", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.scarSupport_eq_scarRegion", "name": "scarSupport_eq_scarRegion", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.origin_uncovered_at_one_over_k_plus_one", "name": "origin_uncovered_at_one_over_k_plus_one", "module": "Semantics.LonelyRunner" }, { "kind": "theorem", "id": "Semantics.LonelyRunner.lonely_k_speeds_1_to_k", "name": "lonely_k_speeds_1_to_k", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.scarRegion", "name": "scarRegion", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.lonelyTimeExists", "name": "lonelyTimeExists", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.cyclicPrev", "name": "cyclicPrev", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.isRisingEdge", "name": "isRisingEdge", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.beta0Circular", "name": "beta0Circular", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.beta0", "name": "beta0", "module": "Semantics.LonelyRunner" }, { "kind": "def", "id": "Semantics.LonelyRunner.lonelyRunnerReceipt", "name": "lonelyRunnerReceipt", "module": "Semantics.LonelyRunner" }, { "kind": "module", "id": "Semantics.MISignal", "name": "MISignal", "path": "Semantics/MISignal.lean", "namespace": "Semantics.MISignal", "doc": "MISignal.lean - Mutual Information Signal Processing Bindings Ports rows 72-76 from MATH_MODEL_MAP.tsv (Python \u2192 Lean). All values are Q16.16. Bits-per-byte range [0, 8] maps to [0, 8\u00b765536].", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 93 }, { "kind": "def", "id": "Semantics.MISignal.epsilon", "name": "epsilon", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.bitsPerByteMax", "name": "bitsPerByteMax", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.mutualInformationSignal", "name": "mutualInformationSignal", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.knnMIPrediction", "name": "knnMIPrediction", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.surpriseMetric", "name": "surpriseMetric", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.structureYield", "name": "structureYield", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.weightedFeatureDistanceSq", "name": "weightedFeatureDistanceSq", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.miInvariant", "name": "miInvariant", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.miCost", "name": "miCost", "module": "Semantics.MISignal" }, { "kind": "def", "id": "Semantics.MISignal.miSignalBind", "name": "miSignalBind", "module": "Semantics.MISignal" }, { "kind": "module", "id": "Semantics.MMRFAMMUnification", "name": "MMRFAMMUnification", "path": "Semantics/MMRFAMMUnification.lean", "namespace": "Semantics.MMRFAMMUnification", "doc": "FAMM cells are MMR leaves \u2014 live, high-resolution delay lines. Merge operations coarsen delay (losing temporal resolution but gaining causal depth). `delayMass` is the MMR depth proxy. ## Energy Invariant (proof target) merge preserves total causal cost: a.delayMass + b.delayMass = merge(a,b).dela", "math_kind": "fixedpoint", "sorry_count": 1, "theorem_count": 3, "def_count": 16, "struct_count": 1, "inductive_count": 1, "line_count": 209 }, { "kind": "theorem", "id": "Semantics.MMRFAMMUnification.famm_merge_preserves_cost", "name": "famm_merge_preserves_cost", "module": "Semantics.MMRFAMMUnification" }, { "kind": "theorem", "id": "Semantics.MMRFAMMUnification.total_causal_cost_invariant_test", "name": "total_causal_cost_invariant_test", "module": "Semantics.MMRFAMMUnification" }, { "kind": "theorem", "id": "Semantics.MMRFAMMUnification.merge_depth_monotone", "name": "merge_depth_monotone", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.mmrLevelEq", "name": "mmrLevelEq", "module": 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"Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.mmrThermalDefrag", "name": "mmrThermalDefrag", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.leafCellA", "name": "leafCellA", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.leafCellB", "name": "leafCellB", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.mergedCell", "name": "mergedCell", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.leafLevel", "name": "leafLevel", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.midLevel", "name": "midLevel", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.mergedLevel", "name": "mergedLevel", "module": "Semantics.MMRFAMMUnification" }, { "kind": "def", "id": "Semantics.MMRFAMMUnification.hotLevel", "name": "hotLevel", "module": "Semantics.MMRFAMMUnification" }, { "kind": "module", "id": "Semantics.MNLOGQuaternionBridge", "name": "MNLOGQuaternionBridge", "path": "Semantics/MNLOGQuaternionBridge.lean", "namespace": "Semantics.MNLOGQuaternionBridge", "doc": "MNLOG-005: Quaternion Scalar Alignment for Semantic Orientation Tracking", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 7, "inductive_count": 2, "line_count": 406 }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.quaternionConjugate", "name": "quaternionConjugate", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.quaternionGradientConnection", "name": "quaternionGradientConnection", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.normalizedSemanticDistance", "name": "normalizedSemanticDistance", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.extractScalarAlignment", "name": "extractScalarAlignment", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.extractDriftVector", "name": "extractDriftVector", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.computeRotationAngle", "name": "computeRotationAngle", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.buildSemanticGradientConnection", "name": "buildSemanticGradientConnection", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.checkGradientConnectionValidity", "name": "checkGradientConnectionValidity", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.antiDriftDetection", "name": "antiDriftDetection", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.noncommutativityCheck", "name": "noncommutativityCheck", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.isNonRhombus", "name": "isNonRhombus", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.quadrilateralToScalar0d", "name": "quadrilateralToScalar0d", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.quadrilateralToNSpace", "name": "quadrilateralToNSpace", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.nspaceToQuaternionScalar", "name": "nspaceToQuaternionScalar", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "def", "id": "Semantics.MNLOGQuaternionBridge.quadrilateralToQuaternionScalar", "name": "quadrilateralToQuaternionScalar", "module": "Semantics.MNLOGQuaternionBridge" }, { "kind": "module", "id": "Semantics.MOFCO2Reduction", "name": "MOFCO2Reduction", "path": "Semantics/MOFCO2Reduction.lean", "namespace": "Semantics.MOFCO2Reduction", "doc": "# MOF-Based CO2 Reduction Electrochemistry This module formalizes the electrochemical reduction equations for CO2 using Metal-Organic Framework (MOF) catalysts. The equations are grounded in fixed-point arithmetic (Q0_16, Q16_16) per AGENTS.md requirements. Key reactions: 2e- reduction: CO2 \u2192 CO, ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 7, "def_count": 10, "struct_count": 1, "inductive_count": 2, "line_count": 156 }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.twoElectron_lt_sixElectron", "name": "twoElectron_lt_sixElectron", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.sixElectron_lt_eightElectron", "name": "sixElectron_lt_eightElectron", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.energyCost_same_potential_equal", "name": "energyCost_same_potential_equal", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.minPotential_CO_raw_eq_CH3OH", "name": "minPotential_CO_raw_eq_CH3OH", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.sampleCOState_potential_sufficient", "name": "sampleCOState_potential_sufficient", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.sampleCH4State_potential_sufficient", "name": "sampleCH4State_potential_sufficient", "module": "Semantics.MOFCO2Reduction" }, { "kind": "theorem", "id": "Semantics.MOFCO2Reduction.sampleCOState_bind_passes", "name": "sampleCOState_bind_passes", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.reactionElectronCount", "name": "reactionElectronCount", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.reactionMinPotential", "name": "reactionMinPotential", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.initCO2ReductionState", "name": "initCO2ReductionState", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.potentialSufficient", "name": "potentialSufficient", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.energyCostPerMole", "name": "energyCostPerMole", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.faradaicEfficiencyBind", "name": "faradaicEfficiencyBind", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.potentialBind", "name": "potentialBind", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.co2ReductionBind", "name": "co2ReductionBind", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.sampleCOState", "name": "sampleCOState", "module": "Semantics.MOFCO2Reduction" }, { "kind": "def", "id": "Semantics.MOFCO2Reduction.sampleCH4State", "name": "sampleCH4State", "module": "Semantics.MOFCO2Reduction" }, { "kind": "module", "id": "Semantics.MagnetoPlasma", "name": "MagnetoPlasma", "path": "Semantics/MagnetoPlasma.lean", "namespace": "Semantics.MagnetoPlasma", "doc": "Standardize on hardware-native scalar type", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 7, "inductive_count": 5, "line_count": 373 }, { "kind": "def", "id": "Semantics.MagnetoPlasma.quantizeNonnegative", "name": "quantizeNonnegative", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.defaultMagnetoCore", "name": "defaultMagnetoCore", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.defaultMagnetoSpectralHook", "name": "defaultMagnetoSpectralHook", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.coreStrength", "name": "coreStrength", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.sampleSpectrallyCompatible", "name": "sampleSpectrallyCompatible", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.spectralAffinityOf", "name": "spectralAffinityOf", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.confinementFromCore", "name": "confinementFromCore", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.reconnectionFromSignature", "name": "reconnectionFromSignature", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.classifyMagnetoPlasmaRegime", "name": "classifyMagnetoPlasmaRegime", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.inferMagnetoPlasmaSignature", "name": "inferMagnetoPlasmaSignature", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.regimeSupportsLink", "name": "regimeSupportsLink", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.regionCompatible", "name": "regionCompatible", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.bodyCouplingStrength", "name": "bodyCouplingStrength", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.applyMagnetoBias", "name": "applyMagnetoBias", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.interactBodies", "name": "interactBodies", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.defaultMagnetoLink", "name": "defaultMagnetoLink", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.defaultHyperFlowSignature", "name": "defaultHyperFlowSignature", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.defaultMagnetoBody2D", "name": "defaultMagnetoBody2D", "module": "Semantics.MagnetoPlasma" }, { "kind": "def", "id": "Semantics.MagnetoPlasma.magnetoCoreBody2D", "name": "magnetoCoreBody2D", "module": "Semantics.MagnetoPlasma" }, { "kind": "module", "id": "Semantics.ManifoldBoundaryAtlas", "name": "ManifoldBoundaryAtlas", "path": "Semantics/ManifoldBoundaryAtlas.lean", "namespace": "Semantics.ManifoldBoundaryAtlas", "doc": "# ManifoldBoundaryAtlas A ManifoldBoundaryAtlas is a deterministic seed-generated set of candidate boundary coordinates for RRC-style projection checks. It generalizes `HexLogogramAtlas`: the seed does not claim a tear, proof, or manifold truth; it generates a finite boundary candidate surface tha", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 9, "def_count": 15, "struct_count": 2, "inductive_count": 1, "line_count": 263 }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.smallBoundaryReplay", "name": "smallBoundaryReplay", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.canonicalBoundaryAtlasPromotable", "name": "canonicalBoundaryAtlasPromotable", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.tinyBoundaryAtlasNotPromotable", "name": "tinyBoundaryAtlasNotPromotable", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.badBoundaryDomainAtlasNotPromotable", "name": "badBoundaryDomainAtlasNotPromotable", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.missingResidualBoundaryAtlasNotPromotable", "name": "missingResidualBoundaryAtlasNotPromotable", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.promotedBoundaryAtlasStructurallyValid", "name": "promotedBoundaryAtlasStructurallyValid", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.promotedBoundaryAtlasSatisfiesByteLaw", "name": "promotedBoundaryAtlasSatisfiesByteLaw", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.promotedBoundaryAtlasSetsRrcTearBoundary", "name": "promotedBoundaryAtlasSetsRrcTearBoundary", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "theorem", "id": "Semantics.ManifoldBoundaryAtlas.boundaryAtlasAloneDoesNotProject", "name": "boundaryAtlasAloneDoesNotProject", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.expectedHexBase", "name": "expectedHexBase", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryAtlasStructurallyValid", "name": "boundaryAtlasStructurallyValid", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryRawValueAt", "name": "boundaryRawValueAt", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryCandidateAt", "name": "boundaryCandidateAt", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.replayBoundaryAtlas", "name": "replayBoundaryAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.explicitBoundaryTableBytes", "name": "explicitBoundaryTableBytes", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryAtlasEncodedBytes", "name": "boundaryAtlasEncodedBytes", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryAtlasByteLawHolds", "name": "boundaryAtlasByteLawHolds", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.boundaryAtlasPromotable", "name": "boundaryAtlasPromotable", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.rrcBoundaryReceiptFromAtlas", "name": "rrcBoundaryReceiptFromAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.smallBoundaryAtlas", "name": "smallBoundaryAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.canonicalBoundaryAtlas", "name": "canonicalBoundaryAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.tinyBoundaryAtlas", "name": "tinyBoundaryAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.badBoundaryDomainAtlas", "name": "badBoundaryDomainAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "def", "id": "Semantics.ManifoldBoundaryAtlas.missingResidualBoundaryAtlas", "name": "missingResidualBoundaryAtlas", "module": "Semantics.ManifoldBoundaryAtlas" }, { "kind": "module", "id": "Semantics.ManifoldFlow", "name": "ManifoldFlow", "path": "Semantics/ManifoldFlow.lean", "namespace": "Semantics.ManifoldFlow", "doc": "Semantics/ManifoldFlow.lean - Anisotropically Frustrated Torsional Gradient Flow This module formalizes the \"n-space foldback-lock\" equation as the authoritative governing physics for the Sovereign Informatic Manifold. Governing Equation: \u2202_t \u03d5 = \u2207_i(M^ij \u2207_j \u03b4F/\u03b4\u03d5) - \u03c3 \u2202\u03d5/\u2202I_lock \u2202_t X^A = -\u0393^A_B", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 4, "inductive_count": 0, "line_count": 123 }, { "kind": "def", "id": "Semantics.ManifoldFlow.lockingPotential", "name": "lockingPotential", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.interlockingEnergy", "name": "interlockingEnergy", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.torsionalStress", "name": "torsionalStress", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.stableDt", "name": "stableDt", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.cflSatisfied", "name": "cflSatisfied", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.flowPhi", "name": "flowPhi", "module": "Semantics.ManifoldFlow" }, { "kind": "def", "id": "Semantics.ManifoldFlow.flowEmbedding", "name": "flowEmbedding", "module": "Semantics.ManifoldFlow" }, { "kind": "module", "id": "Semantics.ManifoldNetworking", "name": "ManifoldNetworking", "path": "Semantics/ManifoldNetworking.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "This module takes the mathematical foundations of Linux kernel networking (queueing theory, Little's Law, token bucket, AIMD, CUBIC) and applies them to a non-normal manifold-based networking abstraction that throws out the kernel's assumptions while preserving the mathematics. **Linux Kernel Assum", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 8, "def_count": 14, "struct_count": 10, "inductive_count": 1, "line_count": 466 }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.isNormalNetworkLimit_fails_nonZeroCurvature", "name": "isNormalNetworkLimit_fails_nonZeroCurvature", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.isNormalNetworkLimit_fails_nonZeroTorsion", "name": "isNormalNetworkLimit_fails_nonZeroTorsion", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.isNormalNetworkLimit_fails_notSinglePath", "name": "isNormalNetworkLimit_fails_notSinglePath", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.isNormalNetworkLimit_fails_notSequential", "name": "isNormalNetworkLimit_fails_notSequential", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.manifoldPacket_preservesSize", "name": "manifoldPacket_preservesSize", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.manifoldQueue_preservesCount_enqueue", "name": "manifoldQueue_preservesCount_enqueue", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.manifoldQueue_preservesCount_dequeue", "name": "manifoldQueue_preservesCount_dequeue", "module": "Semantics.ManifoldNetworking" }, { "kind": "theorem", "id": "Semantics.ManifoldNetworking.normalNetworkLimit", "name": "normalNetworkLimit", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.enqueuePacket", "name": "enqueuePacket", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.dequeuePacket", "name": "dequeuePacket", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.verifyLittleLaw", "name": "verifyLittleLaw", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.consumeTokens", "name": "consumeTokens", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.aimdUpdate", "name": "aimdUpdate", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.cubicComputeK", "name": "cubicComputeK", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.cubicUpdate", "name": "cubicUpdate", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.selectOptimalPath", "name": "selectOptimalPath", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.manifoldInputInvariant", "name": "manifoldInputInvariant", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.manifoldOutputInvariant", "name": "manifoldOutputInvariant", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.manifoldOperationCost", "name": "manifoldOperationCost", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.performManifoldOperation", "name": "performManifoldOperation", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.manifoldBind", "name": "manifoldBind", "module": "Semantics.ManifoldNetworking" }, { "kind": "def", "id": "Semantics.ManifoldNetworking.isNormalNetworkLimit", "name": "isNormalNetworkLimit", "module": "Semantics.ManifoldNetworking" }, { "kind": "module", "id": "Semantics.ManifoldPotential", "name": "ManifoldPotential", "path": "Semantics/ManifoldPotential.lean", "namespace": "Semantics.ManifoldPotential", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 8, "inductive_count": 4, "line_count": 283 }, { "kind": "def", "id": "Semantics.ManifoldPotential.addPulls", "name": "addPulls", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.explicitAliasDetected", "name": "explicitAliasDetected", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.threadAliasDetected", "name": "threadAliasDetected", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.scaffoldingRoleOf", "name": "scaffoldingRoleOf", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.classifyPotentialMorphology", "name": "classifyPotentialMorphology", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.boundaryModeOf", "name": "boundaryModeOf", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.threadCountOf", "name": "threadCountOf", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.potentialSignatureOf", "name": "potentialSignatureOf", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.classifyPotentialRegime", "name": "classifyPotentialRegime", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.classifyPotentialStability", "name": "classifyPotentialStability", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.potentialCompatibleWithBoundary", "name": "potentialCompatibleWithBoundary", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.mergeBasins", "name": "mergeBasins", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.mergeGradients", "name": "mergeGradients", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.mergePotentials", "name": "mergePotentials", "module": "Semantics.ManifoldPotential" }, { "kind": "def", "id": "Semantics.ManifoldPotential.processPotentialTransition", "name": "processPotentialTransition", "module": "Semantics.ManifoldPotential" }, { "kind": "module", "id": "Semantics.ManifoldStructures", "name": "ManifoldStructures", "path": "Semantics/ManifoldStructures.lean", "namespace": "Semantics.ManifoldStructures", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 4, "inductive_count": 5, "line_count": 107 }, { "kind": "module", "id": "Semantics.ManifoldTopology", "name": "ManifoldTopology", "path": "Semantics/ManifoldTopology.lean", "namespace": "Semantics.ManifoldTopology", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ManifoldTopology.lean \u2014 Topological Perception and Reshaping of Research Stack This module formalizes the problem: a human cannot see the complete manifold that their project represents. The manifold h", "math_kind": "geometry", "sorry_count": 4, "theorem_count": 1, "def_count": 7, "struct_count": 5, "inductive_count": 5, "line_count": 258 }, { "kind": "theorem", "id": "Semantics.ManifoldTopology.reshape_preserves_integrity", "name": "reshape_preserves_integrity", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.DimensionRange", "name": "DimensionRange", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.mkManifoldPoint", "name": "mkManifoldPoint", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.isAtBoundary", "name": "isAtBoundary", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.mkHole", "name": "mkHole", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.observerCapacity", "name": "observerCapacity", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.projectToHumanPerception", "name": "projectToHumanPerception", "module": "Semantics.ManifoldTopology" }, { "kind": "def", "id": "Semantics.ManifoldTopology.isLawfulReshape", "name": "isLawfulReshape", "module": "Semantics.ManifoldTopology" }, { "kind": "module", "id": "Semantics.ManyWorldsAddress", "name": "ManyWorldsAddress", "path": "Semantics/ManyWorldsAddress.lean", "namespace": "Semantics.ManyWorlds", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ManyWorldsAddress.lean \u2014 Observer-Relative Addressing via Many-Worlds Spawning Core insight: Remove the speed limit \u2192 no global simultaneity \u2192 every observer frame is its own world. A person is a world", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 8, "def_count": 12, "struct_count": 2, "inductive_count": 1, "line_count": 274 }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.spawnProducesN2Children", "name": "spawnProducesN2Children", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.worldCountDepthZero", "name": "worldCountDepthZero", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.branchingFactorPos", "name": "branchingFactorPos", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.shoreTransitionPreservesIfNonDegenerate", "name": "shoreTransitionPreservesIfNonDegenerate", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.shoreTransitionAdvancesAtShore", "name": "shoreTransitionAdvancesAtShore", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.nanIsTerminal", "name": "nanIsTerminal", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.restAddressDepthZero", "name": "restAddressDepthZero", "module": "Semantics.ManyWorldsAddress" }, { "kind": "theorem", "id": "Semantics.ManyWorldsAddress.spawnedAddressDepth", "name": "spawnedAddressDepth", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.validityLeq", "name": "validityLeq", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.rootFrame", "name": "rootFrame", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.restAddress", "name": "restAddress", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.spawnedAddress", "name": "spawnedAddress", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.spawnBranchingFactor", "name": "spawnBranchingFactor", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.worldCountAtDepth", "name": "worldCountAtDepth", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.totalAddressableWorlds", "name": "totalAddressableWorlds", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.childLocalCoord", "name": "childLocalCoord", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.spawnWorlds", "name": "spawnWorlds", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.validityStep", "name": "validityStep", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.shoreTransition", "name": "shoreTransition", "module": "Semantics.ManyWorldsAddress" }, { "kind": "def", "id": "Semantics.ManyWorldsAddress.isComputable", "name": "isComputable", "module": "Semantics.ManyWorldsAddress" }, { "kind": "module", "id": "Semantics.MassNumberAdapter", "name": "MassNumberAdapter", "path": "Semantics/MassNumberAdapter.lean", "namespace": "Semantics.MassNumberAdapter", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MassNumberAdapter.lean \u2014 Information-Theoretic Mass Number Classification Defines information-theoretic mass classification for mass numbers based on Shannon entropy, Kolmogorov complexity approximatio", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 5, "def_count": 6, "struct_count": 1, "inductive_count": 1, "line_count": 250 }, { "kind": "theorem", "id": "Semantics.MassNumberAdapter.shannonEntropyNonNegative", "name": "shannonEntropyNonNegative", "module": "Semantics.MassNumberAdapter" }, { "kind": "theorem", "id": "Semantics.MassNumberAdapter.kolmogorovComplexityBounded", "name": "kolmogorovComplexityBounded", "module": "Semantics.MassNumberAdapter" }, { "kind": "theorem", "id": "Semantics.MassNumberAdapter.informationDensityNonNegative", "name": "informationDensityNonNegative", "module": "Semantics.MassNumberAdapter" }, { "kind": "theorem", "id": "Semantics.MassNumberAdapter.compressibilityBounded", "name": "compressibilityBounded", "module": "Semantics.MassNumberAdapter" }, { "kind": "theorem", "id": "Semantics.MassNumberAdapter.classificationExhaustive", "name": "classificationExhaustive", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.computeShannonEntropy", "name": "computeShannonEntropy", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.approximateKolmogorovComplexity", "name": "approximateKolmogorovComplexity", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.computeInformationDensity", "name": "computeInformationDensity", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.computeCompressibility", "name": "computeCompressibility", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.calculateInformationMass", "name": "calculateInformationMass", "module": "Semantics.MassNumberAdapter" }, { "kind": "def", "id": "Semantics.MassNumberAdapter.classifyMassNumber", "name": "classifyMassNumber", "module": "Semantics.MassNumberAdapter" }, { "kind": "module", "id": "Semantics.MassNumberLinter", "name": "MassNumberLinter", "path": "Semantics/MassNumberLinter.lean", "namespace": "Semantics.MassNumberLinter", "doc": "Linter based on MNLOG-001 through MNLOG-007 doctrines: MNLOG-001: Logic can have a mass-number value only after we say which reality is weighing it MNLOG-002: Mass-number valuation supports G\u00f6del-style stress testing MNLOG-003: Mass numbers act as imaginary-number-like semantic coordinates MNLOG-004", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 3, "inductive_count": 0, "line_count": 240 }, { "kind": "def", "id": "Semantics.MassNumberLinter.defaultConfig", "name": "defaultConfig", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.isMassNumberName", "name": "isMassNumberName", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.matchesNamespaceFilter", "name": "matchesNamespaceFilter", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.hasMassNumberValuation", "name": "hasMassNumberValuation", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.checkValuationComponents", "name": "checkValuationComponents", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.createDecagonZetaValuation", "name": "createDecagonZetaValuation", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.decagonInvariants", "name": "decagonInvariants", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.isTheorem", "name": "isTheorem", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.runLinter", "name": "runLinter", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.printResults", "name": "printResults", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.runLinterAndPrint", "name": "runLinterAndPrint", "module": "Semantics.MassNumberLinter" }, { "kind": "def", "id": "Semantics.MassNumberLinter.myLinter", "name": "myLinter", "module": "Semantics.MassNumberLinter" }, { "kind": "module", "id": "Semantics.MassNumberMetricClosure", "name": "MassNumberMetricClosure", "path": "Semantics/MassNumberMetricClosure.lean", "namespace": "HolyDiver.ENE", "doc": "Mass-Number Metric Closure \u2014 Clean Rewrite Formalizes the Mass-Number Admissibility Closure Conjecture: Mass numbers + symmetrized edge cost \u2192 admissibility graph \u2192 shortest-path closure \u2192 pseudometric \u2192 quotient metric. 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It is treated as a component of the larger manifold.", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 3, "inductive_count": 0, "line_count": 36 }, { "kind": "module", "id": "Semantics.MeshRouting", "name": "MeshRouting", "path": "Semantics/MeshRouting.lean", "namespace": "Semantics.MeshRouting", "doc": "MeshRouting.lean \u2014 Unified transport encoding across all channels. Binds together the agent designs for: TMDS lane encoding (HDMI/DP PHY \u2014 Agent 1) VCN video encode/decode (MKV trick \u2014 Agent 2) Multi-transport selection, fragmentation, fallback (Agent 3) No dependency on NICProbe or ASICTopology t", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 6, "def_count": 33, "struct_count": 15, "inductive_count": 6, "line_count": 648 }, { "kind": "theorem", "id": "Semantics.MeshRouting.resolution_mono", "name": "resolution_mono", "module": "Semantics.MeshRouting" }, { "kind": "theorem", "id": "Semantics.MeshRouting.goxelFieldEnergyConservation", "name": "goxelFieldEnergyConservation", "module": "Semantics.MeshRouting" }, { "kind": "theorem", "id": "Semantics.MeshRouting.goxelTopologyPreserved", "name": "goxelTopologyPreserved", "module": "Semantics.MeshRouting" }, { "kind": "theorem", "id": "Semantics.MeshRouting.vcnFrameSizeYuv420Correct", "name": "vcnFrameSizeYuv420Correct", "module": "Semantics.MeshRouting" }, { "kind": "theorem", "id": "Semantics.MeshRouting.vcnFrameSizeRgb24Correct", "name": "vcnFrameSizeRgb24Correct", "module": "Semantics.MeshRouting" }, { "kind": "theorem", "id": "Semantics.MeshRouting.vcnReceiptValidCompression", "name": "vcnReceiptValidCompression", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.VCNResolution", "name": "VCNResolution", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.VCNFrameRate", "name": "VCNFrameRate", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.computeFrameSizeDynamic", "name": "computeFrameSizeDynamic", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.selectOptimalResolution", "name": "selectOptimalResolution", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.selectFrameFormat", "name": "selectFrameFormat", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.computeFrameSize", "name": "computeFrameSize", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.mkFrameSpec", "name": "mkFrameSpec", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.mkFrameSpecDynamic", "name": "mkFrameSpecDynamic", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.projectGoxelToVoxel", "name": "projectGoxelToVoxel", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.projectVoxelToFrame", "name": "projectVoxelToFrame", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.projectGoxelFieldToFrame", "name": "projectGoxelFieldToFrame", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.vcnCompressionRatio", "name": "vcnCompressionRatio", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.vcnSpaceSaving", "name": "vcnSpaceSaving", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.transportMTU", "name": "transportMTU", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.transportLatency", "name": "transportLatency", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.transportPriority", "name": "transportPriority", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.transportTag", "name": "transportTag", "module": "Semantics.MeshRouting" }, { "kind": "def", "id": "Semantics.MeshRouting.transportHeaderSize", "name": "transportHeaderSize", "module": "Semantics.MeshRouting" }, { "kind": "module", "id": "Semantics.MetaManifoldProver", "name": "MetaManifoldProver", "path": "Semantics/MetaManifoldProver.lean", "namespace": "Semantics.MetaManifoldProver", "doc": "Q16_16 format: 16-bit integer part + 16-bit fractional part Value: integer * 65536 + fractional Range: [-32768, 32767.999985]", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 8, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 252 }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.massNumberGate_monotonic", "name": "massNumberGate_monotonic", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.weighted_term_bounded", "name": "weighted_term_bounded", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.shiftRight_eq_div", "name": "shiftRight_eq_div", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.shiftRight_monotone", "name": "shiftRight_monotone", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.div_le_div_of_lt", "name": "div_le_div_of_lt", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.surfaceCheck_reflexive", "name": "surfaceCheck_reflexive", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.foldEnergy_bounded", "name": "foldEnergy_bounded", "module": "Semantics.MetaManifoldProver" }, { "kind": "theorem", "id": "Semantics.MetaManifoldProver.metaManifoldProverBind_lawful", "name": "metaManifoldProverBind_lawful", "module": "Semantics.MetaManifoldProver" }, { "kind": "def", "id": "Semantics.MetaManifoldProver.massNumberGate", "name": "massNumberGate", "module": "Semantics.MetaManifoldProver" }, { "kind": "def", "id": "Semantics.MetaManifoldProver.foldEnergy", "name": "foldEnergy", "module": "Semantics.MetaManifoldProver" }, { "kind": "def", "id": "Semantics.MetaManifoldProver.surfaceCheck", "name": "surfaceCheck", "module": "Semantics.MetaManifoldProver" }, { "kind": "def", "id": "Semantics.MetaManifoldProver.metaManifoldProver", "name": "metaManifoldProver", "module": "Semantics.MetaManifoldProver" }, { "kind": "def", "id": "Semantics.MetaManifoldProver.metaManifoldProverBind", "name": "metaManifoldProverBind", "module": "Semantics.MetaManifoldProver" }, { "kind": "module", "id": "Semantics.MetadataSurfaceComputation", "name": "MetadataSurfaceComputation", "path": "Semantics/MetadataSurfaceComputation.lean", "namespace": "Semantics.MetadataSurfaceComputation", "doc": "MetadataSurfaceComputation.lean \u2014 Metadata Surface Computation with No Payload Transmission This module formalizes metadata surface computation: the payload never moves, only the metadata surface is exposed. Per AGENTS.md \u00a71.6: No proof placeholders in committed code. Per AGENTS.md \u00a71.4: Uses Q16_", "math_kind": "avm", "sorry_count": 0, "theorem_count": 2, "def_count": 3, "struct_count": 4, "inductive_count": 0, "line_count": 94 }, { "kind": "theorem", "id": "Semantics.MetadataSurfaceComputation.payloadReceiptUsesOnlyObjectId", "name": "payloadReceiptUsesOnlyObjectId", "module": "Semantics.MetadataSurfaceComputation" }, { "kind": "theorem", "id": "Semantics.MetadataSurfaceComputation.exposedSurfaceForgetsPayload", "name": "exposedSurfaceForgetsPayload", "module": "Semantics.MetadataSurfaceComputation" }, { "kind": "def", "id": "Semantics.MetadataSurfaceComputation.exposeMetadataSurface", "name": "exposeMetadataSurface", "module": "Semantics.MetadataSurfaceComputation" }, { "kind": "def", "id": "Semantics.MetadataSurfaceComputation.computeFromSurface", "name": "computeFromSurface", "module": "Semantics.MetadataSurfaceComputation" }, { "kind": "def", "id": "Semantics.MetadataSurfaceComputation.generateReceipt", "name": "generateReceipt", "module": "Semantics.MetadataSurfaceComputation" }, { "kind": "module", "id": "Semantics.Metatype", "name": "Metatype", "path": "Semantics/Metatype.lean", "namespace": "Semantics.Metatype", "doc": "The three pillars of the Research Stack.", "math_kind": "general", "sorry_count": 0, "theorem_count": 1, "def_count": 2, "struct_count": 1, "inductive_count": 1, "line_count": 43 }, { "kind": "theorem", "id": "Semantics.Metatype.emergenceViaIntegration", "name": "emergenceViaIntegration", "module": "Semantics.Metatype" }, { "kind": "def", "id": "Semantics.Metatype.containsLayer", "name": "containsLayer", "module": "Semantics.Metatype" }, { "kind": "def", "id": "Semantics.Metatype.isMetastack", "name": "isMetastack", "module": "Semantics.Metatype" }, { "kind": "module", "id": "Semantics.MetricCore", "name": "MetricCore", "path": "Semantics/MetricCore.lean", "namespace": "Semantics.MetricCore", "doc": "MetricCore.lean - Minimal stub for LocalDerivative dependency", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 1, "inductive_count": 0, "line_count": 22 }, { "kind": "def", "id": "Semantics.MetricCore.metricInvariant", "name": "metricInvariant", "module": "Semantics.MetricCore" }, { "kind": "module", "id": "Semantics.MinimalBitcoinL3", "name": "MinimalBitcoinL3", "path": "Semantics/MinimalBitcoinL3.lean", "namespace": "Semantics.MinimalBitcoinL3", "doc": "**Goal:** Nearly impossibly small surface for Bitcoin L3 internal compute layer. **Principle:** Layer 3 = computation (local, private, no transmission) Layer 2 = aggregation (optional, semi-global) Layer 1 = commitment (global, public anchor) **Minimal Interface:** Internal transition: (from, to, ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 13, "def_count": 6, "struct_count": 4, "inductive_count": 0, "line_count": 245 }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.localOnlyNoTransmissionWithoutGrant", "name": "localOnlyNoTransmissionWithoutGrant", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.refusedTransitionPreservesState", "name": "refusedTransitionPreservesState", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.zeroDeltaPreservesState", "name": "zeroDeltaPreservesState", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.externalAnchorPreservesReceiptRoot", "name": "externalAnchorPreservesReceiptRoot", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.anchorDoesNotExpandScope", "name": "anchorDoesNotExpandScope", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.deltaWithinBound_valid", "name": "deltaWithinBound_valid", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.replayResistance", "name": "replayResistance", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.executeTransition_localOnly", "name": "executeTransition_localOnly", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.transitionAllowed_true_whenValid", "name": "transitionAllowed_true_whenValid", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.transitionAllowed_false_whenFromEqualsTo", "name": "transitionAllowed_false_whenFromEqualsTo", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.transitionAllowed_false_whenDeltaZero", "name": "transitionAllowed_false_whenDeltaZero", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.applyTransition_preservesWhenNotAllowed", "name": "applyTransition_preservesWhenNotAllowed", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "theorem", "id": "Semantics.MinimalBitcoinL3.applyTransition_changesToTarget", "name": "applyTransition_changesToTarget", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.executeTransition", "name": "executeTransition", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.transitionAllowed", "name": "transitionAllowed", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.applyTransition", "name": "applyTransition", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.tryAnchorReceipt", "name": "tryAnchorReceipt", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.isLocalOnly", "name": "isLocalOnly", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "def", "id": "Semantics.MinimalBitcoinL3.deltaWithinBound", "name": "deltaWithinBound", "module": "Semantics.MinimalBitcoinL3" }, { "kind": "module", "id": "Semantics.MinimalLayer3Eval", "name": "MinimalLayer3Eval", "path": "Semantics/MinimalLayer3Eval.lean", "namespace": "Semantics.MinimalLayer3Eval", "doc": "**Purpose:** 8/8 local-commit quiz cases passed for minimal Bitcoin L3 surface. Test local transitions, receipts, and optional external anchoring. **Test Cases:** 1. valid_internal_transition \u2192 ALLOW_LOCAL_TRANSITION 2. missing_policy_root \u2192 REFUSE_TRANSITION_IF_UNSCOPED 3. domain_mismatch_batch \u2192 ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 2, "inductive_count": 0, "line_count": 236 }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.computeTransitionHash", "name": "computeTransitionHash", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase1_validInternalTransition", "name": "testCase1_validInternalTransition", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase2_missingPolicyRoot", "name": "testCase2_missingPolicyRoot", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase3_domainMismatchBatch", "name": "testCase3_domainMismatchBatch", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase4_missingTransitionProof", "name": "testCase4_missingTransitionProof", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase5_localOnlyTransition", "name": "testCase5_localOnlyTransition", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase6_validExternalAnchor", "name": "testCase6_validExternalAnchor", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase7_anchorScopeExpansion", "name": "testCase7_anchorScopeExpansion", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.testCase8_replayedTransition", "name": "testCase8_replayedTransition", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.executeMinimalQuiz", "name": "executeMinimalQuiz", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.countMinimalPassed", "name": "countMinimalPassed", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "def", "id": "Semantics.MinimalLayer3Eval.generateMinimalQuizSummary", "name": "generateMinimalQuizSummary", "module": "Semantics.MinimalLayer3Eval" }, { "kind": "module", "id": "Semantics.MoECache", "name": "MoECache", "path": "Semantics/MoECache.lean", "namespace": "Semantics.MoECache", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MoECache.lean \u2014 MoE Cache Data Structures and Eviction Policy Replaces infra/moe_ene_cache.py cache logic with a formal Lean module. Defines MoE (Mixture-of-Experts) cache structures and eviction polic", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 8, "struct_count": 6, "inductive_count": 0, "line_count": 175 }, { "kind": "theorem", "id": "Semantics.MoECache.hitCountIncreases", "name": "hitCountIncreases", "module": "Semantics.MoECache" }, { "kind": "theorem", "id": "Semantics.MoECache.lruInitBounded", "name": "lruInitBounded", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.zero", "name": "zero", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.one", "name": "one", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.ofFrac", "name": "ofFrac", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.initLRUCache", "name": "initLRUCache", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.lruAccess", "name": "lruAccess", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.getLRUEvictionKey", "name": "getLRUEvictionKey", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.incrementHitCount", "name": "incrementHitCount", "module": "Semantics.MoECache" }, { "kind": "def", "id": "Semantics.MoECache.computeHitRate", "name": "computeHitRate", "module": "Semantics.MoECache" }, { "kind": "module", "id": "Semantics.MorphicDSP", "name": "MorphicDSP", "path": "Semantics/MorphicDSP.lean", "namespace": "Semantics.MorphicDSP", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphicDSP.lean \u2014 Reconfigurable DSP via Morphic Scalar This module reconfigures the concept of DSP (Digital Signal Processing) from fixed-function hardware to morphic-scalar-controlled reconfigurable ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 36, "struct_count": 10, "inductive_count": 2, "line_count": 531 }, { "kind": "theorem", "id": "Semantics.MorphicDSP.superposedMapsToAdaptive", "name": "superposedMapsToAdaptive", "module": "Semantics.MorphicDSP" }, { "kind": "theorem", "id": "Semantics.MorphicDSP.criticalOepiAllocatesAll", "name": "criticalOepiAllocatesAll", "module": "Semantics.MorphicDSP" }, { "kind": "theorem", "id": "Semantics.MorphicDSP.lowOepiAllocatesOne", "name": "lowOepiAllocatesOne", "module": "Semantics.MorphicDSP" }, { "kind": "theorem", "id": "Semantics.MorphicDSP.initDspBankHasFiveSlices", "name": "initDspBankHasFiveSlices", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.stateToDspMode", "name": "stateToDspMode", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.configureDspSlice", "name": "configureDspSlice", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.executeDspOp", "name": "executeDspOp", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.initDspBank", "name": "initDspBank", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.configureDspBank", "name": "configureDspBank", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.allocateDspSlices", "name": "allocateDspSlices", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.admissibleBasis", "name": "admissibleBasis", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.isInAdmissibleBasis", "name": "isInAdmissibleBasis", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.checkCollapseGate", "name": "checkCollapseGate", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.checkMergeGate", "name": "checkMergeGate", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.checkSplitGate", "name": "checkSplitGate", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.checkTopologyGate", "name": "checkTopologyGate", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.checkDeterminismGate", "name": "checkDeterminismGate", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizValidModeCollapse", "name": "quizValidModeCollapse", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizInvalidMode", "name": "quizInvalidMode", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizMergeWithinBounds", "name": "quizMergeWithinBounds", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizMergeExceedsResources", "name": "quizMergeExceedsResources", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizSplitPreservesPrecision", "name": "quizSplitPreservesPrecision", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizSplitLosesPrecision", "name": "quizSplitLosesPrecision", "module": "Semantics.MorphicDSP" }, { "kind": "def", "id": "Semantics.MorphicDSP.quizTopologyAdaptationValid", "name": "quizTopologyAdaptationValid", "module": "Semantics.MorphicDSP" }, { "kind": "module", "id": "Semantics.MorphicLocalField", "name": "MorphicLocalField", "path": "Semantics/MorphicLocalField.lean", "namespace": "MorphicLocalField", "doc": "MorphicLocalField.lean Independently derived local-force emergence model for morphic scalar niche dynamics. Conceptually compared against particle-fluid toy simulations. This model defines the dynamics of scalar entities migrating through a topology space driven by local fields representing unmet ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 4, "inductive_count": 0, "line_count": 285 }, { "kind": "def", "id": "Semantics.MorphicLocalField.needFieldGradient", "name": "needFieldGradient", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.riskFieldGradient", "name": "riskFieldGradient", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.curveField", "name": "curveField", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.noiseField", "name": "noiseField", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.computeForce", "name": "computeForce", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.projectToAdmissibleTopology", "name": "projectToAdmissibleTopology", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.successScore", "name": "successScore", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.failureScore", "name": "failureScore", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.unsafeScore", "name": "unsafeScore", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.normalizeAmplitude", "name": "normalizeAmplitude", "module": "Semantics.MorphicLocalField" }, { "kind": "def", "id": "Semantics.MorphicLocalField.updateAmplitude", "name": "updateAmplitude", "module": "Semantics.MorphicLocalField" }, { "kind": "module", "id": "Semantics.MorphicNeuralNetwork", "name": "MorphicNeuralNetwork", "path": "Semantics/MorphicNeuralNetwork.lean", "namespace": "Semantics", "doc": "inductive RoutingAction where | local : RoutingAction | atlas : RoutingAction | reject : RoutingAction deriving Repr, Inhabited, BEq, DecidableEq instance : ToString RoutingAction where toString | .local => \"local\" | .atlas => \"atlas\" | .reject => \"reject\" /-- Finite types for operation goals", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 5, "inductive_count": 3, "line_count": 251 }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.scalarToGoal", "name": "scalarToGoal", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.goalToCodon", "name": "goalToCodon", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.canSatisfyLocally", "name": "canSatisfyLocally", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.selectPath", "name": "selectPath", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.mnnRoute", "name": "mnnRoute", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.scalarInvariant", "name": "scalarInvariant", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.stateInvariant", "name": "stateInvariant", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.carrierInvariant", "name": "carrierInvariant", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.decisionInvariant", "name": "decisionInvariant", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.mnnRoutingCost", "name": "mnnRoutingCost", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "def", "id": "Semantics.MorphicNeuralNetwork.mnnRoutingBind", "name": "mnnRoutingBind", "module": "Semantics.MorphicNeuralNetwork" }, { "kind": "module", "id": "Semantics.MorphicScalar", "name": "MorphicScalar", "path": "Semantics/MorphicScalar.lean", "namespace": "Semantics.Morphic", "doc": "inductive ScalarState where | superposed : ScalarState | scouting : ScalarState | measureLocalNeed : ScalarState | collapsedProfile : ScalarState | execute : ScalarState | receipt : ScalarState | amplitudeUpdate : ScalarState | queryCollective : ScalarState | collectiveResponse : ScalarState | query", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 9, "struct_count": 5, "inductive_count": 1, "line_count": 198 }, { "kind": "theorem", "id": "Semantics.MorphicScalar.exampleOepiNonnegative", "name": "exampleOepiNonnegative", "module": "Semantics.MorphicScalar" }, { "kind": "theorem", "id": "Semantics.MorphicScalar.initializedSuperposedScalarHasNoNiche", "name": "initializedSuperposedScalarHasNoNiche", "module": "Semantics.MorphicScalar" }, { "kind": "theorem", "id": "Semantics.MorphicScalar.stateTransitionDeterministic", "name": "stateTransitionDeterministic", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.calculateOEPI", "name": "calculateOEPI", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.initMorphicScalar", "name": "initMorphicScalar", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.collapseProfile", "name": "collapseProfile", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.updateAmplitude", "name": "updateAmplitude", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.addLineageMemory", "name": "addLineageMemory", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.addQueryHistory", "name": "addQueryHistory", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.enterLowPowerPassiveMode", "name": "enterLowPowerPassiveMode", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.exitLowPowerPassiveMode", "name": "exitLowPowerPassiveMode", "module": "Semantics.MorphicScalar" }, { "kind": "def", "id": "Semantics.MorphicScalar.scalarCollapseBind", "name": "scalarCollapseBind", "module": "Semantics.MorphicScalar" }, { "kind": "module", "id": "Semantics.MultiBodyField", "name": "MultiBodyField", "path": "Semantics/MultiBodyField.lean", "namespace": "Semantics.MultiBodyField", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 4, "inductive_count": 2, "line_count": 143 }, { "kind": "def", "id": "Semantics.MultiBodyField.interactionEffectiveMass", "name": "interactionEffectiveMass", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.interactionEffectiveCharge", "name": "interactionEffectiveCharge", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.bodyDistance", "name": "bodyDistance", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.interactionMagnitude", "name": "interactionMagnitude", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.bodyInteraction", "name": "bodyInteraction", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.assemblyStability", "name": "assemblyStability", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.interactionCoupling", "name": "interactionCoupling", "module": "Semantics.MultiBodyField" }, { "kind": "def", "id": "Semantics.MultiBodyField.multiBodySignatureOf", "name": "multiBodySignatureOf", "module": "Semantics.MultiBodyField" }, { "kind": "module", "id": "Semantics.N3L_Energy", "name": "N3L_Energy", "path": "Semantics/N3L_Energy.lean", "namespace": "Semantics.N3L_Energy", "doc": "N3L_Energy.lean \u2014 No-Three-in-Line energy rigidity theorem Formalizes the energy-minimization approach to the No-Three-in-Line problem in \u211d\u00b2 with Gaussian ansatz. Main result: no_collinear_at_zero_energy E = 0 (energy of all lines) \u21d2 no three peaks collinear", "math_kind": "analysis", "sorry_count": 0, "theorem_count": 26, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 774 }, { "kind": "theorem", "id": "Semantics.N3L_Energy.integral_comp_add_right_\u211d", "name": "integral_comp_add_right_\u211d", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.integral_gaussian_1d", "name": "integral_gaussian_1d", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.integral_gaussian_1d_shifted", "name": "integral_gaussian_1d_shifted", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.exp_sum_of_sq", "name": "exp_sum_of_sq", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.gaussian_line_integral_at_distance", "name": "gaussian_line_integral_at_distance", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.peak_contribution_on_axis", "name": "peak_contribution_on_axis", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.on_line_contribution", "name": "on_line_contribution", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.penalty_nonneg", "name": "penalty_nonneg", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.penalty_zero_iff", "name": "penalty_zero_iff", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.energy_zero_iff", "name": "energy_zero_iff", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.energy_nonneg", "name": "energy_nonneg", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.energy_pos_of_exceeds", "name": "energy_pos_of_exceeds", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.\u03c3_crit_pos", "name": "\u03c3_crit_pos", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.three_over_sroot2pi_gt_two", "name": "three_over_sroot2pi_gt_two", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.sq_add_sq_ge_half_sq_sub_sq", "name": "sq_add_sq_ge_half_sq_sub_sq", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.peak_integrable_over_R", "name": "peak_integrable_over_R", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.ansatzLineDensity_decomp", "name": "ansatzLineDensity_decomp", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.peak_contribution_nonneg", "name": "peak_contribution_nonneg", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.signedArea_zero_implies_perpDist_zero", "name": "signedArea_zero_implies_perpDist_zero", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.integrand_simp", "name": "integrand_simp", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.integrand_simp2", "name": "integrand_simp2", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.collinear_line_density_exceeds_two", "name": "collinear_line_density_exceeds_two", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.gaussian_line_integral_unit_dir", "name": "gaussian_line_integral_unit_dir", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.on_line_contribution_general", "name": "on_line_contribution_general", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.collinear_line_density_exceeds_two_general", "name": "collinear_line_density_exceeds_two_general", "module": "Semantics.N3L_Energy" }, { "kind": "theorem", "id": "Semantics.N3L_Energy.no_collinear_at_zero_energy", "name": "no_collinear_at_zero_energy", "module": "Semantics.N3L_Energy" }, { "kind": "def", "id": "Semantics.N3L_Energy.signedArea", "name": "signedArea", "module": "Semantics.N3L_Energy" }, { "kind": "def", "id": "Semantics.N3L_Energy.perpDistance", "name": "perpDistance", "module": "Semantics.N3L_Energy" }, { "kind": "module", "id": "Semantics.NGemetry", "name": "NGemetry", "path": "Semantics/NGemetry.lean", "namespace": "Semantics.NGemetry", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NGemetry.lean \u2014 N-Dimensional Geometry Extension Extends SpatialEvo from 3D to n-dimensional geometry for VLSI design and general spatial reasoning applications. Key contributions: 1. Generic PointND ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 27, "struct_count": 7, "inductive_count": 0, "line_count": 333 }, { "kind": "theorem", "id": "Semantics.NGemetry.originDistanceZero", "name": "originDistanceZero", "module": "Semantics.NGemetry" }, { "kind": "theorem", "id": "Semantics.NGemetry.euclideanDistanceSymmetric", "name": "euclideanDistanceSymmetric", "module": "Semantics.NGemetry" }, { "kind": "theorem", "id": "Semantics.NGemetry.manhattanTriangleInequality", "name": "manhattanTriangleInequality", "module": "Semantics.NGemetry" }, { "kind": "theorem", "id": "Semantics.NGemetry.dotProductCommutative", "name": "dotProductCommutative", "module": "Semantics.NGemetry" }, { "kind": "theorem", "id": "Semantics.NGemetry.zeroVectorMagnitude", "name": "zeroVectorMagnitude", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.zero", "name": "zero", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.one", "name": "one", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.ofNat", "name": "ofNat", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.add", "name": "add", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.sub", "name": "sub", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.mul", "name": "mul", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.div", "name": "div", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.abs", "name": "abs", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.min", "name": "min", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.max", "name": "max", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.fromArray", "name": "fromArray", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.getCoord", "name": "getCoord", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.euclideanDistance", "name": "euclideanDistance", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.manhattanDistance", "name": "manhattanDistance", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.origin", "name": "origin", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.getComp", "name": "getComp", "module": "Semantics.NGemetry" }, { "kind": "def", "id": "Semantics.NGemetry.dot", "name": "dot", "module": "Semantics.NGemetry" }, { "kind": "module", "id": "Semantics.NIICore.CognitiveLoadIntegration", "name": "CognitiveLoadIntegration", "path": "Semantics/NIICore/CognitiveLoadIntegration.lean", "namespace": "Semantics.NIICore.CognitiveLoadIntegration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CognitiveLoadIntegration.lean \u2014 Cognitive Load Integration for Morphing This module integrates cognitive load calculations with the morphing mechanism to trigger state transitions based on workload req", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 18, "struct_count": 5, "inductive_count": 2, "line_count": 226 }, { "kind": "theorem", "id": "Semantics.NIICore.CognitiveLoadIntegration.cognitive_load_non_negative", "name": "cognitive_load_non_negative", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "theorem", "id": "Semantics.NIICore.CognitiveLoadIntegration.update_increases_timestamp", "name": "update_increases_timestamp", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "theorem", "id": "Semantics.NIICore.CognitiveLoadIntegration.morphing_decision_confidence_valid", "name": "morphing_decision_confidence_valid", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "theorem", "id": "Semantics.NIICore.CognitiveLoadIntegration.load_based_morphing_preserves_thresholds", "name": "load_based_morphing_preserves_thresholds", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.zero", "name": "zero", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.one", "name": "one", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.ofNat", "name": "ofNat", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.initial", "name": "initial", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.update", "name": "update", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.isOverloaded", "name": "isOverloaded", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.isIncreasing", "name": "isIncreasing", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.default", "name": "default", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.shouldMorph", "name": "shouldMorph", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.getTargetMode", "name": "getTargetMode", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.noMorph", "name": "noMorph", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.toPolysemantic", "name": "toPolysemantic", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.toAdaptive", "name": "toAdaptive", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.evaluate", "name": "evaluate", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.updateLoad", "name": "updateLoad", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.shouldTriggerMorphing", "name": "shouldTriggerMorphing", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "def", "id": "Semantics.NIICore.CognitiveLoadIntegration.testCognitiveLoadIntegration", "name": "testCognitiveLoadIntegration", "module": "Semantics.NIICore.CognitiveLoadIntegration" }, { "kind": "module", "id": "Semantics.NIICore.DifferentialAttentionMorphing", "name": "DifferentialAttentionMorphing", "path": "Semantics/NIICore/DifferentialAttentionMorphing.lean", "namespace": "Semantics.NIICore.DifferentialAttentionMorphing", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DifferentialAttentionMorphing.lean \u2014 Differential Attention for Morphing Requirements This module implements differential attention mechanisms for identifying morphing requirements by comparing current", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 15, "struct_count": 4, "inductive_count": 3, "line_count": 267 }, { "kind": "theorem", "id": "Semantics.NIICore.DifferentialAttentionMorphing.differentialAttentionMagnitudeNonNegative", "name": "differentialAttentionMagnitudeNonNegative", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "theorem", "id": "Semantics.NIICore.DifferentialAttentionMorphing.attentionBasedControllerPreservesCoreId", "name": "attentionBasedControllerPreservesCoreId", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "theorem", "id": "Semantics.NIICore.DifferentialAttentionMorphing.morphingRequirementThreshold", "name": "morphingRequirementThreshold", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.zero", "name": "zero", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.one", "name": "one", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.ofNat", "name": "ofNat", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.abs", "name": "abs", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.monosemantic", "name": "monosemantic", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.polysemantic", "name": "polysemantic", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.domainAttention", "name": "domainAttention", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.compute", "name": "compute", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.significantDomains", "name": "significantDomains", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.morphingRequirement", "name": "morphingRequirement", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.create", "name": "create", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.evaluateMorphingNeed", "name": "evaluateMorphingNeed", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.determineAction", "name": "determineAction", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.executeAction", "name": "executeAction", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "def", "id": "Semantics.NIICore.DifferentialAttentionMorphing.testDifferentialAttentionMorphing", "name": "testDifferentialAttentionMorphing", "module": "Semantics.NIICore.DifferentialAttentionMorphing" }, { "kind": "module", "id": "Semantics.NIICore.HierarchicalController", "name": "HierarchicalController", "path": "Semantics/NIICore/HierarchicalController.lean", "namespace": "Semantics.NIICore.HierarchicalController", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HierarchicalController.lean \u2014 Hierarchical Morphing with Multi-Level Controllers This module implements a hierarchical controller system for NII core morphing, inspired by NeuroVM's dynamic virtualizat", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 16, "struct_count": 4, "inductive_count": 3, "line_count": 285 }, { "kind": "theorem", "id": "Semantics.NIICore.HierarchicalController.localControllerPreservesCoreId", "name": "localControllerPreservesCoreId", "module": "Semantics.NIICore.HierarchicalController" }, { "kind": "theorem", "id": "Semantics.NIICore.HierarchicalController.globalControllerPreservesLocalControllerCount", "name": "globalControllerPreservesLocalControllerCount", "module": "Semantics.NIICore.HierarchicalController" }, { "kind": "theorem", "id": "Semantics.NIICore.HierarchicalController.controllerStateTimestampIncreases", "name": "controllerStateTimestampIncreases", "module": 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"Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "theorem", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.rewriteDeterminism", "name": "rewriteDeterminism", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "theorem", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.sheafPreservedUnderRewrite", "name": "sheafPreservedUnderRewrite", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "theorem", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.partWholePreservedUnderRewrite", "name": "partWholePreservedUnderRewrite", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "theorem", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.partWholeConsistentRewriting", "name": "partWholeConsistentRewriting", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "def", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.zero", "name": "zero", "module": 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"Semantics.NIICore.MereotopologicalSheafHypergraph.applyRewriteAndVerify", "name": "applyRewriteAndVerify", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "def", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.runHybridTest", "name": "runHybridTest", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "def", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.printHybridTestResults", "name": "printHybridTestResults", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "def", "id": "Semantics.NIICore.MereotopologicalSheafHypergraph.main", "name": "main", "module": "Semantics.NIICore.MereotopologicalSheafHypergraph" }, { "kind": "module", "id": "Semantics.NIICore.MetaLearning", "name": "MetaLearning", "path": "Semantics/NIICore/MetaLearning.lean", "namespace": "Semantics.NIICore.MetaLearning", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MetaLearning.lean \u2014 Meta-Learning for Adaptive Morphing Policies This module implements meta-learning for adaptive morphing policies, enabling cores to learn morphing policies that generalize across di", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 13, "struct_count": 6, "inductive_count": 3, "line_count": 281 }, { "kind": "theorem", "id": "Semantics.NIICore.MetaLearning.metaPolicyHistoryGrows", "name": "metaPolicyHistoryGrows", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "theorem", "id": "Semantics.NIICore.MetaLearning.metaPolicyPerformanceHistoryGrows", "name": "metaPolicyPerformanceHistoryGrows", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "theorem", "id": "Semantics.NIICore.MetaLearning.metaLearningControllerPreservesCoreId", "name": "metaLearningControllerPreservesCoreId", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.zero", "name": "zero", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.one", "name": "one", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.ofNat", "name": "ofNat", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.fromTasks", "name": "fromTasks", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.initial", "name": "initial", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.selectAction", "name": "selectAction", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.updatePolicy", "name": "updatePolicy", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.generalizeAcrossDistributions", "name": "generalizeAcrossDistributions", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.create", "name": "create", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.processTask", "name": "processTask", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.updateWithResult", "name": "updateWithResult", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.adaptToNewDistribution", "name": "adaptToNewDistribution", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "def", "id": "Semantics.NIICore.MetaLearning.testMetaLearning", "name": "testMetaLearning", "module": "Semantics.NIICore.MetaLearning" }, { "kind": "module", "id": "Semantics.NIICore.MorphicCoreId", "name": "MorphicCoreId", "path": "Semantics/NIICore/MorphicCoreId.lean", "namespace": "Semantics.NIICore.MorphicCoreId", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphicCoreId.lean \u2014 Morphic Core ID Inductive Type This module defines the MorphicCoreId inductive type for NII cores to become n-semantic morphic. This extends the existing monosemantic CoreId struct", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 17, "struct_count": 2, "inductive_count": 3, "line_count": 197 }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicCoreId.morphic_core_is_morphic_after_transition", "name": "morphic_core_is_morphic_after_transition", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicCoreId.transition_cost_non_negative", "name": "transition_cost_non_negative", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicCoreId.base_cores_not_morphic", "name": "base_cores_not_morphic", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.zero", "name": "zero", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.one", "name": "one", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.ofNat", "name": "ofNat", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.nii01", "name": "nii01", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.nii02", "name": "nii02", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.nii03", "name": "nii03", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.morphicNii01", "name": "morphicNii01", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.morphicNii02", "name": "morphicNii02", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.morphicNii03", "name": "morphicNii03", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.hybridCore", "name": "hybridCore", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.isMorphic", "name": "isMorphic", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.getMorphicMode", "name": "getMorphicMode", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.toMorphic", "name": "toMorphic", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.morphicModeTransition", "name": "morphicModeTransition", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.toHybrid", "name": "toHybrid", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.testBaseCores", "name": "testBaseCores", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "def", "id": "Semantics.NIICore.MorphicCoreId.testMorphicTransition", "name": "testMorphicTransition", "module": "Semantics.NIICore.MorphicCoreId" }, { "kind": "module", "id": "Semantics.NIICore.MorphicFieldCategory", "name": "MorphicFieldCategory", "path": "Semantics/NIICore/MorphicFieldCategory.lean", "namespace": "Semantics.NIICore.MorphicFieldCategory", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphicFieldCategory.lean \u2014 Category Theory Formalization of Morphic Field Theory This module formalizes the relationship between morphic fields and semantic state spaces using category theory. It prov", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 6, "struct_count": 5, "inductive_count": 2, "line_count": 293 }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicFieldCategory.morphicModeTensorAssociative", "name": "morphicModeTensorAssociative", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicFieldCategory.functorPreservesIdentity", "name": "functorPreservesIdentity", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicFieldCategory.functorPreservesComposition", "name": "functorPreservesComposition", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicFieldCategory.identityMorphismPreservesCoreId", "name": "identityMorphismPreservesCoreId", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "theorem", "id": "Semantics.NIICore.MorphicFieldCategory.compositionPreservesCoreId", "name": "compositionPreservesCoreId", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.zero", "name": "zero", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.one", "name": "one", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.ofNat", "name": "ofNat", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.morphicFieldToSemanticStateFunctor", "name": "morphicFieldToSemanticStateFunctor", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.morphicModeTensor", "name": "morphicModeTensor", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "def", "id": "Semantics.NIICore.MorphicFieldCategory.testCategoryTheoryFormalization", "name": "testCategoryTheoryFormalization", "module": "Semantics.NIICore.MorphicFieldCategory" }, { "kind": "module", "id": "Semantics.NIICore.MorphingTests", "name": "MorphingTests", "path": "Semantics/NIICore/MorphingTests.lean", "namespace": "Semantics.NIICore.MorphingTests", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team MorphingTests.lean \u2014 Test Suite for NII Core Morphing This module provides a comprehensive test suite for the morphing mechanism to validate morphing behavior and integration across all components. 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Authors: Research Stack Team PredictiveResourceAllocation.lean \u2014 Predictive Resource Allocation for Morphing This module implements predictive resource allocation using time-series forecasting to anticipate cognitive load changes ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 19, "struct_count": 7, "inductive_count": 2, "line_count": 298 }, { "kind": "theorem", "id": "Semantics.NIICore.PredictiveResourceAllocation.timeSeriesLengthIncreases", "name": "timeSeriesLengthIncreases", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "theorem", "id": "Semantics.NIICore.PredictiveResourceAllocation.predictiveControllerPreservesCoreId", "name": "predictiveControllerPreservesCoreId", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "theorem", "id": "Semantics.NIICore.PredictiveResourceAllocation.forecastModelWeightsPreserveCount", "name": "forecastModelWeightsPreserveCount", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.zero", "name": "zero", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.one", "name": "one", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.ofNat", "name": "ofNat", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.abs", "name": "abs", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.empty", "name": "empty", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.addPoint", "name": "addPoint", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.latest", "name": "latest", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.movingAverage", "name": "movingAverage", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.trend", "name": "trend", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.initial", "name": "initial", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.predict", "name": "predict", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.updateWeights", "name": "updateWeights", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.create", "name": "create", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.recordLoad", "name": "recordLoad", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.predictFutureLoad", "name": "predictFutureLoad", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.preemptiveMorphing", "name": "preemptiveMorphing", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.updateAllocation", "name": "updateAllocation", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.updateModel", "name": "updateModel", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "def", "id": "Semantics.NIICore.PredictiveResourceAllocation.testPredictiveAllocation", "name": "testPredictiveAllocation", "module": "Semantics.NIICore.PredictiveResourceAllocation" }, { "kind": "module", "id": "Semantics.NIICore.SemanticAnalysis", "name": "SemanticAnalysis", "path": "Semantics/NIICore/SemanticAnalysis.lean", "namespace": "Semantics.NIICore.SemanticAnalysis", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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Authors: Research Stack Team SemanticCapabilitySystem.lean \u2014 Semantic Capability System for NII Cores This module defines the Semantic Capability System for dynamic semantic assignment to NII cores. 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"Semantics.NIICore.SemanticRGFlow.computeBasinGeometry", "name": "computeBasinGeometry", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.performAttractorDescent", "name": "performAttractorDescent", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.verifySemanticSheafConsistency", "name": "verifySemanticSheafConsistency", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.defaultLatentVector", "name": "defaultLatentVector", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.defaultSemanticField", "name": "defaultSemanticField", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.applyDecimationAndShow", "name": "applyDecimationAndShow", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.performAttractorDescentAndShow", "name": "performAttractorDescentAndShow", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.runRGFlowTest", "name": "runRGFlowTest", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.printRGFlowTestResults", "name": "printRGFlowTestResults", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "def", "id": "Semantics.NIICore.SemanticRGFlow.main", "name": "main", "module": "Semantics.NIICore.SemanticRGFlow" }, { "kind": "module", "id": "Semantics.NIICore.SemanticStateMorphism", "name": "SemanticStateMorphism", "path": "Semantics/NIICore/SemanticStateMorphism.lean", "namespace": "Semantics.NIICore.SemanticStateMorphism", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SemanticStateMorphism.lean \u2014 Semantic State Morphism State Machine This module implements the SemanticStateMorphism state machine for core mode transitions. It defines state types, transition functions", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 14, "struct_count": 4, "inductive_count": 3, "line_count": 215 }, { "kind": "theorem", "id": "Semantics.NIICore.SemanticStateMorphism.transition_cost_non_negative", "name": "transition_cost_non_negative", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "theorem", "id": "Semantics.NIICore.SemanticStateMorphism.state_machine_preserves_core_id", "name": "state_machine_preserves_core_id", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "theorem", "id": "Semantics.NIICore.SemanticStateMorphism.idle_state_has_zero_cognitive_load", "name": "idle_state_has_zero_cognitive_load", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.zero", "name": "zero", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.one", "name": "one", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.ofNat", "name": "ofNat", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.initial", "name": "initial", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.transitionTo", "name": "transitionTo", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.setIdle", "name": "setIdle", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.setError", "name": "setError", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.calculate", "name": "calculate", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.isTransitionValid", "name": "isTransitionValid", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.transition", "name": "transition", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.canTransition", "name": "canTransition", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "def", "id": "Semantics.NIICore.SemanticStateMorphism.testStateMachine", "name": "testStateMachine", "module": "Semantics.NIICore.SemanticStateMorphism" }, { "kind": "module", "id": "Semantics.NIICore.SheafPersistentRGHybrid", "name": "SheafPersistentRGHybrid", "path": "Semantics/NIICore/SheafPersistentRGHybrid.lean", "namespace": "Semantics.NIICore", "doc": "structure Q16_16 where value : Int deriving Repr, BEq /-- Q16_16 arithmetic operations", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 15, "inductive_count": 3, "line_count": 222 }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.Q16_16", "name": "Q16_16", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.defaultSheafPersistentRGHybrid", "name": "defaultSheafPersistentRGHybrid", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.defaultMorphicStateHybrid", "name": "defaultMorphicStateHybrid", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.verifyMorphicTransitionHybrid", "name": "verifyMorphicTransitionHybrid", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.runHybridConsistencyTest", "name": "runHybridConsistencyTest", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.printHybridTestResults", "name": "printHybridTestResults", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "def", "id": "Semantics.NIICore.SheafPersistentRGHybrid.main", "name": "main", "module": "Semantics.NIICore.SheafPersistentRGHybrid" }, { "kind": "module", "id": "Semantics.NIICore.SurfaceDriver", "name": "SurfaceDriver", "path": "Semantics/NIICore/SurfaceDriver.lean", "namespace": "Semantics.NIICore.SurfaceDriver", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NIICore Surface Driver - Mathematically Defendable NII Core Driver Improvement Formalization of surface driver for NII cores based on first principles from Canonical Core v1 architecture: Layer 6: Ste", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 16, "struct_count": 8, "inductive_count": 1, "line_count": 340 }, { "kind": "theorem", "id": "Semantics.NIICore.SurfaceDriver.sssConstantBounded", "name": "sssConstantBounded", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "theorem", "id": "Semantics.NIICore.SurfaceDriver.effectiveVelocityBounded", "name": "effectiveVelocityBounded", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "theorem", "id": "Semantics.NIICore.SurfaceDriver.warpMetricNonNegative", "name": "warpMetricNonNegative", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "theorem", "id": "Semantics.NIICore.SurfaceDriver.slipThresholdMonotonic", "name": "slipThresholdMonotonic", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.computeSSS", "name": "computeSSS", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.isSlipThresholdCrossed", "name": "isSlipThresholdCrossed", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.computeWarp", "name": "computeWarp", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.computeEffectiveVelocity", "name": "computeEffectiveVelocity", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.computeWarpMetric", "name": "computeWarpMetric", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.computeFAMMLoad", "name": "computeFAMMLoad", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.makeScheduleDecision", "name": "makeScheduleDecision", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.adaptTopology", "name": "adaptTopology", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.initSurfaceDriver", "name": "initSurfaceDriver", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.executeWorkItem", "name": "executeWorkItem", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleSSSConstant", "name": "exampleSSSConstant", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleSlipCondition", "name": "exampleSlipCondition", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleWarpFunction", "name": "exampleWarpFunction", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleEffectiveVelocity", "name": "exampleEffectiveVelocity", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleWarpMetric", "name": "exampleWarpMetric", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "def", "id": "Semantics.NIICore.SurfaceDriver.exampleSurfaceDriver", "name": "exampleSurfaceDriver", "module": "Semantics.NIICore.SurfaceDriver" }, { "kind": "module", "id": "Semantics.NIICore.TranslationEngine", "name": "TranslationEngine", "path": "Semantics/NIICore/TranslationEngine.lean", "namespace": "Semantics.NIICore.TranslationEngine", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team TranslationEngineCore.lean - NII-02 Rust \u2192 Lean Translation Automated translation from Rust syntax to Lean 4: Enum \u2192 Inductive type Function \u2192 Lean function with pattern matching Type mappings (u8 \u2192 UI", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 9, "struct_count": 6, "inductive_count": 1, "line_count": 285 }, { "kind": "theorem", "id": "Semantics.NIICore.TranslationEngine.primitiveTypesMapped", "name": "primitiveTypesMapped", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "theorem", "id": "Semantics.NIICore.TranslationEngine.unknownTypesMarked", "name": "unknownTypesMarked", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "theorem", "id": "Semantics.NIICore.TranslationEngine.geometricScoreBounded", "name": "geometricScoreBounded", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.primitiveMappings", "name": "primitiveMappings", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.translateType", "name": "translateType", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.translateVariant", "name": "translateVariant", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.translateEnum", "name": "translateEnum", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.translateMatchArm", "name": "translateMatchArm", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.translateDecoder", "name": "translateDecoder", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.exampleInductiveConstructor", "name": "exampleInductiveConstructor", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.exampleInductiveType", "name": "exampleInductiveType", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "def", "id": "Semantics.NIICore.TranslationEngine.exampleLeanFunction", "name": "exampleLeanFunction", "module": "Semantics.NIICore.TranslationEngine" }, { "kind": "module", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential", "name": "UncertaintyMetaPredictiveDifferential", "path": "Semantics/NIICore/UncertaintyMetaPredictiveDifferential.lean", "namespace": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 2, "inductive_count": 0, "line_count": 74 }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.zero", "name": "zero", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.one", "name": "one", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.ofNat", "name": "ofNat", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.abs", "name": "abs", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.executeHybridActionLogic", "name": "executeHybridActionLogic", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential.runHybridTest", "name": "runHybridTest", "module": "Semantics.NIICore.UncertaintyMetaPredictiveDifferential" }, { "kind": "module", "id": "Semantics.NIICore.UncertaintyQuantification", "name": "UncertaintyQuantification", "path": "Semantics/NIICore/UncertaintyQuantification.lean", "namespace": "Semantics.NIICore.UncertaintyQuantification", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team UncertaintyQuantification.lean \u2014 Uncertainty Quantification for Morphing Decisions This module implements uncertainty quantification for morphing decisions, inspired by AMB-DSGDN's differential attenti", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 17, "struct_count": 4, "inductive_count": 3, "line_count": 306 }, { "kind": "theorem", "id": "Semantics.NIICore.UncertaintyQuantification.uncertaintyEstimateSamplesIncrease", "name": "uncertaintyEstimateSamplesIncrease", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "theorem", "id": "Semantics.NIICore.UncertaintyQuantification.uncertaintyEstimateConfidenceNonDecreasing", "name": "uncertaintyEstimateConfidenceNonDecreasing", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "theorem", "id": "Semantics.NIICore.UncertaintyQuantification.uncertaintyAwareControllerPreservesCoreId", "name": "uncertaintyAwareControllerPreservesCoreId", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "theorem", "id": "Semantics.NIICore.UncertaintyQuantification.differentialAttentionDiffIsDifference", "name": "differentialAttentionDiffIsDifference", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.zero", "name": "zero", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.one", "name": "one", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.ofNat", "name": "ofNat", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.initial", "name": "initial", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.updateSample", "name": "updateSample", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.standardDeviation", "name": "standardDeviation", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.isReliable", "name": "isReliable", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.getUncertainty", "name": "getUncertainty", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.isReliableDecision", "name": "isReliableDecision", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.create", "name": "create", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.evaluateMorphing", "name": "evaluateMorphing", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.updateUncertainty", "name": "updateUncertainty", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.executeDecision", "name": "executeDecision", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.compute", "name": "compute", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.isSignificantChange", "name": "isSignificantChange", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.uncertaintyAdjustedDiff", "name": "uncertaintyAdjustedDiff", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "def", "id": "Semantics.NIICore.UncertaintyQuantification.testUncertaintyQuantification", "name": "testUncertaintyQuantification", "module": "Semantics.NIICore.UncertaintyQuantification" }, { "kind": "module", "id": "Semantics.NIICore.Verification", "name": "Verification", "path": "Semantics/NIICore/Verification.lean", "namespace": "Semantics.NIICore.Verification", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team VerificationCore.lean - NII-03 Proof Generation Automated proof generation and verification: Total function proofs Type safety verification Invariant preservation FFI boundary soundness Integrated wit", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 4, "inductive_count": 1, "line_count": 267 }, { "kind": "theorem", "id": "Semantics.NIICore.Verification.provedNotExceedTotal", "name": "provedNotExceedTotal", "module": "Semantics.NIICore.Verification" }, { "kind": "theorem", "id": "Semantics.NIICore.Verification.fullCoverageAllProved", "name": "fullCoverageAllProved", "module": "Semantics.NIICore.Verification" }, { "kind": "theorem", "id": "Semantics.NIICore.Verification.emptyReportFullCoverage", "name": "emptyReportFullCoverage", "module": "Semantics.NIICore.Verification" }, { "kind": "theorem", "id": "Semantics.NIICore.Verification.geometricScoreBounded", "name": "geometricScoreBounded", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.generateTotalObligation", "name": "generateTotalObligation", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.generateInverseObligation", "name": "generateInverseObligation", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.countProved", "name": "countProved", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.verificationCoverage", "name": "verificationCoverage", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.verifyTranslationUnit", "name": "verifyTranslationUnit", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.exampleObligation", "name": "exampleObligation", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.exampleFunctionVerification", "name": "exampleFunctionVerification", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.exampleFFIVerification", "name": "exampleFFIVerification", "module": "Semantics.NIICore.Verification" }, { "kind": "def", "id": "Semantics.NIICore.Verification.exampleVerificationReport", "name": "exampleVerificationReport", "module": "Semantics.NIICore.Verification" }, { "kind": "module", "id": "Semantics.NIICore", "name": "NIICore", "path": "Semantics/NIICore.lean", "namespace": "Semantics.NIICore", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NIICore.lean - Non-Isotropic Informatic Core Foundation Foundation module defining the NII core abstractions for the Lean Domain Expert Swarm. 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Authors: Research Stack Team NNonEuclideanGeometry.lean \u2014 N-Dimensional Non-Euclidean Geometry Extension Extends NonEuclideanGeometry from 3D to n-dimensional geometry for parallel transport writhe and path validation in higher di", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 16, "struct_count": 1, "inductive_count": 1, "line_count": 223 }, { "kind": "theorem", "id": "Semantics.NNonEuclideanGeometry.phiWeightsBounded", "name": "phiWeightsBounded", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "theorem", "id": "Semantics.NNonEuclideanGeometry.phiWeightedDistanceSymmetric", "name": "phiWeightedDistanceSymmetric", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "theorem", "id": "Semantics.NNonEuclideanGeometry.straightLineWritheZero", "name": "straightLineWritheZero", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.phi", "name": "phi", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.cosQtrPi", "name": "cosQtrPi", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.half", "name": "half", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.dOblique", "name": "dOblique", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.fromArray", "name": "fromArray", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.getCoord", "name": "getCoord", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.euclideanDistance", "name": "euclideanDistance", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.obliqueProjectND", "name": "obliqueProjectND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.parallelTransportWritheND", "name": "parallelTransportWritheND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.phiWeightsND", "name": "phiWeightsND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.phiWeightedDistSqND", "name": "phiWeightedDistSqND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.maxJumpThreshold", "name": "maxJumpThreshold", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.maxWrithe", "name": "maxWrithe", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.validatePathND", "name": "validatePathND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.phiWeightedDistSymmetric", "name": "phiWeightedDistSymmetric", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NNonEuclideanGeometry.straightLineWritheZeroND", "name": "straightLineWritheZeroND", "module": "Semantics.NNonEuclideanGeometry" }, { "kind": "module", "id": "Semantics.NS_MD", "name": "NS_MD", "path": "Semantics/NS_MD.lean", "namespace": "Semantics.NS_MD", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. 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Authors: Research Stack Team NeighborCoupling.lean \u2014 Neighbor Coupling for Resonant Field Propagation Defines neighbor coupling mechanisms for Resonant Field Propagation (RFP). Fields couple to neighbors via Laplacian operator for", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 12, "struct_count": 3, "inductive_count": 0, "line_count": 201 }, { "kind": "theorem", "id": "Semantics.NeighborCoupling.computeCouplingWeightZeroBeyondRadius", "name": "computeCouplingWeightZeroBeyondRadius", "module": "Semantics.NeighborCoupling" }, { "kind": "theorem", "id": "Semantics.NeighborCoupling.computeDistanceSymmetric", "name": "computeDistanceSymmetric", "module": "Semantics.NeighborCoupling" }, { "kind": "theorem", "id": "Semantics.NeighborCoupling.computeLaplacianWithCouplingZeroWhenNoNeighbors", "name": "computeLaplacianWithCouplingZeroWhenNoNeighbors", "module": "Semantics.NeighborCoupling" }, { "kind": "theorem", "id": "Semantics.NeighborCoupling.initializeCouplingParametersHasPositiveStrength", "name": "initializeCouplingParametersHasPositiveStrength", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.zero", "name": "zero", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.one", "name": "one", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.ofFrac", "name": "ofFrac", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.add", "name": "add", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.sub", "name": "sub", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.mul", "name": "mul", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.getNeighborPositions", "name": "getNeighborPositions", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.computeCouplingWeight", "name": "computeCouplingWeight", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.computeDistance", "name": "computeDistance", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.computeWeightedNeighborSum", "name": "computeWeightedNeighborSum", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.computeLaplacianWithCoupling", "name": "computeLaplacianWithCoupling", "module": "Semantics.NeighborCoupling" }, { "kind": "def", "id": "Semantics.NeighborCoupling.initializeCouplingParameters", "name": "initializeCouplingParameters", "module": "Semantics.NeighborCoupling" }, { "kind": "module", "id": "Semantics.NetworkCapacity", "name": "NetworkCapacity", "path": "Semantics/NetworkCapacity.lean", "namespace": "Semantics.NetworkCapacity", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NetworkCapacity.lean \u2014 Network Resource Capacity Monitor Replaces scripts/swarm_network_capacity.py with a formal Lean module that defines network capacity structures and calculations. Per AGENTS.md: ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 6, "inductive_count": 1, "line_count": 218 }, { "kind": "def", "id": "Semantics.NetworkCapacity.zero", "name": "zero", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.one", "name": "one", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.ofNat", "name": "ofNat", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.toNat", "name": "toNat", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.ofFrac", "name": "ofFrac", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.isOnline", "name": "isOnline", "module": "Semantics.NetworkCapacity" }, { "kind": "def", "id": "Semantics.NetworkCapacity.estimateNodeResources", "name": "estimateNodeResources", "module": 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"\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 11, "def_count": 21, "struct_count": 4, "inductive_count": 0, "line_count": 411 }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.solitonConvergence", "name": "solitonConvergence", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.boundedPropagationTime", "name": "boundedPropagationTime", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.asyncSelfSolvingPreservation", "name": "asyncSelfSolvingPreservation", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.eventualConsistency", "name": "eventualConsistency", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.globalConsistency", "name": "globalConsistency", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.communicationCostMonotonicity", "name": "communicationCostMonotonicity", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.networkedDescentConvergence", "name": "networkedDescentConvergence", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "theorem", "id": "Semantics.NetworkedSelfSolvingSpace.mengerSpongeErasureBasin", "name": "mengerSpongeErasureBasin", "module": 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"Semantics.NetworkedSelfSolvingSpace.stochasticDelay", "name": "stochasticDelay", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.solitonPhase", "name": "solitonPhase", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.generateSolitonMessages", "name": "generateSolitonMessages", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.solitonArrives", "name": "solitonArrives", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.propagateSolitons", "name": "propagateSolitons", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.applyStateUpdates", "name": "applyStateUpdates", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.gossip", "name": "gossip", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.masterEquation", "name": "masterEquation", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.getTorusDistance", "name": "getTorusDistance", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.isNetworkedActionLawful", "name": "isNetworkedActionLawful", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.networkedBind", "name": "networkedBind", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "def", "id": "Semantics.NetworkedSelfSolvingSpace.whichPathInformationErased", "name": "whichPathInformationErased", "module": "Semantics.NetworkedSelfSolvingSpace" }, { "kind": "module", "id": "Semantics.NeurodivergentPatternLUT", "name": "NeurodivergentPatternLUT", "path": 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"NextGenAgentDesign", "path": "Semantics/NextGenAgentDesign.lean", "namespace": "Semantics.NextGenAgentDesign", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NextGenAgentDesign.lean \u2014 Swarm-Designed Next-Generation Agent Architecture Replaces scripts/swarm_design_nextgen_agents.py with a formal Lean module that analyzes current agent performance and designs", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 8, "inductive_count": 4, "line_count": 294 }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.zero", "name": "zero", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.one", "name": "one", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.ofNat", "name": "ofNat", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.toNat", "name": "toNat", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.ofFrac", "name": "ofFrac", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.currentBaseline", "name": "currentBaseline", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.identifyBottlenecks", "name": "identifyBottlenecks", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.designNextGenFeatures", "name": "designNextGenFeatures", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.calculateCumulativeImprovement", "name": "calculateCumulativeImprovement", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.calculateProjectedEfficiency", "name": "calculateProjectedEfficiency", "module": "Semantics.NextGenAgentDesign" }, { "kind": "def", "id": "Semantics.NextGenAgentDesign.runDesignProcess", "name": "runDesignProcess", "module": "Semantics.NextGenAgentDesign" }, { "kind": "module", "id": "Semantics.NonEuclideanGeometry", "name": "NonEuclideanGeometry", "path": "Semantics/NonEuclideanGeometry.lean", "namespace": "Semantics.NonEuclideanGeometry", "doc": "NonEuclideanGeometry.lean - Parallel Transport Writhe and Path Validation Ports rows 135-136 from MATH_MODEL_MAP.tsv (Python \u2192 Lean). Concept vectors are 14D arrays of Q16.16. PHI = golden ratio \u2248 1.6180 = 106039 in Q16.16. Window W = 16 points for writhe integral.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 14, "struct_count": 1, "inductive_count": 1, "line_count": 118 }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.phi", "name": "phi", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.cosQtrPi", "name": "cosQtrPi", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.half", "name": "half", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.dOblique", "name": "dOblique", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.obliqueProject", "name": "obliqueProject", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.parallelTransportWrithe", "name": "parallelTransportWrithe", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.phiWeights", "name": "phiWeights", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.phiWeightedDistSq", "name": "phiWeightedDistSq", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.maxJumpThreshold", "name": "maxJumpThreshold", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.maxWrithe", "name": "maxWrithe", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.validatePath", "name": "validatePath", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.pathInvariant", "name": "pathInvariant", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.pathCost", "name": "pathCost", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "def", "id": "Semantics.NonEuclideanGeometry.nEGeomBind", "name": "nEGeomBind", "module": "Semantics.NonEuclideanGeometry" }, { "kind": "module", "id": "Semantics.NonStandardInterfaces", "name": "NonStandardInterfaces", "path": "Semantics/NonStandardInterfaces.lean", "namespace": "Semantics.NonStandardInterfaces", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 7, "inductive_count": 5, "line_count": 89 }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.zero", "name": "zero", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.one", "name": "one", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.ofNat", "name": "ofNat", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.toNat", "name": "toNat", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.ofFrac", "name": "ofFrac", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.abs", "name": "abs", "module": "Semantics.NonStandardInterfaces" }, { "kind": "def", "id": "Semantics.NonStandardInterfaces.getCoverage", "name": "getCoverage", "module": "Semantics.NonStandardInterfaces" }, { "kind": "module", "id": "Semantics.OEPI", "name": "OEPI", "path": "Semantics/OEPI.lean", "namespace": "Semantics.OEPI", "doc": "structure OEPIComponents where uncertainty : Q16_16 impact : Q16_16 timeSensitivity : Q16_16 irreversibility : Q16_16 liveVoltageRisk : Q16_16 deriving Repr, BEq /-- OEPI threshold levels", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 4, "struct_count": 1, "inductive_count": 1, "line_count": 126 }, { "kind": "theorem", "id": "Semantics.OEPI.exampleOepiNonnegative", "name": "exampleOepiNonnegative", "module": "Semantics.OEPI" }, { "kind": "theorem", "id": "Semantics.OEPI.lowThresholdWitness", "name": "lowThresholdWitness", "module": "Semantics.OEPI" }, { "kind": "theorem", "id": "Semantics.OEPI.criticalThresholdWitness", "name": "criticalThresholdWitness", "module": "Semantics.OEPI" }, { "kind": "theorem", "id": "Semantics.OEPI.criticalAlwaysAlerts", "name": "criticalAlwaysAlerts", "module": "Semantics.OEPI" }, { "kind": "def", "id": "Semantics.OEPI.determineThreshold", "name": "determineThreshold", "module": "Semantics.OEPI" }, { "kind": "def", "id": "Semantics.OEPI.calculateOEPI", "name": "calculateOEPI", "module": "Semantics.OEPI" }, { "kind": "def", "id": "Semantics.OEPI.oepiCalculationBind", "name": "oepiCalculationBind", "module": "Semantics.OEPI" }, { "kind": "def", "id": "Semantics.OEPI.shouldAlertOperator", "name": "shouldAlertOperator", "module": "Semantics.OEPI" }, { "kind": "module", "id": "Semantics.OTOMOntology", "name": "OTOMOntology", "path": "Semantics/OTOMOntology.lean", "namespace": "Semantics.OTOM", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team OTOMOntology.lean \u2014 Formal Organization of All Work Under OTOM Label This module establishes OTOM (Ordered Transformation & Orchestration Model) as the unifying label for all Research Stack work. It fo", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 16, "struct_count": 2, "inductive_count": 2, "line_count": 341 }, { "kind": "theorem", "id": "Semantics.OTOMOntology.totalModuleCount", "name": "totalModuleCount", "module": "Semantics.OTOMOntology" }, { "kind": "theorem", "id": "Semantics.OTOMOntology.allModulesUnderOTOM", "name": "allModulesUnderOTOM", "module": "Semantics.OTOMOntology" }, { "kind": "theorem", "id": "Semantics.OTOMOntology.coreLayerSize", "name": "coreLayerSize", "module": "Semantics.OTOMOntology" }, { "kind": "theorem", "id": "Semantics.OTOMOntology.allModulesImportCore", "name": "allModulesImportCore", "module": "Semantics.OTOMOntology" }, { "kind": "theorem", "id": "Semantics.OTOMOntology.otomVersionIsCambrianBind", "name": "otomVersionIsCambrianBind", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomLabel", "name": "otomLabel", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomVersion", "name": "otomVersion", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomTagline", "name": "otomTagline", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomRepository", "name": "otomRepository", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomOrigin", "name": "otomOrigin", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.displayName", "name": "displayName", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.moduleCount", "name": "moduleCount", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.allDomains", "name": "allDomains", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomModuleRegistry", "name": "otomModuleRegistry", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.description", "name": "description", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.repository", "name": "repository", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.principleCoreDependency", "name": "principleCoreDependency", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.principleVerification", "name": "principleVerification", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.principleUnifiedLabel", "name": "principleUnifiedLabel", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.verifyOTOMPrinciples", "name": "verifyOTOMPrinciples", "module": "Semantics.OTOMOntology" }, { "kind": "def", "id": "Semantics.OTOMOntology.otomGitHub", "name": "otomGitHub", "module": "Semantics.OTOMOntology" }, { "kind": "module", "id": "Semantics.Omindirection", "name": "Omindirection", "path": "Semantics/Omindirection.lean", "namespace": "Semantics.Omindirection", "doc": "# Omindirection Logogram Contract This module turns the repo-local omindirection design into executable Lean rules. It formalizes the implicit contract currently spread across: * `6-Documentation/reports/typst/omindirection.typ` * `6-Documentation/tiddlywiki-local/wiki/tiddlers/Typst Omindirection", "math_kind": "avm", "sorry_count": 0, "theorem_count": 12, "def_count": 21, "struct_count": 3, "inductive_count": 5, "line_count": 325 }, { "kind": "theorem", "id": "Semantics.Omindirection.chirality_prefixes_match_typst_surface", "name": "chirality_prefixes_match_typst_surface", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.row_witness_atom_admissible", "name": "row_witness_atom_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.auto_direction_atom_not_admissible", "name": "auto_direction_atom_not_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.unreceipted_atom_not_admissible", "name": "unreceipted_atom_not_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.mirror_right_atom_admissible", "name": "mirror_right_atom_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.bad_mirror_atom_not_admissible", "name": "bad_mirror_atom_not_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.board_tile_atom_admissible", "name": "board_tile_atom_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.captured_board_atom_admissible", "name": "captured_board_atom_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.dead_board_atom_not_admissible", "name": "dead_board_atom_not_admissible", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.quarantine_atom_routes_to_quarantine_not_accept", "name": "quarantine_atom_routes_to_quarantine_not_accept", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.admissible_atom_has_explicit_direction", "name": "admissible_atom_has_explicit_direction", "module": "Semantics.Omindirection" }, { "kind": "theorem", "id": "Semantics.Omindirection.admissible_atom_has_receipt", "name": "admissible_atom_has_receipt", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.chiralityPrefix", "name": "chiralityPrefix", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.validPhase", "name": "validPhase", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.chiralityCompatibleWithPhase", "name": "chiralityCompatibleWithPhase", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.explicitDirection", "name": "explicitDirection", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.receiptComplete", "name": "receiptComplete", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.boardPlacementAdmissible", "name": "boardPlacementAdmissible", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.mirrorPlacementAdmissible", "name": "mirrorPlacementAdmissible", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.quarantinePlacementAdmissible", "name": "quarantinePlacementAdmissible", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.atomAdmissible", "name": "atomAdmissible", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.atomHeld", "name": "atomHeld", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.atomQuarantined", "name": "atomQuarantined", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.exampleReceipt", "name": "exampleReceipt", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.rowWitnessAtom", "name": "rowWitnessAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.autoDirectionAtom", "name": "autoDirectionAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.unreceiptedAtom", "name": "unreceiptedAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.mirrorRightAtom", "name": "mirrorRightAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.badMirrorAtom", "name": "badMirrorAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.boardTileAtom", "name": "boardTileAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.capturedBoardAtom", "name": "capturedBoardAtom", "module": "Semantics.Omindirection" }, { "kind": "def", "id": "Semantics.Omindirection.deadBoardAtom", "name": "deadBoardAtom", "module": "Semantics.Omindirection" }, { "kind": "module", "id": "Semantics.OmniNetwork", "name": "OmniNetwork", "path": "Semantics/OmniNetwork.lean", "namespace": "Semantics.OmniNetwork", "doc": "Transport: Defines the allowed communication channels.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 1, "line_count": 63 }, { "kind": "def", "id": "Semantics.OmniNetwork.isLawfulPeer", "name": "isLawfulPeer", "module": "Semantics.OmniNetwork" }, { "kind": "def", "id": "Semantics.OmniNetwork.networkTension", "name": "networkTension", "module": "Semantics.OmniNetwork" }, { "kind": "def", "id": "Semantics.OmniNetwork.omniBind", "name": "omniBind", "module": "Semantics.OmniNetwork" }, { "kind": "def", "id": "Semantics.OmniNetwork.canAutobalance", "name": "canAutobalance", "module": "Semantics.OmniNetwork" 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Authors: Research Stack Team OmnidirectionalInterface.lean \u2014 Unified Query Router in Lean Central coordinator that routes queries to appropriate swarm subsystems. 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The cost comparison is over `Nat` (Q16.16-scaled fixed-point arithmetic), so `native_decide` closes the inequality gate. 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Python is used strictly as a shim for ENE API / Database persistence.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 2, "inductive_count": 0, "line_count": 64 }, { "kind": "def", "id": "Semantics.Orchestrate.SigmaDeploy.currentSession", "name": "currentSession", "module": "Semantics.Orchestrate.SigmaDeploy" }, { "kind": "def", "id": "Semantics.Orchestrate.SigmaDeploy.initiateDeployment", "name": "initiateDeployment", "module": "Semantics.Orchestrate.SigmaDeploy" }, { "kind": "module", "id": "Semantics.Orchestrate", "name": "Orchestrate", "path": "Semantics/Orchestrate.lean", "namespace": "Semantics", "doc": "Ported from `infra/access_control/pipeline/unified_pipeline.py`. Orchestrates the multi-layer control system: Raw Input \u2192 Geometry Features \u2192 Canonical State \u2192 Temporal Buffer \u2192 PBACS \u2192 Action I/O and statistics shells (JSON export, file writing) are deleted per the formalization boundary: only the ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 3, "inductive_count": 0, "line_count": 195 }, { "kind": "def", "id": "Semantics.Orchestrate.empty", "name": "empty", "module": "Semantics.Orchestrate" }, { "kind": "def", "id": "Semantics.Orchestrate.computeAngularMomentum", "name": "computeAngularMomentum", "module": "Semantics.Orchestrate" }, { "kind": "def", "id": "Semantics.Orchestrate.update", "name": "update", "module": "Semantics.Orchestrate" }, { "kind": "def", "id": "Semantics.Orchestrate.rawToManifold", "name": "rawToManifold", "module": "Semantics.Orchestrate" }, { "kind": "def", "id": "Semantics.Orchestrate.step", "name": "step", "module": "Semantics.Orchestrate" }, { "kind": "module", "id": "Semantics.OrderedFieldTokens", "name": "OrderedFieldTokens", "path": "Semantics/OrderedFieldTokens.lean", "namespace": "Semantics.OrderedFieldTokens", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team OrderedFieldTokens.lean \u2014 Test-Time Search with Ordered Field Tokens This module formalizes the AMMR-backed projection solver architecture with ordered field tokenization for verifiable, composable, se", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 33, "struct_count": 11, "inductive_count": 3, "line_count": 417 }, { "kind": "theorem", "id": "Semantics.OrderedFieldTokens.ammrLeafIntegrity", "name": "ammrLeafIntegrity", "module": "Semantics.OrderedFieldTokens" }, { "kind": "theorem", "id": "Semantics.OrderedFieldTokens.stepCountAdvances", "name": "stepCountAdvances", "module": "Semantics.OrderedFieldTokens" }, { "kind": "theorem", "id": "Semantics.OrderedFieldTokens.beamSearchInvariant", "name": "beamSearchInvariant", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.zero", "name": "zero", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.one", "name": "one", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.epsilon", "name": "epsilon", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.ofNat", "name": "ofNat", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.add", "name": "add", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.sub", "name": "sub", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.mul", "name": "mul", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.div", "name": "div", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.le", "name": "le", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.weightedSum", "name": "weightedSum", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.toString", "name": "toString", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.category", "name": "category", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.toNat", "name": "toNat", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.toList", "name": "toList", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.wellFormed", "name": "wellFormed", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.default", "name": "default", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.normalized", "name": "normalized", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.projectionScore", "name": "projectionScore", "module": "Semantics.OrderedFieldTokens" }, { "kind": "def", "id": "Semantics.OrderedFieldTokens.routingScore", "name": "routingScore", "module": "Semantics.OrderedFieldTokens" }, { "kind": "module", "id": "Semantics.OrthogonalAmmr", "name": "OrthogonalAmmr", "path": "Semantics/OrthogonalAmmr.lean", "namespace": "Semantics.OrthogonalAmmr", "doc": "Finite shape witness for quantized basis data.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 14, "struct_count": 5, "inductive_count": 0, "line_count": 200 }, { "kind": "theorem", "id": "Semantics.OrthogonalAmmr.coeffEnergyConsistent", "name": "coeffEnergyConsistent", "module": "Semantics.OrthogonalAmmr" }, { "kind": "theorem", "id": "Semantics.OrthogonalAmmr.mirrorLutIndexDeterministic", "name": "mirrorLutIndexDeterministic", "module": "Semantics.OrthogonalAmmr" }, { "kind": "theorem", "id": "Semantics.OrthogonalAmmr.commitParentLaw", "name": "commitParentLaw", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.residualEnergy", "name": "residualEnergy", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.projectionSimilarity", "name": "projectionSimilarity", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.coeffEnergy", "name": "coeffEnergy", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.dimensionConsistent", "name": "dimensionConsistent", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.energyConsistent", "name": "energyConsistent", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.basisVectorHash", "name": "basisVectorHash", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.summaryHash", "name": "summaryHash", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.commitHash", "name": "commitHash", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.mergeSummary", "name": "mergeSummary", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.commitParent", "name": "commitParent", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.mirrorLutIndex", "name": "mirrorLutIndex", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.unitVec", "name": "unitVec", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.leafSummary", "name": "leafSummary", "module": "Semantics.OrthogonalAmmr" }, { "kind": "def", "id": "Semantics.OrthogonalAmmr.leafNode", "name": "leafNode", "module": "Semantics.OrthogonalAmmr" }, { "kind": "module", "id": "Semantics.PBACSSignal", "name": "PBACSSignal", "path": "Semantics/PBACSSignal.lean", "namespace": "Semantics.PBACSSignal", "doc": "Neutralized Specification. Anchored to: linear/RES-2311", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 1, "inductive_count": 0, "line_count": 83 }, { "kind": "def", "id": "Semantics.PBACSSignal.default", "name": "default", "module": "Semantics.PBACSSignal" }, { "kind": "def", "id": "Semantics.PBACSSignal.nextPhi", "name": "nextPhi", "module": "Semantics.PBACSSignal" }, { "kind": "def", "id": "Semantics.PBACSSignal.getThreshold", "name": "getThreshold", "module": "Semantics.PBACSSignal" }, { "kind": "def", "id": "Semantics.PBACSSignal.update", "name": "update", "module": "Semantics.PBACSSignal" }, { "kind": "module", "id": "Semantics.PBACSVerilogEquivalence", "name": "PBACSVerilogEquivalence", "path": "Semantics/PBACSVerilogEquivalence.lean", "namespace": "Semantics.PBACSSignal", "doc": "Formal equivalence proof between Lean 4 specification and Verilog HDL. Anchored to: scripts/pbacs_rev3_hdl.v", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 50 }, { "kind": "theorem", "id": "Semantics.PBACSVerilogEquivalence.hardwareEquivalence", "name": "hardwareEquivalence", "module": "Semantics.PBACSVerilogEquivalence" }, { "kind": "def", "id": "Semantics.PBACSVerilogEquivalence.verilogStep", "name": "verilogStep", "module": "Semantics.PBACSVerilogEquivalence" }, { "kind": "module", "id": "Semantics.PIST.Classify", "name": "Classify", "path": "Semantics/PIST/Classify.lean", "namespace": "Semantics.PIST.Classify", "doc": "Semantics.PIST.Classify \u2014 RRC shape classifier over braid adjacency matrices", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 12, "def_count": 32, "struct_count": 3, "inductive_count": 1, "line_count": 842 }, { "kind": "theorem", "id": "Semantics.PIST.Classify.q16_add_comm", "name": "q16_add_comm", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.blendBand_comm", "name": "blendBand_comm", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.kubelkaMunk_comm", "name": "kubelkaMunk_comm", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.photonic_roundtrip", "name": "photonic_roundtrip", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.array_eq_of_toList_eq", "name": "array_eq_of_toList_eq", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.array_foldl_append_eq_flatMap", "name": "array_foldl_append_eq_flatMap", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.list_channel_isolation", "name": "list_channel_isolation", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.photonic_channel_isolation", "name": "photonic_channel_isolation", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.totalKS_512MACs_value", "name": "totalKS_512MACs_value", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.guarantees", "name": "guarantees", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.km_residual_bounds_energy_loss", "name": "km_residual_bounds_energy_loss", "module": "Semantics.PIST.Classify" }, { "kind": "theorem", "id": "Semantics.PIST.Classify.kmResidual_value", "name": "kmResidual_value", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.oberthHighThreshold", "name": "oberthHighThreshold", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.signalThreshold", "name": "signalThreshold", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.spectralRadiusToColor", "name": "spectralRadiusToColor", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.colorToShapeName", "name": "colorToShapeName", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blend_additive", "name": "blend_additive", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blend_rms", "name": "blend_rms", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blend_vortex", "name": "blend_vortex", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blendRadii", "name": "blendRadii", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.hashMatrix", "name": "hashMatrix", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.classifyProxy", "name": "classifyProxy", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.classifyExact", "name": "classifyExact", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.spectralProfileToDistribution", "name": "spectralProfileToDistribution", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.kubelkaMunkRatio", "name": "kubelkaMunkRatio", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blendBand", "name": "blendBand", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.defaultBand", "name": "defaultBand", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.kubelkaMunkBlend", "name": "kubelkaMunkBlend", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.photonicDemux", "name": "photonicDemux", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.photonicMux", "name": "photonicMux", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blendSpectra_additive", "name": "blendSpectra_additive", "module": "Semantics.PIST.Classify" }, { "kind": "def", "id": "Semantics.PIST.Classify.blendSpectra_rms", "name": "blendSpectra_rms", "module": "Semantics.PIST.Classify" }, { "kind": "module", "id": "Semantics.PIST.Matrices250", "name": "Matrices250", "path": "Semantics/PIST/Matrices250.lean", "namespace": "Semantics.PIST.Matrices250", "doc": "Semantics.PIST.Matrices250 \u2014 AUTO-GENERATED by build_pist_matrices_250.py", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 2525 }, { "kind": "def", "id": "Semantics.PIST.Matrices250.pistMatrices250", "name": "pistMatrices250", "module": "Semantics.PIST.Matrices250" }, { "kind": "def", "id": "Semantics.PIST.Matrices250.findMatrix", "name": "findMatrix", "module": "Semantics.PIST.Matrices250" }, { "kind": "module", "id": "Semantics.PIST.Motif", "name": "Motif", "path": "Semantics/PIST/Motif.lean", "namespace": "Semantics.PIST.Motif", "doc": "Semantics.PIST.Motif \u2014 Q16_16 motif scoring for proof-trace classification", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 6, "def_count": 6, "struct_count": 2, "inductive_count": 0, "line_count": 206 }, { "kind": "theorem", "id": "Semantics.PIST.Motif.motifScore_bonus_pos", "name": "motifScore_bonus_pos", "module": "Semantics.PIST.Motif" }, { "kind": "theorem", "id": "Semantics.PIST.Motif.motifScore_match_ge_base", "name": "motifScore_match_ge_base", "module": "Semantics.PIST.Motif" }, { "kind": "theorem", "id": "Semantics.PIST.Motif.motifScore_zero_freq_base", "name": "motifScore_zero_freq_base", "module": "Semantics.PIST.Motif" }, { "kind": "theorem", "id": "Semantics.PIST.Motif.motifScore_zero_freq_no_match", "name": "motifScore_zero_freq_no_match", "module": "Semantics.PIST.Motif" }, { "kind": "theorem", "id": "Semantics.PIST.Motif.motifScore_zero_freq_match_witness", "name": "motifScore_zero_freq_match_witness", "module": "Semantics.PIST.Motif" }, { "kind": "theorem", "id": "Semantics.PIST.Motif.rankMotifs_match_beats_no_match", "name": "rankMotifs_match_beats_no_match", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.familyMatchBonus", "name": "familyMatchBonus", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.baseScore", "name": "baseScore", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.motifScore", "name": "motifScore", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.mkCandidate", "name": "mkCandidate", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.rankMotifs", "name": "rankMotifs", "module": "Semantics.PIST.Motif" }, { "kind": "def", "id": "Semantics.PIST.Motif.topKMotifs", "name": "topKMotifs", "module": "Semantics.PIST.Motif" }, { "kind": "module", "id": "Semantics.PIST.Spectral", "name": "Spectral", "path": "Semantics/PIST/Spectral.lean", "namespace": "Semantics.PIST.Spectral", "doc": "Semantics.PIST.Spectral \u2014 Q16_16 proof-trace spectral feature extraction", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 1, "inductive_count": 1, "line_count": 317 }, { "kind": "def", "id": "Semantics.PIST.Spectral.classifyTacticFromName", "name": "classifyTacticFromName", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.isqrt", "name": "isqrt", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.getEntry", "name": "getEntry", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.rowSum", "name": "rowSum", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.symmetrize", "name": "symmetrize", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.buildLaplacian", "name": "buildLaplacian", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.buildATA", "name": "buildATA", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.normSqRaw", "name": "normSqRaw", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.matVecMul", "name": "matVecMul", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.powerIteration", "name": "powerIteration", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.emptyProfile", "name": "emptyProfile", "module": "Semantics.PIST.Spectral" }, { "kind": "def", "id": "Semantics.PIST.Spectral.computeSpectral", "name": "computeSpectral", "module": "Semantics.PIST.Spectral" }, { "kind": "module", "id": "Semantics.PIST", "name": "PIST", "path": "Semantics/PIST.lean", "namespace": "PIST", "doc": "This module formalizes a defensible discrete core for the PIST state machine. It avoids speculative geometry and focuses on an interval-local coordinate model. The main idea is that a natural number between consecutive squares is represented by a shell index `k` and an offset `t` with `0 \u2264 t \u2264 2*k+", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 11, "def_count": 21, "struct_count": 4, "inductive_count": 2, "line_count": 517 }, { "kind": "theorem", "id": "Semantics.PIST.a_add_b", "name": "a_add_b", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.mass_eq_zero_iff", "name": "mass_eq_zero_iff", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.mass_pos_iff", "name": "mass_pos_iff", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.Resonant", "name": "Resonant", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.not_fixed_of_nonterminal", "name": "not_fixed_of_nonterminal", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.potential_decreases", "name": "potential_decreases", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.preservesMass_resonance", "name": "preservesMass_resonance", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.chosen_transition_decreases", "name": "chosen_transition_decreases", "module": "Semantics.PIST" }, { "kind": "theorem", "id": "Semantics.PIST.chosen_transition_not_fixed", "name": "chosen_transition_not_fixed", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.n", "name": "n", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.a", "name": "a", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.b", "name": "b", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.mass", "name": "mass", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.mirror", "name": "mirror", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.lower", "name": "lower", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.upper", "name": "upper", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.isResonantPair", "name": "isResonantPair", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.resonance", "name": "resonance", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.rejection", "name": "rejection", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.ofCoord", "name": "ofCoord", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.potential", "name": "potential", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.appendLog", "name": "appendLog", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.penalize", "name": "penalize", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.accept", "name": "accept", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.relocate", "name": "relocate", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.resonanceJump", "name": "resonanceJump", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.rejectWithPenalty", "name": "rejectWithPenalty", "module": "Semantics.PIST" }, { "kind": "def", "id": "Semantics.PIST.PreservesMass", "name": "PreservesMass", "module": "Semantics.PIST" }, { "kind": "module", "id": "Semantics.PISTMachine", "name": "PISTMachine", "path": "Semantics/PISTMachine.lean", "namespace": "Semantics.PISTMachine", "doc": "Revised and Neutralized Language Specification. Anchored to: ChatGPT-Making_It_Rigorous.md (Definitions 1-11)", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 5, "inductive_count": 2, "line_count": 176 }, { "kind": "theorem", "id": "Semantics.PISTMachine.mirror_preserves_mass", "name": "mirror_preserves_mass", "module": "Semantics.PISTMachine" }, { "kind": "theorem", "id": "Semantics.PISTMachine.zero_mass_iff_square", "name": "zero_mass_iff_square", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.a", "name": "a", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.b", "name": "b", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.hyperbolaIndex", "name": "hyperbolaIndex", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.rho", "name": "rho", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.classifyPhase", "name": "classifyPhase", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.mirror", "name": "mirror", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.lambda", "name": "lambda", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.PISTLogicalMass", "name": "PISTLogicalMass", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.mirrorPreservesMassMass", "name": "mirrorPreservesMassMass", "module": "Semantics.PISTMachine" }, { "kind": "def", "id": "Semantics.PISTMachine.zeroMassIffSquareMass", "name": "zeroMassIffSquareMass", "module": "Semantics.PISTMachine" }, { "kind": "module", "id": "Semantics.PVGS_DQ_Bridge", "name": "PVGS_DQ_Bridge", "path": "Semantics/PVGS_DQ_Bridge.lean", "namespace": "Semantics.PVGS_DQ_Bridge", "doc": "PVGS_DQ_Bridge.lean \u2014 Photon-Varied Gaussian States \u2192 DualQuaternion Bridge Structural isomorphism between PVGS framework (Giani, Win, Falb, Conti 2025\u20132026) and DQ effective bound theory (EffectiveBoundDQ).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 158 }, { "kind": "theorem", "id": "Semantics.PVGS_DQ_Bridge.pvgs_energy_to_dq", "name": "pvgs_energy_to_dq", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "theorem", "id": "Semantics.PVGS_DQ_Bridge.hermite_sieve_isomorphism", "name": "hermite_sieve_isomorphism", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "theorem", "id": "Semantics.PVGS_DQ_Bridge.variety_isomorphism", "name": "variety_isomorphism", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "def", "id": "Semantics.PVGS_DQ_Bridge.pvgsToDQ", "name": "pvgsToDQ", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "def", "id": "Semantics.PVGS_DQ_Bridge.hermitianRRCKernel", "name": "hermitianRRCKernel", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "def", "id": "Semantics.PVGS_DQ_Bridge.pvgsDQBridgeReceipt", "name": "pvgsDQBridgeReceipt", "module": "Semantics.PVGS_DQ_Bridge" }, { "kind": "module", "id": "Semantics.PandigitalEpigeneticSwitch", "name": "PandigitalEpigeneticSwitch", "path": "Semantics/PandigitalEpigeneticSwitch.lean", "namespace": "Semantics.PandigitalEpigeneticSwitch", "doc": "PandigitalEpigeneticSwitch.lean Mathematical model for compacting distributed gene regulatory elements into a single epigenetic switch state. Core insight: Gene regulation is spatial compression. Distributed marks (methylation, histone modifications, enhancer contacts) collapse into a binary/trans", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 3, "inductive_count": 3, "line_count": 320 }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.effectStrength", "name": "effectStrength", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.effectPolarity", "name": "effectPolarity", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.collapseLandscapeToZN", "name": "collapseLandscapeToZN", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.encodeEpigeneticSwitch", "name": "encodeEpigeneticSwitch", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.decodeEpigeneticSwitch", "name": "decodeEpigeneticSwitch", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.deriveSwitchState", "name": "deriveSwitchState", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.expressionProbability", "name": "expressionProbability", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.transcriptionRate", "name": "transcriptionRate", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.calculateMetrics", "name": "calculateMetrics", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.exampleActiveGene", "name": "exampleActiveGene", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.exampleSilentGene", "name": "exampleSilentGene", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "def", "id": "Semantics.PandigitalEpigeneticSwitch.exampleBivalentGene", "name": "exampleBivalentGene", "module": "Semantics.PandigitalEpigeneticSwitch" }, { "kind": "module", "id": "Semantics.PandigitalSpectralMass", "name": "PandigitalSpectralMass", "path": "Semantics/PandigitalSpectralMass.lean", "namespace": "Semantics.PandigitalSpectralMass", "doc": "PandigitalSpectralMass.lean \u2014 Compact \"pandigital\" representations for eigenvectors and semantic mass. Core insight: Just as \u03c0 = 3.8415926 - 0.7 uses each digit once, eigenvectors and mass triples can be encoded with minimal unique components and reconstructed via simple operations. Three compress", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 17, "struct_count": 5, "inductive_count": 3, "line_count": 282 }, { "kind": "theorem", "id": "Semantics.PandigitalSpectralMass.znRoundTrip", "name": "znRoundTrip", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.cfConvergentToQ16", "name": "cfConvergentToQ16", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.phiConvergents", "name": "phiConvergents", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.piConvergents", "name": "piConvergents", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.selectConvergent", "name": "selectConvergent", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.encodeZNCompact", "name": "encodeZNCompact", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.decodeZNCompact", "name": "decodeZNCompact", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.deriveAFromCompact", "name": "deriveAFromCompact", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.deriveBiasFromCompact", "name": "deriveBiasFromCompact", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.reconstructComponent", "name": "reconstructComponent", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.reconstructEigenvectorComponent", "name": "reconstructEigenvectorComponent", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.fromFullComponents", "name": "fromFullComponents", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.reconstructShellAddress", "name": "reconstructShellAddress", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.deriveMassPhase", "name": "deriveMassPhase", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.exampleCompact400k", "name": "exampleCompact400k", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.exampleCompactSmall", "name": "exampleCompactSmall", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.examplePiComponent", "name": "examplePiComponent", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "def", "id": "Semantics.PandigitalSpectralMass.examplePhiWeightedComponent", "name": "examplePhiWeightedComponent", "module": "Semantics.PandigitalSpectralMass" }, { "kind": "module", "id": "Semantics.ParameterSensitivity", "name": "ParameterSensitivity", "path": "Semantics/ParameterSensitivity.lean", "namespace": "Semantics.ParameterSensitivity", "doc": "ParameterSensitivity.lean -- Sensitivity of Predictions to z = 7/27 This module computes how much each prediction changes when the core parameter z = 7/27 is perturbed by the look-elsewhere width (the distance to the nearest competitive fraction, 13/50 = 0.26). If a prediction shifts by MORE than ", "math_kind": "avm", "sorry_count": 0, "theorem_count": 16, "def_count": 27, "struct_count": 0, "inductive_count": 0, "line_count": 302 }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.for", "name": "for", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p01Stable", "name": "p01Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p02Stable", "name": "p02Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p03Stable", "name": "p03Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p04Stable", "name": "p04Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p05Stable", "name": "p05Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p06Stable", "name": "p06Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p07Stable", "name": "p07Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p08Stable", "name": "p08Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p09Stable", "name": "p09Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p10Stable", "name": "p10Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p11Stable", "name": "p11Stable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.allPredictionsStable", "name": "allPredictionsStable", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p02StabilityRatio", "name": "p02StabilityRatio", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p04StabilityRatio", "name": "p04StabilityRatio", "module": "Semantics.ParameterSensitivity" }, { "kind": "theorem", "id": "Semantics.ParameterSensitivity.p05StabilityRatio", "name": "p05StabilityRatio", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.lookElsewhereWidth", "name": "lookElsewhereWidth", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.corrFactor", "name": "corrFactor", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP01", "name": "derivP01", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP02", "name": "derivP02", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP03", "name": "derivP03", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP04", "name": "derivP04", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP05", "name": "derivP05", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP06", "name": "derivP06", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP07", "name": "derivP07", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP08", "name": "derivP08", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP09", "name": "derivP09", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP10", "name": "derivP10", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.derivP11", "name": "derivP11", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.maxPerturbation", "name": "maxPerturbation", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP01", "name": "sigmaP01", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP02", "name": "sigmaP02", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP03", "name": "sigmaP03", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP04", "name": "sigmaP04", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP05", "name": "sigmaP05", "module": "Semantics.ParameterSensitivity" }, { "kind": "def", "id": "Semantics.ParameterSensitivity.sigmaP06", "name": "sigmaP06", "module": "Semantics.ParameterSensitivity" }, { "kind": "module", "id": "Semantics.PassiveComputation", "name": "PassiveComputation", "path": "Semantics/PassiveComputation.lean", "namespace": "Semantics.PassiveComputation", "doc": "PassiveComputation.lean \u2014 Passive Computation Formalization This module formalizes passive computation: computation performed by the lawful movement, routing, delay, collision, transformation, and boundary-crossing of packets through a structured medium. Per AGENTS.md \u00a71.6: No proof placeholders i", "math_kind": "avm", "sorry_count": 0, "theorem_count": 3, "def_count": 8, "struct_count": 4, "inductive_count": 0, "line_count": 152 }, { "kind": "theorem", "id": "Semantics.PassiveComputation.routeEqualsCompute", "name": "routeEqualsCompute", "module": "Semantics.PassiveComputation" }, { "kind": "theorem", "id": "Semantics.PassiveComputation.generatedReceiptCommitsEndpoints", "name": "generatedReceiptCommitsEndpoints", "module": "Semantics.PassiveComputation" }, { "kind": "theorem", "id": "Semantics.PassiveComputation.passiveComputationIncreasesYield", "name": "passiveComputationIncreasesYield", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.pathLength", "name": "pathLength", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.computeRoutingCost", "name": "computeRoutingCost", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.computeDelay", "name": "computeDelay", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.countBoundaryCrossings", "name": "countBoundaryCrossings", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.isValidPath", "name": "isValidPath", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.computeValueFromTransit", "name": "computeValueFromTransit", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.generateReceipt", "name": "generateReceipt", "module": "Semantics.PassiveComputation" }, { "kind": "def", "id": "Semantics.PassiveComputation.informationYield", "name": "informationYield", "module": "Semantics.PassiveComputation" }, { "kind": "module", "id": "Semantics.Path", "name": "Path", "path": "Semantics/Path.lean", "namespace": "Semantics.ENE", "doc": "Atomic Paths", "math_kind": "general", "sorry_count": 0, "theorem_count": 6, "def_count": 11, "struct_count": 3, "inductive_count": 0, "line_count": 131 }, { "kind": "theorem", "id": "Semantics.Path.AtomicPath", "name": "AtomicPath", "module": "Semantics.Path" }, { "kind": "module", "id": "Semantics.Pbacs", "name": "Pbacs", "path": "Semantics/Pbacs.lean", "namespace": "Semantics", "doc": "Ported from `infra/access_control/core/pbacs_core.py`. Domain-agnostic control runtime with hysteretic gate, projection family, and stable convex update law. All scalars use Q16_16 fixed-point.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 4, "inductive_count": 0, "line_count": 178 }, { "kind": "def", "id": "Semantics.Pbacs.lookup", "name": "lookup", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.lookupD", "name": "lookupD", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.clamp01", "name": "clamp01", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.q16_16Neg", "name": "q16_16Neg", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.project", "name": "project", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.computeScore", "name": "computeScore", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.nextControlState", "name": "nextControlState", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.engramLengthMs", "name": "engramLengthMs", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.alpha", "name": "alpha", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.update", "name": "update", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.updateAccumulation", "name": "updateAccumulation", "module": "Semantics.Pbacs" }, { "kind": "def", "id": "Semantics.Pbacs.step", "name": "step", "module": "Semantics.Pbacs" }, { "kind": "module", "id": "Semantics.PenguinDecayLUT", "name": "PenguinDecayLUT", "path": "Semantics/PenguinDecayLUT.lean", "namespace": "Semantics.PenguinDecayLUT", "doc": "PenguinDecayLUT.lean \u2014 B\u2192K*\u03bc\u03bc Penguin Decay as Degeneracy Conversion LUT This module maps the LHCb B\u2192K*\u03bc\u03bc penguin decay anomaly (4\u03c3 tension with SM) onto the OTOM framework, treating the Standard Model as a LUT generator rule. Key mappings (from arXiv:hep-ph/2505.xxxxx, ScienceDaily 2026-05-26): \u2022", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 7, "inductive_count": 0, "line_count": 357 }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.zero", "name": "zero", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.normSq", "name": "normSq", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.computeObservable", "name": "computeObservable", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.smPrediction", "name": "smPrediction", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.deltaC9_anomaly", "name": "deltaC9_anomaly", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.c9Effective", "name": "c9Effective", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.rgeEvolve", "name": "rgeEvolve", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.detectAnomaly", "name": "detectAnomaly", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.isBasinEscape", "name": "isBasinEscape", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.extractBSMScale", "name": "extractBSMScale", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.defaultSMLUT", "name": "defaultSMLUT", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.smToLadderPacket", "name": "smToLadderPacket", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.flavorLadder", "name": "flavorLadder", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.penguinRGFlow", "name": "penguinRGFlow", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.penguinSpectralProfile", "name": "penguinSpectralProfile", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.wc_anomalous", "name": "wc_anomalous", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.testAnomaly", "name": "testAnomaly", "module": "Semantics.PenguinDecayLUT" }, { "kind": "def", "id": "Semantics.PenguinDecayLUT.b_quark", "name": "b_quark", "module": "Semantics.PenguinDecayLUT" }, { "kind": "module", "id": "Semantics.PeptideMoE", "name": "PeptideMoE", "path": "Semantics/PeptideMoE.lean", "namespace": "PeptideMoE", "doc": "PeptideMoE.lean \u2014 Mixture-of-Experts for Peptide Conformational Analysis This module formalizes a Mixture-of-Experts (MoE) system for peptide conformational state analysis, incorporating thermodynamic parameters, admissibility constraints, and expert coordination. Purpose: Mathematical formalizati", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 6, "def_count": 7, "struct_count": 12, "inductive_count": 0, "line_count": 314 }, { "kind": "theorem", "id": "Semantics.PeptideMoE.filteredScore_of_not_admissible", "name": "filteredScore_of_not_admissible", "module": "Semantics.PeptideMoE" }, { "kind": "theorem", "id": "Semantics.PeptideMoE.filteredScore_of_admissible", "name": "filteredScore_of_admissible", "module": "Semantics.PeptideMoE" }, { "kind": "theorem", "id": "Semantics.PeptideMoE.expertHelpful_iff", "name": "expertHelpful_iff", "module": "Semantics.PeptideMoE" }, { "kind": "theorem", "id": "Semantics.PeptideMoE.gate_mass_one", "name": "gate_mass_one", "module": "Semantics.PeptideMoE" }, { "kind": "theorem", "id": "Semantics.PeptideMoE.filteredScore_zero_of_not_admissible", "name": "filteredScore_zero_of_not_admissible", "module": "Semantics.PeptideMoE" }, { "kind": "theorem", "id": "Semantics.PeptideMoE.filteredScore_eq_phiPeptide_of_admissible", "name": "filteredScore_eq_phiPeptide_of_admissible", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.admissible", "name": "admissible", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.expertUsefulness", "name": "expertUsefulness", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.expertHelpful", "name": "expertHelpful", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.moeDrift", "name": "moeDrift", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.gatesNormalized", "name": "gatesNormalized", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.denominatorSafe", "name": "denominatorSafe", "module": "Semantics.PeptideMoE" }, { "kind": "def", "id": "Semantics.PeptideMoE.allDenominatorsSafe", "name": "allDenominatorsSafe", "module": "Semantics.PeptideMoE" }, { "kind": "module", "id": "Semantics.PeptideMoEExamples", "name": "PeptideMoEExamples", "path": "Semantics/PeptideMoEExamples.lean", "namespace": "PeptideMoEExamples", "doc": "", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 63 }, { "kind": "module", "id": "Semantics.PeptideMoEFailure", "name": "PeptideMoEFailure", "path": "Semantics/PeptideMoEFailure.lean", "namespace": "PeptideMoEFailure", "doc": "", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 31 }, { "kind": "module", "id": "Semantics.PeptideMoERepair", "name": "PeptideMoERepair", "path": "Semantics/PeptideMoERepair.lean", "namespace": "PeptideMoERepair", "doc": "Repair theorems for the peptide-MoE specification. These statements document the guardrails that restore safety: 1. positive denominator offset c0, 2. strict steric admissibility, 3. nonnegative simplex-normalized gates, 4. bounded expert advice.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 2, "struct_count": 1, "inductive_count": 0, "line_count": 71 }, { "kind": "theorem", "id": "Semantics.PeptideMoERepair.repair_gate_mass_one", "name": "repair_gate_mass_one", "module": "Semantics.PeptideMoERepair" }, { "kind": "def", "id": "Semantics.PeptideMoERepair.adviceBoundedAt", "name": "adviceBoundedAt", "module": "Semantics.PeptideMoERepair" }, { "kind": "def", "id": "Semantics.PeptideMoERepair.allAdviceBoundedAt", "name": "allAdviceBoundedAt", "module": "Semantics.PeptideMoERepair" }, { "kind": "module", "id": "Semantics.PhiShellEncoding", "name": "PhiShellEncoding", "path": "Semantics/PhiShellEncoding.lean", "namespace": "Semantics.PhiShellEncoding", "doc": "PhiShellEncoding.lean \u2014 \u03c6-Shell Encoding for Topology/Manifold Routing Extraction-friendly \u03c6-shell routing surface. The shell spacing uses a rational golden-ratio approximation for executable metadata, while the verified invariants stay structural: receipts preserve endpoints, paths are nonempty, ", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 4, "def_count": 10, "struct_count": 5, "inductive_count": 0, "line_count": 110 }, { "kind": "theorem", "id": "Semantics.PhiShellEncoding.phiShellPathPreservesEndpoints", "name": "phiShellPathPreservesEndpoints", "module": "Semantics.PhiShellEncoding" }, { "kind": "theorem", "id": "Semantics.PhiShellEncoding.phiShellCapacityGrowth", "name": "phiShellCapacityGrowth", "module": "Semantics.PhiShellEncoding" }, { "kind": "theorem", "id": "Semantics.PhiShellEncoding.phiShellRadiusGrowth", "name": "phiShellRadiusGrowth", "module": "Semantics.PhiShellEncoding" }, { "kind": "theorem", "id": "Semantics.PhiShellEncoding.decodePreservesRequestedLevel", "name": "decodePreservesRequestedLevel", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.phiNum", "name": "phiNum", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.phiDen", "name": "phiDen", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.computePhiShellRadius", "name": "computePhiShellRadius", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.computePhiShellCapacity", "name": "computePhiShellCapacity", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.isValidPhiShellAddress", "name": "isValidPhiShellAddress", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.rangeBetween", "name": "rangeBetween", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.computePhiShellPath", "name": "computePhiShellPath", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.findShellForScale", "name": "findShellForScale", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.encodeNanoKernelShell", "name": "encodeNanoKernelShell", "module": "Semantics.PhiShellEncoding" }, { "kind": "def", "id": "Semantics.PhiShellEncoding.decodeNanoKernelShell", "name": "decodeNanoKernelShell", "module": "Semantics.PhiShellEncoding" }, { "kind": "module", "id": "Semantics.PhinaryNumberSystem", "name": "PhinaryNumberSystem", "path": "Semantics/PhinaryNumberSystem.lean", "namespace": "Phinary", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Adapted from MOIM for Research Stack equation indexing. The golden ratio \u03c6 = (1 + \u221a5)/2 \u2248 1.6180339887... satisfies: \u03c6^2 = \u03c6 + 1 In phinary (base \u03c6): \u2022 Digits are only 0 and 1 \u2022 No two adjacent 1s are allowed (Zeckendo", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 3, "def_count": 10, "struct_count": 0, "inductive_count": 0, "line_count": 155 }, { "kind": "theorem", "id": "Semantics.PhinaryNumberSystem.phi_squared", "name": "phi_squared", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "theorem", "id": "Semantics.PhinaryNumberSystem.round_trip_conversion", "name": "round_trip_conversion", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "theorem", "id": "Semantics.PhinaryNumberSystem.valid_phinary_constraint", "name": "valid_phinary_constraint", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.phi_pow", "name": "phi_pow", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.fib", "name": "fib", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.validPhinaryDigits", "name": "validPhinaryDigits", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.zeckendorfToNat", "name": "zeckendorfToNat", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.natToZeckendorf", "name": "natToZeckendorf", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.equationIdToPhinary", "name": "equationIdToPhinary", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.phinaryToEquationId", "name": "phinaryToEquationId", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.validEquationPhinary", "name": "validEquationPhinary", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.phinarySimplify", "name": "phinarySimplify", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "def", "id": "Semantics.PhinaryNumberSystem.phinaryNormalize", "name": "phinaryNormalize", "module": "Semantics.PhinaryNumberSystem" }, { "kind": "module", "id": "Semantics.Physics.AdjacentCoprimeClassification", "name": "AdjacentCoprimeClassification", "path": "Semantics/Physics/AdjacentCoprimeClassification.lean", "namespace": "Semantics.Physics.AdjacentCoprimeClassification", "doc": "AdjacentCoprimeClassification.lean", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 8, "def_count": 1, "struct_count": 0, "inductive_count": 0, "line_count": 78 }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.fibGcdAll", "name": "fibGcdAll", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.fibSupport", "name": "fibSupport", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.fibCore", "name": "fibCore", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.badAll", "name": "badAll", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.ex3All", "name": "ex3All", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.ex3Core", "name": "ex3Core", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.bad2All", "name": "bad2All", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "theorem", "id": "Semantics.Physics.AdjacentCoprimeClassification.ex5All", "name": "ex5All", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "def", "id": "Semantics.Physics.AdjacentCoprimeClassification.step", "name": "step", "module": "Semantics.Physics.AdjacentCoprimeClassification" }, { "kind": "module", "id": "Semantics.Physics.BindPhysics", "name": "BindPhysics", "path": "Semantics/Physics/BindPhysics.lean", "namespace": "Semantics.Physics", "doc": "Physical binding: the cost of an interaction between particle configurations. 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"Semantics.Physics.DESIModelProjection" }, { "kind": "theorem", "id": "Semantics.Physics.DESIModelProjection.omegaMResidualWithin1Sigma", "name": "omegaMResidualWithin1Sigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "theorem", "id": "Semantics.Physics.DESIModelProjection.sigma8ResidualWithinModelSigma", "name": "sigma8ResidualWithinModelSigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "theorem", "id": "Semantics.Physics.DESIModelProjection.waResidualWithin1SigmaDr2", "name": "waResidualWithin1SigmaDr2", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "theorem", "id": "Semantics.Physics.DESIModelProjection.omegaMResidualWithin2SigmaDr2", "name": "omegaMResidualWithin2SigmaDr2", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.scale", "name": "scale", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.q16Abs", "name": "q16Abs", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.q16Div", "name": "q16Div", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.mengerDH", "name": "mengerDH", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.kochDim", "name": "kochDim", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.mkDivergenceBase", "name": "mkDivergenceBase", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.hornVolumeBound", "name": "hornVolumeBound", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.hornSurfaceGrowthRate", "name": "hornSurfaceGrowthRate", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.torsionCoupling", "name": "torsionCoupling", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictW0", "name": "predictW0", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictW0Sigma", "name": "predictW0Sigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictWa", "name": "predictWa", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictWaSigma", "name": "predictWaSigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictOmegaM", "name": "predictOmegaM", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictOmegaMSigma", "name": "predictOmegaMSigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictSigma8", "name": "predictSigma8", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "def", "id": "Semantics.Physics.DESIModelProjection.predictSigma8Sigma", "name": "predictSigma8Sigma", "module": "Semantics.Physics.DESIModelProjection" }, { "kind": "module", "id": "Semantics.Physics.Examples", "name": "Examples", "path": "Semantics/Physics/Examples.lean", "namespace": "Semantics.Physics", "doc": "---------------------------------------------------------------------------", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 0, "inductive_count": 0, "line_count": 88 }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleElectron", "name": "exampleElectron", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.examplePhoton", "name": "examplePhoton", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.examplePositron", "name": "examplePositron", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleProton", "name": "exampleProton", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleNeutron", "name": "exampleNeutron", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleNeutrino", "name": "exampleNeutrino", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleUpQuark", "name": "exampleUpQuark", "module": "Semantics.Physics.Examples" }, { "kind": "def", "id": "Semantics.Physics.Examples.exampleDownQuark", "name": "exampleDownQuark", "module": "Semantics.Physics.Examples" }, { "kind": "module", "id": "Semantics.Physics.H0ValveTest", "name": "H0ValveTest", "path": "Semantics/Physics/H0ValveTest.lean", "namespace": "Semantics.Physics.H0ValveTest", "doc": "H0ValveTest.lean", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 8, "struct_count": 0, "inductive_count": 0, "line_count": 54 }, { "kind": "theorem", "id": "Semantics.Physics.H0ValveTest.modelConsistentWithPlanck", "name": "modelConsistentWithPlanck", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "theorem", "id": "Semantics.Physics.H0ValveTest.modelConsistentWithDesi", "name": "modelConsistentWithDesi", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "theorem", "id": "Semantics.Physics.H0ValveTest.modelInconsistentWithSh0es", "name": "modelInconsistentWithSh0es", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "theorem", "id": "Semantics.Physics.H0ValveTest.sh0esTensionModelFlag", "name": "sh0esTensionModelFlag", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0Planck", "name": "h0Planck", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0PlanckSigma", "name": "h0PlanckSigma", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0SH0ES", "name": "h0SH0ES", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0SH0ESSigma", "name": "h0SH0ESSigma", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0DESI", "name": "h0DESI", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0DESISigma", "name": "h0DESISigma", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0Model", "name": "h0Model", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "def", "id": "Semantics.Physics.H0ValveTest.h0ModelSigma", "name": "h0ModelSigma", "module": "Semantics.Physics.H0ValveTest" }, { "kind": "module", "id": "Semantics.Physics.Interaction", "name": "Interaction", "path": "Semantics/Physics/Interaction.lean", "namespace": "Semantics.Physics", "doc": "Core conserved quantities used to judge physical lawfulness of an interaction. This list can be extended as the framework grows.", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 1, "inductive_count": 0, "line_count": 31 }, { "kind": "def", "id": "Semantics.Physics.Interaction.coreConservedQuantities", "name": "coreConservedQuantities", "module": "Semantics.Physics.Interaction" }, { "kind": "module", "id": "Semantics.Physics.NBody", "name": "NBody", "path": "Semantics/Physics/NBody.lean", "namespace": "Semantics.Physics.NBody", "doc": "NBody.lean - N-Space Manifold Multi-Body Physics Fixed-point Hamiltonian dynamics with thermodynamic cost tracking. Symplectic integrator preserving Liouville theorem. Integrates with Wormhole.lean for rare transition shortcuts. Author: Sovereign Stack Research Date: 2026-04-18 License: Research-O", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 13, "def_count": 83, "struct_count": 15, "inductive_count": 3, "line_count": 1420 }, { "kind": "theorem", "id": "Semantics.Physics.NBody.hamiltonian_total", "name": "hamiltonian_total", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.kepler_particle_count", "name": "kepler_particle_count", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.kepler_particle_conservation", "name": "kepler_particle_conservation", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.nuvMapAssignmentsBounded", "name": "nuvMapAssignmentsBounded", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.repeatChainsMinOccurrences_empty", "name": "repeatChainsMinOccurrences_empty", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.lookupSolveHint_mem", "name": "lookupSolveHint_mem", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.nuvCounterMonotone", "name": "nuvCounterMonotone", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.inBank_freq", "name": "inBank_freq", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.braidDecompressValid", "name": "braidDecompressValid", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.slug3SortPreserves", "name": "slug3SortPreserves", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.oiscCompressionRatio", "name": "oiscCompressionRatio", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.mkvContainerPreserves", "name": "mkvContainerPreserves", "module": "Semantics.Physics.NBody" }, { "kind": "theorem", "id": "Semantics.Physics.NBody.particle_conservation", "name": "particle_conservation", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.empty", "name": "empty", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.addParticle", "name": "addParticle", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.particleCount", "name": "particleCount", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.vecScale", "name": "vecScale", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.vecAdd", "name": "vecAdd", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.vecSub", "name": "vecSub", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.vecDot", "name": "vecDot", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.fix16FromNat", "name": "fix16FromNat", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.gravitationalForce", "name": "gravitationalForce", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.coulombForce", "name": "coulombForce", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.repulsiveForce", "name": "repulsiveForce", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.totalForceOnParticle", "name": "totalForceOnParticle", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.quadrupoleGWPowerLoss", "name": "quadrupoleGWPowerLoss", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.isRelativisticParticle", "name": "isRelativisticParticle", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.detectRelativisticRegime", "name": "detectRelativisticRegime", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.totalInformation", "name": "totalInformation", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.transferInformationPhase", "name": "transferInformationPhase", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.velocityVerletStep", "name": "velocityVerletStep", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.computeKineticEnergy", "name": "computeKineticEnergy", "module": "Semantics.Physics.NBody" }, { "kind": "def", "id": "Semantics.Physics.NBody.computeGravitationalPotential", "name": "computeGravitationalPotential", "module": "Semantics.Physics.NBody" }, { "kind": "module", "id": "Semantics.Physics.ParticleDomain", "name": "ParticleDomain", "path": "Semantics/Physics/ParticleDomain.lean", "namespace": "Semantics.Physics", "doc": "============================================================================", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 8, "line_count": 189 }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.domain", "name": "domain", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.maxParticleKinds", "name": "maxParticleKinds", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.maxQuantitiesPerParticle", "name": "maxQuantitiesPerParticle", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.maxInteractionArity", "name": "maxInteractionArity", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.toNat", "name": "toNat", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "def", "id": "Semantics.Physics.ParticleDomain.toAddress", "name": "toAddress", "module": "Semantics.Physics.ParticleDomain" }, { "kind": "module", "id": "Semantics.Physics.PreRegisteredPredictions", "name": "PreRegisteredPredictions", "path": "Semantics/Physics/PreRegisteredPredictions.lean", "namespace": "Semantics.Physics.PreRegisteredPredictions", "doc": "PreRegisteredPredictions.lean \u2014 Formalized 10 Pre-Registered Predictions This module locks the 10 pre-registered predictions from the BraidCore framework (registration date: 2026-05-22). Each prediction carries an explicit numerical value, honest uncertainty envelope, falsification criterion, and ", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 21, "def_count": 26, "struct_count": 3, "inductive_count": 0, "line_count": 484 }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.for", "name": "for", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p01CentralNonneg", "name": "p01CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p01EnvelopeValid", "name": "p01EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p02CentralNonneg", "name": "p02CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p02EnvelopeValid", "name": "p02EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p03CentralNonneg", "name": "p03CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p03EnvelopeValid", "name": "p03EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p04CentralNonneg", "name": "p04CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p04EnvelopeValid", "name": "p04EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p05CentralNonneg", "name": "p05CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p05EnvelopeValid", "name": "p05EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p06CentralNonneg", "name": "p06CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p06EnvelopeValid", "name": "p06EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p07CentralNonneg", "name": "p07CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p07EnvelopeValid", "name": "p07EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p08CentralNonneg", "name": "p08CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p08EnvelopeValid", "name": "p08EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p09CentralNonneg", "name": "p09CentralNonneg", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p09EnvelopeValid", "name": "p09EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p10UpperBoundPositive", "name": "p10UpperBoundPositive", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "theorem", "id": "Semantics.Physics.PreRegisteredPredictions.p10EnvelopeValid", "name": "p10EnvelopeValid", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.scale", "name": "scale", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p01RydbergDelta1", "name": "p01RydbergDelta1", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p02MagneticWallFraction", "name": "p02MagneticWallFraction", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p03PercolationThreshold", "name": "p03PercolationThreshold", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p04EcologicalRegimeShift", "name": "p04EcologicalRegimeShift", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p05MottCriterion", "name": "p05MottCriterion", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p06WeakValueLimit", "name": "p06WeakValueLimit", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p07SpeciesAreaExponent", "name": "p07SpeciesAreaExponent", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p08GranularVoidFraction", "name": "p08GranularVoidFraction", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p09FQHEFillingFactor", "name": "p09FQHEFillingFactor", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p10JupiterResonanceNull", "name": "p10JupiterResonanceNull", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.p11MengerPeriodRatio", "name": "p11MengerPeriodRatio", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.isConfirmed", "name": "isConfirmed", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.isFalsified", "name": "isFalsified", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.gradeThresholds", "name": "gradeThresholds", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.totalPredictions", "name": "totalPredictions", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.totalActivePredictions", "name": "totalActivePredictions", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.braidcorePredictionRegistry", "name": "braidcorePredictionRegistry", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.f01DopingRange", "name": "f01DopingRange", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "def", "id": "Semantics.Physics.PreRegisteredPredictions.f02FineStructure28_27", "name": "f02FineStructure28_27", "module": "Semantics.Physics.PreRegisteredPredictions" }, { "kind": "module", "id": "Semantics.Physics.Projection", "name": "Projection", "path": "Semantics/Physics/Projection.lean", "namespace": "Semantics.Physics", "doc": "Measurement is the projection of a quantum (hidden / N-space) particle state into an observable (visible) particle state. 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Wavelengths in nm stored as Q16.16 (1.0 = 1 nm). Energies in eV stored as Q16.16 (1.0 = 1 eV). 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Pipeline phas", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 16, "def_count": 111, "struct_count": 13, "inductive_count": 4, "line_count": 2119 }, { "kind": "theorem", "id": "Semantics.PistSimulation.phiSpiral_contracts_normSq", "name": "phiSpiral_contracts_normSq", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.phiSpiral_rotates", "name": "phiSpiral_rotates", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.for", "name": "for", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.toInt_eq_clamp", "name": "toInt_eq_clamp", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.mul_self_monotone", "name": "mul_self_monotone", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.add_add_monotone", "name": "add_add_monotone", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.div_two_monotone", "name": "div_two_monotone", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.mul_phiInv_le", "name": "mul_phiInv_le", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.div_nonneg_nonneg", "name": "div_nonneg_nonneg", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.sub_nonneg_toInt", "name": "sub_nonneg_toInt", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.add_sub_cancel_toInt", "name": "add_sub_cancel_toInt", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.q16_mul_self_nonneg", "name": "q16_mul_self_nonneg", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.q16_add_nonneg", "name": "q16_add_nonneg", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.squareFoldNonneg", "name": "squareFoldNonneg", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.squareFoldMonotoneAux", "name": "squareFoldMonotoneAux", "module": "Semantics.PistSimulation" }, { "kind": "theorem", "id": "Semantics.PistSimulation.goldenContractionEnergyDecrease", "name": "goldenContractionEnergyDecrease", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.TensorData", "name": "TensorData", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.injectDataSlice", "name": "injectDataSlice", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.injectFromShellStates", "name": "injectFromShellStates", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.predictViability", "name": "predictViability", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.phase2Pruning", "name": "phase2Pruning", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.picardBlitStep", "name": "picardBlitStep", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.localGossip", "name": "localGossip", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.phase3Tick", "name": "phase3Tick", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.executePipeline", "name": "executePipeline", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.executeFromShellIndices", "name": "executeFromShellIndices", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.pseudoVoigtQ16", "name": "pseudoVoigtQ16", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.chiSqWindow", "name": "chiSqWindow", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.domainSizeFromWidth", "name": "domainSizeFromWidth", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.regimeToString", "name": "regimeToString", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.domainRegime", "name": "domainRegime", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.swapRows", "name": "swapRows", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.scaleRow", "name": "scaleRow", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.addScaledRow", "name": "addScaledRow", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.findPivot", "name": "findPivot", "module": "Semantics.PistSimulation" }, { "kind": "def", "id": "Semantics.PistSimulation.eliminateColumn", "name": "eliminateColumn", "module": "Semantics.PistSimulation" }, { "kind": "module", "id": "Semantics.PostQuantumEscrow", "name": "PostQuantumEscrow", "path": "Semantics/PostQuantumEscrow.lean", "namespace": "Semantics", "doc": "structure EscrowCapsule where capsuleId : String layer0PublicTheory : String layer1ReviewerVerifier : String layer2OpenWormOnlyShell : String layer3PrivateMethodCapsule : String thresholdRelease : String -- e.g., \"3-of-5\" or \"4-of-7\" stagedDisclosureOnly : Bool eachLayerAngrySphinxGoverned : Bool d", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 4, "struct_count": 2, "inductive_count": 0, "line_count": 63 }, { "kind": "def", "id": "Semantics.PostQuantumEscrow.defaultEscrowRules", "name": "defaultEscrowRules", "module": "Semantics.PostQuantumEscrow" }, { "kind": "def", "id": "Semantics.PostQuantumEscrow.createAngrySphinxEscrowCapsule", "name": "createAngrySphinxEscrowCapsule", "module": "Semantics.PostQuantumEscrow" }, { "kind": "def", "id": "Semantics.PostQuantumEscrow.escrowReleaseLaw", "name": "escrowReleaseLaw", "module": "Semantics.PostQuantumEscrow" }, { "kind": "def", "id": "Semantics.PostQuantumEscrow.checkEscrowCompliance", "name": "checkEscrowCompliance", "module": "Semantics.PostQuantumEscrow" }, { "kind": "module", "id": "Semantics.PrimeLut", "name": "PrimeLut", "path": "Semantics/PrimeLut.lean", "namespace": "Semantics.PrimeLut", "doc": "Generated from: https://data.kennethjorgensen.com/primes/primes.html This module provides a constant-time lookup table for prime numbers used in the research stack for: Shell geometry calculations Resonance frequency selection Cryptographic parameter generation Hash table sizing Per AGENTS.md \u00a71.4", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 125 }, { "kind": "def", "id": "Semantics.PrimeLut.arrayGet", "name": "arrayGet", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.firstPrimes", "name": "firstPrimes", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.primeAt", "name": "primeAt", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.nthPrime", "name": "nthPrime", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.isPrimeInLut", "name": "isPrimeInLut", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.primeFloor", "name": "primeFloor", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.shellPrimes", "name": "shellPrimes", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.shellPrime", "name": "shellPrime", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.twinPrimes", "name": "twinPrimes", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.safePrimes", "name": "safePrimes", "module": "Semantics.PrimeLut" }, { "kind": "def", "id": "Semantics.PrimeLut.safePrimeAt", "name": "safePrimeAt", "module": "Semantics.PrimeLut" }, { "kind": "module", "id": "Semantics.PrimitiveMatrix", "name": "PrimitiveMatrix", "path": "Semantics/PrimitiveMatrix.lean", "namespace": "Semantics.PrimitiveMatrix", "doc": "PrimitiveMatrix.lean \u2014 Division-Free Matrix Inversion via Common Denominator Instead of computing adj(A)/det(A) in Q16_16 (which truncates), we keep adjugate entries as raw integers with a common denominator det(A). All intermediate arithmetic is exact integer computation. The single final division", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 96 }, { "kind": "theorem", "id": "Semantics.PrimitiveMatrix.prim_adj_identity_exact", "name": "prim_adj_identity_exact", "module": "Semantics.PrimitiveMatrix" }, { "kind": "def", "id": "Semantics.PrimitiveMatrix.PrimEntry", "name": "PrimEntry", "module": "Semantics.PrimitiveMatrix" }, { "kind": "def", "id": "Semantics.PrimitiveMatrix.demo_exact", "name": "demo_exact", "module": "Semantics.PrimitiveMatrix" }, { "kind": "def", "id": "Semantics.PrimitiveMatrix.demo_q16_lossy", "name": "demo_q16_lossy", "module": "Semantics.PrimitiveMatrix" }, { "kind": "module", "id": "Semantics.ProductSidon", "name": "ProductSidon", "path": "Semantics/ProductSidon.lean", "namespace": "Semantics.ProductSidon", "doc": "## The Equation Stripping away all social-network semantics from the atproto architecture, the central claim reduces to one equation: **If `\u03b1(x\u2081) + \u03b2(y\u2081) = \u03b1(x\u2082) + \u03b2(y\u2082)` then `x\u2081 = x\u2082` and `y\u2081 = y\u2082`.** This is exactly the injectivity condition on the joint encoding `f(x,y) = \u03b1(x) + \u03b2(y)`. ## Si", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 7, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 191 }, { "kind": "theorem", "id": "Semantics.ProductSidon.product_sidon_injective", "name": "product_sidon_injective", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.is_product_sidon_iff_cross_diff_disjoint", "name": "is_product_sidon_iff_cross_diff_disjoint", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.sidon_partition_implies_product_sidon", "name": "sidon_partition_implies_product_sidon", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.atmosphere_sidon_principle", "name": "atmosphere_sidon_principle", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.atmosphere_host_eq", "name": "atmosphere_host_eq", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.atmosphere_app_eq", "name": "atmosphere_app_eq", "module": "Semantics.ProductSidon" }, { "kind": "theorem", "id": "Semantics.ProductSidon.is_product_sidon_symm", "name": "is_product_sidon_symm", "module": "Semantics.ProductSidon" }, { "kind": "def", "id": "Semantics.ProductSidon.IsProductSidon", "name": "IsProductSidon", "module": "Semantics.ProductSidon" }, { "kind": "def", "id": "Semantics.ProductSidon.CrossDiffDisjoint", "name": "CrossDiffDisjoint", "module": "Semantics.ProductSidon" }, { "kind": "mathlib", "id": "Mathlib.Data.Int.Defs", "name": "Mathlib.Data.Int.Defs" }, { "kind": "module", "id": "Semantics.Prohibited", "name": "Prohibited", "path": "Semantics/Prohibited.lean", "namespace": "Semantics.ENE", "doc": "# Prohibitions: What is NOT allowed in the ENE model This module defines the negative space of the semantic universe: every structure, transition, and collapse that violates the constitutional membrane is explicitly ruled out.", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 10, "def_count": 30, "struct_count": 0, "inductive_count": 0, "line_count": 302 }, { "kind": "theorem", "id": "Semantics.Prohibited.no_quarantine_implies_prohibition", "name": "no_quarantine_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.faithfulness_implies_prohibition", "name": "faithfulness_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.lawfulness_implies_prohibition", "name": "lawfulness_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.provenance_implies_prohibition", "name": "provenance_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.universality_projection_implies_prohibition", "name": "universality_projection_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.determinism_implies_prohibition", "name": "determinism_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.core_schema_implies_prohibition", "name": "core_schema_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.evolution_audit_implies_prohibition", "name": "evolution_audit_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.scalar_admissible_implies_ancestry_prohibition", "name": "scalar_admissible_implies_ancestry_prohibition", "module": "Semantics.Prohibited" }, { "kind": "theorem", "id": "Semantics.Prohibited.full_admissibility_implies_prohibition", "name": "full_admissibility_implies_prohibition", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_EmptyLemma", "name": "NotAllowed_EmptyLemma", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UnfaithfulDecomposition", "name": "NotAllowed_UnfaithfulDecomposition", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_NegativeWeightInNormalForm", "name": "NotAllowed_NegativeWeightInNormalForm", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_ActiveQuarantine", "name": "NotAllowed_ActiveQuarantine", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_OrphanObservation", "name": "NotAllowed_OrphanObservation", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UncertifiedCapabilityEdge", "name": "NotAllowed_UncertifiedCapabilityEdge", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_MagicSemanticJump", "name": "NotAllowed_MagicSemanticJump", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UnlawfulPath", "name": "NotAllowed_UnlawfulPath", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_DisconnectedPathComposition", "name": "NotAllowed_DisconnectedPathComposition", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_WitnessWithoutProvenance", "name": "NotAllowed_WitnessWithoutProvenance", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_NegativeLoad", "name": "NotAllowed_NegativeLoad", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UngroundedNode", "name": "NotAllowed_UngroundedNode", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_InvisibleUniversality", "name": "NotAllowed_InvisibleUniversality", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UniversalityLossUnderProjection", "name": "NotAllowed_UniversalityLossUnderProjection", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UniversalityLossUnderCollapse", "name": "NotAllowed_UniversalityLossUnderCollapse", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_UniversalityLossUnderEvolution", "name": "NotAllowed_UniversalityLossUnderEvolution", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_AdversarialCanonicalInput", "name": "NotAllowed_AdversarialCanonicalInput", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_WeirdMachineInput", "name": "NotAllowed_WeirdMachineInput", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_NondeterministicCanonicalForm", "name": "NotAllowed_NondeterministicCanonicalForm", "module": "Semantics.Prohibited" }, { "kind": "def", "id": "Semantics.Prohibited.NotAllowed_NonCoreCanonicalSchema", "name": "NotAllowed_NonCoreCanonicalSchema", "module": "Semantics.Prohibited" }, { "kind": "module", "id": "Semantics.ProjectableGeometryCanonical", "name": "ProjectableGeometryCanonical", "path": "Semantics/ProjectableGeometryCanonical.lean", "namespace": "Semantics.ProjectableGeometryCanonical", "doc": "# Projectable Geometry Canonical Representation This module records the current canonical representation for the projectable geometry compressor: * signed 16-axis envelope, * 12D source/residual plane, * 4D primitive keel, * genus-3 residual boat, * 0D closure witness. It is an accounting gate fo", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 14, "struct_count": 3, "inductive_count": 0, "line_count": 146 }, { "kind": "theorem", "id": "Semantics.ProjectableGeometryCanonical.canonicalShellCloses", "name": "canonicalShellCloses", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "theorem", "id": "Semantics.ProjectableGeometryCanonical.sampleClosedRepAdmissible", "name": "sampleClosedRepAdmissible", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "theorem", "id": "Semantics.ProjectableGeometryCanonical.brokenResidualRepNotAdmissible", "name": "brokenResidualRepNotAdmissible", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "theorem", "id": "Semantics.ProjectableGeometryCanonical.unresolvedShellRepNotAdmissible", "name": "unresolvedShellRepNotAdmissible", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.signedEnvelopeAxes", "name": "signedEnvelopeAxes", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.sourcePlaneAxes", "name": "sourcePlaneAxes", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.primitiveKeelAxes", "name": "primitiveKeelAxes", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.genusHandles", "name": "genusHandles", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.closurePointAxes", "name": "closurePointAxes", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.canonicalShell", "name": "canonicalShell", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.shellCloses", "name": "shellCloses", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.residualBoatCloses", "name": "residualBoatCloses", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.sourceRehydrates", "name": "sourceRehydrates", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.axesCanonical", "name": "axesCanonical", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.canonicalRepAdmissible", "name": "canonicalRepAdmissible", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.sampleClosedRep", "name": "sampleClosedRep", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.brokenResidualRep", "name": "brokenResidualRep", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "def", "id": "Semantics.ProjectableGeometryCanonical.unresolvedShellRep", "name": "unresolvedShellRep", "module": "Semantics.ProjectableGeometryCanonical" }, { "kind": "module", "id": "Semantics.Projections", "name": "Projections", "path": "Semantics/Projections.lean", "namespace": "Semantics", "doc": "Cognitive Load metrics. Mirrors `docs/cognitive/COGNITIVE_LOAD_FUNCTIONS_SPEC.md`.", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 1, "inductive_count": 0, "line_count": 16 }, { "kind": "module", "id": "Semantics.Protocol", "name": "Protocol", "path": "Semantics/Protocol.lean", "namespace": "Semantics.Protocol", "doc": "Protocol: A formal set of rules for research, data, or network behavior. Examples: Hutter Prize, Signal Policy, ENE Sync.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 2, "struct_count": 1, "inductive_count": 0, "line_count": 46 }, { "kind": "theorem", "id": "Semantics.Protocol.protocolInheritance", "name": "protocolInheritance", "module": "Semantics.Protocol" }, { "kind": "def", "id": "Semantics.Protocol.isInherited", "name": "isInherited", "module": "Semantics.Protocol" }, { "kind": "def", "id": "Semantics.Protocol.protocolBind", "name": "protocolBind", "module": "Semantics.Protocol" }, { "kind": "module", "id": "Semantics.ProtonDecayAnchor", "name": "ProtonDecayAnchor", "path": "Semantics/ProtonDecayAnchor.lean", "namespace": "Semantics.ProtonDecayAnchor", "doc": "ProtonDecayAnchor.lean -- Can Proton Decay Time Anchor P0? The user proposes: use the proton decay lifetime as the natural anchor for P0. Proton decay is a hypothetical process predicted by Grand Unified Theories (GUTs). If it occurs, it would provide a universal, fundamental timescale. This modul", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 10, "struct_count": 0, "inductive_count": 0, "line_count": 228 }, { "kind": "theorem", "id": "Semantics.ProtonDecayAnchor.for", "name": "for", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "theorem", "id": "Semantics.ProtonDecayAnchor.protonLifetimePositive", "name": "protonLifetimePositive", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "theorem", "id": "Semantics.ProtonDecayAnchor.protonLifetimeEnormous", "name": "protonLifetimeEnormous", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "theorem", "id": "Semantics.ProtonDecayAnchor.nProtonDecayEnormous", "name": "nProtonDecayEnormous", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "theorem", "id": "Semantics.ProtonDecayAnchor.frameworkCannotPredictProtonDecay", "name": "frameworkCannotPredictProtonDecay", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimeLowerBoundYears", "name": "protonLifetimeLowerBoundYears", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimeGUTMin", "name": "protonLifetimeGUTMin", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimeGUTMax", "name": "protonLifetimeGUTMax", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimeUncertaintySpan", "name": "protonLifetimeUncertaintySpan", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.nForProtonDecayLower", "name": "nForProtonDecayLower", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.nForProtonDecaySU5", "name": "nForProtonDecaySU5", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.frameworkPredictsProtonDecay", "name": "frameworkPredictsProtonDecay", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.frameworkHasParticlePhysics", "name": "frameworkHasParticlePhysics", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimeMeasured", "name": "protonLifetimeMeasured", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "def", "id": "Semantics.ProtonDecayAnchor.protonLifetimePredictionsSpanDecades", "name": "protonLifetimePredictionsSpanDecades", "module": "Semantics.ProtonDecayAnchor" }, { "kind": "module", "id": "Semantics.ProvenanceSource", "name": "ProvenanceSource", "path": "Semantics/ProvenanceSource.lean", "namespace": "Semantics.ProvenanceSource", "doc": "ProvenanceSource is the open-future event surface for artifact lifecycle reports. A source event is a report, not a theorem: observation changes the receipt surface, not the underlying law. The backend and reference kinds deliberately carry strings instead of closed enums. The stack should accept f", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 13, "struct_count": 4, "inductive_count": 2, "line_count": 148 }, { "kind": "def", "id": "Semantics.ProvenanceSource.CostPolicy", "name": "CostPolicy", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.actorKey", "name": "actorKey", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.isTrusted", "name": "isTrusted", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.visibilityToken", "name": "visibilityToken", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.backendToken", "name": "backendToken", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.invariant", "name": "invariant", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.legacyInvariant", "name": "legacyInvariant", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.targetInvariant", "name": "targetInvariant", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.legacyTargetInvariant", "name": "legacyTargetInvariant", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.cost", "name": "cost", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.bind", "name": "bind", "module": "Semantics.ProvenanceSource" }, { "kind": "def", "id": "Semantics.ProvenanceSource.legacyBind", "name": "legacyBind", "module": "Semantics.ProvenanceSource" }, { "kind": "module", "id": "Semantics.Purify", "name": "Purify", "path": "Semantics/Purify.lean", "namespace": "Semantics.Purify", "doc": "Verified Purification Engine: Reads raw metadata and produces formally hardened JSON records.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 30 }, { "kind": "def", "id": "Semantics.Purify.purifyRecords", "name": "purifyRecords", "module": "Semantics.Purify" }, { "kind": "def", "id": "Semantics.Purify.runPurification", "name": "runPurification", "module": "Semantics.Purify" }, { "kind": "module", "id": "Semantics.PutinarBackbone", "name": "PutinarBackbone", "path": "Semantics/PutinarBackbone.lean", "namespace": "Semantics.PutinarBackbone", "doc": "============================================================ PUTINAR'S POSITIVSTELLENSATZ \u2014 THE GENERALIZED BACKBONE The backbone theorem: \u03a3 f\u1d62\u00b2 = 0 \u2194 each f\u1d62 = 0 Putinar's Positivstellensatz: p \u2265 0 on K \u2194 p has SOS certificate The backbone is the ZERO SET of Putinar. Putinar is the INEQUALITY GEN", "math_kind": "algebra", "sorry_count": 2, "theorem_count": 12, "def_count": 4, "struct_count": 4, "inductive_count": 0, "line_count": 624 }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.foldl_nonneg", "name": "foldl_nonneg", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.sos_nonneg", "name": "sos_nonneg", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.sos_zero_iff", "name": "sos_zero_iff", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.foldl_weighted_nonneg", "name": "foldl_weighted_nonneg", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.putinar_nonneg", "name": "putinar_nonneg", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.backbone_is_putinar_zero_case", "name": "backbone_is_putinar_zero_case", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.baker_replacement", "name": "baker_replacement", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.stars_convergence", "name": "stars_convergence", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.softplus_complementarity", "name": "softplus_complementarity", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.softplus_derivative_bounded", "name": "softplus_derivative_bounded", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.smoothPenalty_nonneg", "name": "smoothPenalty_nonneg", "module": "Semantics.PutinarBackbone" }, { "kind": "theorem", "id": "Semantics.PutinarBackbone.unified_polynomial", "name": "unified_polynomial", "module": "Semantics.PutinarBackbone" }, { "kind": "def", "id": "Semantics.PutinarBackbone.SemialgebraicSet", "name": "SemialgebraicSet", "module": "Semantics.PutinarBackbone" }, { "kind": "def", "id": "Semantics.PutinarBackbone.goormaghtighDomain", "name": "goormaghtighDomain", "module": "Semantics.PutinarBackbone" }, { "kind": "def", "id": "Semantics.PutinarBackbone.noCollisionDomain", "name": "noCollisionDomain", "module": "Semantics.PutinarBackbone" }, { "kind": "def", "id": "Semantics.PutinarBackbone.verifySDPSolution", "name": "verifySDPSolution", "module": "Semantics.PutinarBackbone" }, { "kind": "module", "id": "Semantics.Q0_2", "name": "Q0_2", "path": "Semantics/Q0_2.lean", "namespace": "Semantics.Q0_2", "doc": "Q0_2.lean \u2014 Q0_2 Fixed-Point Type for Braid Crossing Matrices Q0_2 represents 2-bit fixed-point values in the range [0, 0.75] with 0.25 resolution. The Q16_16 encoding is: 0 \u2192 0x00000000 0.25 \u2192 0x00004000 0.5 \u2192 0x00008000 0.75 \u2192 0x0000C000 Per AGENTS.md \u00a74.1: Q16_16 integer arithmetic is d", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 71 }, { "kind": "theorem", "id": "Semantics.Q0_2.allValues_are_Q0_2", "name": "allValues_are_Q0_2", "module": "Semantics.Q0_2" }, { "kind": "theorem", "id": "Semantics.Q0_2.allValues_length", "name": "allValues_length", "module": "Semantics.Q0_2" }, { "kind": "theorem", "id": "Semantics.Q0_2.q0_2_mul_self_nonneg", "name": "q0_2_mul_self_nonneg", "module": "Semantics.Q0_2" }, { "kind": "theorem", "id": "Semantics.Q0_2.q0_2_mul_nonneg", "name": "q0_2_mul_nonneg", "module": "Semantics.Q0_2" }, { "kind": "theorem", "id": "Semantics.Q0_2.q0_2_add_nonneg", "name": "q0_2_add_nonneg", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.q0_2_zero", "name": "q0_2_zero", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.q0_2_quarter", "name": "q0_2_quarter", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.q0_2_half", "name": "q0_2_half", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.q0_2_three_quarter", "name": "q0_2_three_quarter", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.allValues", "name": "allValues", "module": "Semantics.Q0_2" }, { "kind": "def", "id": "Semantics.Q0_2.IsQ0_2", "name": "IsQ0_2", "module": "Semantics.Q0_2" }, { "kind": "module", "id": "Semantics.Q16InverseProof", "name": "Q16InverseProof", "path": "Semantics/Q16InverseProof.lean", "namespace": "", "doc": "Q16InverseProof.lean Complete proof: A \u00d7 A\u207b\u00b9 = I for Q16_16 fixed-point matrices when all intermediate computations are exact. All mathematical axioms eliminated. Remaining axioms are implementation specs only.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 44, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 977 }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_injective", "name": "toRat_injective", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.ofRawInt_inRange", "name": "ofRawInt_inRange", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_mul_exact", "name": "toRat_mul_exact", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.ofRawInt_val", "name": "ofRawInt_val", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_add_exact", "name": "toRat_add_exact", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_div_exact", "name": "toRat_div_exact", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_zero", "name": "toRat_zero", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_one", "name": "toRat_one", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.mul_one_eq", "name": "mul_one_eq", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.one_mul_eq", "name": "one_mul_eq", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.foldl_toRat_sum", "name": "foldl_toRat_sum", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_ofInt_neg_one", "name": "toRat_ofInt_neg_one", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRat_cofactor_sign", "name": "toRat_cofactor_sign", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.cofactor_sign_mul_exact_full", "name": "cofactor_sign_mul_exact_full", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.list_range_sum_eq_finset_sum", "name": "list_range_sum_eq_finset_sum", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.list_map_congr", "name": "list_map_congr", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.getEntry", "name": "getEntry", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRM_identity", "name": "toRM_identity", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.identity8_wf", "name": "identity8_wf", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRM_entry_eq", "name": "toRM_entry_eq", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.matrix8_ext", "name": "matrix8_ext", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRM_injective_of_sizes", "name": "toRM_injective_of_sizes", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRM_injective_of_wf", "name": "toRM_injective_of_wf", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.Array", "name": "Array", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.foldl_range_push_size", "name": "foldl_range_push_size", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.foldl_range_push_get", "name": "foldl_range_push_get", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.getEntryQ_minorQ", "name": "getEntryQ_minorQ", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.minorQ_wf", "name": "minorQ_wf", "module": "Semantics.Q16InverseProof" }, { "kind": "theorem", "id": "Semantics.Q16InverseProof.toRMn_minorQ", "name": "toRMn_minorQ", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.toRat", "name": "toRat", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.Q16_16", "name": "Q16_16", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.toRM", "name": "toRM", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.Matrix8_wf", "name": "Matrix8_wf", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.toRMn", "name": "toRMn", "module": "Semantics.Q16InverseProof" }, { "kind": "def", "id": "Semantics.Q16InverseProof.DetQExact", "name": "DetQExact", "module": "Semantics.Q16InverseProof" }, { "kind": "module", "id": "Semantics.Q16_16Numerics", "name": "Q16_16Numerics", "path": "Semantics/Q16_16Numerics.lean", "namespace": "Semantics.Q16_16Numerics", "doc": "Q16_16Numerics.lean \u2014 Rigorous Fixed-Point Numerical Functions This module provides Q16_16 versions of exp, sqrt, ln, sin, cos, etc. Functions delegate to Semantics.FixedPoint.Q16_16 where integer-only implementations exist. ARCHITECTURE: Constants: Precomputed raw integers (no ofFloat at definiti", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 20, "struct_count": 0, "inductive_count": 0, "line_count": 248 }, { "kind": "theorem", "id": "Semantics.Q16_16Numerics.exp_zero", "name": "exp_zero", "module": "Semantics.Q16_16Numerics" }, { "kind": "theorem", "id": "Semantics.Q16_16Numerics.sqrt_zero", "name": "sqrt_zero", "module": "Semantics.Q16_16Numerics" }, { "kind": "theorem", "id": "Semantics.Q16_16Numerics.ln_one", "name": "ln_one", "module": "Semantics.Q16_16Numerics" }, { "kind": "theorem", "id": "Semantics.Q16_16Numerics.sin_zero", "name": "sin_zero", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.pi", "name": "pi", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.e", "name": "e", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.ln2", "name": "ln2", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.sqrt2", "name": "sqrt2", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.exp", "name": "exp", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.expNeg", "name": "expNeg", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.sqrt", "name": "sqrt", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.ln", "name": "ln", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.log2", "name": "log2", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.sin", "name": "sin", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.cos", "name": "cos", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.tan", "name": "tan", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.asin", "name": "asin", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.acos", "name": "acos", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.atan", "name": "atan", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.atan2", "name": "atan2", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.sinh", "name": "sinh", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.cosh", "name": "cosh", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.tanh", "name": "tanh", "module": "Semantics.Q16_16Numerics" }, { "kind": "def", "id": "Semantics.Q16_16Numerics.pow", "name": "pow", "module": "Semantics.Q16_16Numerics" }, { "kind": "module", "id": "Semantics.Q16_16_Unification_Demo", "name": "Q16_16_Unification_Demo", "path": "Semantics/Q16_16_Unification_Demo.lean", "namespace": "", "doc": "Q16_16 Unification Demonstration This file demonstrates the approach for unifying the multiple Q16_16 type definitions in the Research Stack codebase. Problem: There are 6 different Q16_16 type definitions: 1. Semantics.FixedPoint.Q16_16 (canonical - Int subtype) - Used by ~421 files 2. 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Authors: Research Stack Team QRGridState.lean \u2014 QR Grid State Management Defines QR grid state management for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10). 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(2012). Symmetry and Boundness of Four-Particle Coulomb Systems. Physics of Atomic Nuclei, 75(4), 455\u2013463. A quadrion a\u207ab\u207ac\u207bd\u207b has Hamiltonian: H = \u03a3 s\u2c7c\u00b7t\u2c7c + 1/r\u2081\u2082 + 1/r\u2083\u2084 - 1/r\u2081\u2083 - 1/r\u2081\u2084 - 1/r\u2082\u2083", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 1, "def_count": 10, "struct_count": 2, "inductive_count": 1, "line_count": 161 }, { "kind": "theorem", "id": "Semantics.QuadrionBoundness.rebound_quadrion_fraction", "name": "rebound_quadrion_fraction", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.sidonAddress", "name": "sidonAddress", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.particleMass", "name": "particleMass", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.totalQuadrions", "name": "totalQuadrions", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.quadrionSidonSumset", "name": "quadrionSidonSumset", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.sidonSumsAllDistinct", "name": "sidonSumsAllDistinct", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.boundnessRatio", "name": "boundnessRatio", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.boundnessThreshold", "name": "boundnessThreshold", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.isPredictedBound", "name": "isPredictedBound", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.positroniumMolecule", "name": "positroniumMolecule", "module": "Semantics.QuadrionBoundness" }, { "kind": "def", "id": "Semantics.QuadrionBoundness.hydrogenMolecule", "name": "hydrogenMolecule", "module": "Semantics.QuadrionBoundness" }, { "kind": "module", "id": "Semantics.Quantization", "name": "Quantization", "path": "Semantics/Quantization.lean", "namespace": "Semantics.Quantization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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Quaternion-based Dimensionless Scalar Field Set and Bracketed PBACS Style Representation Based on quaternionic algebra: q = q\u2080 + q\u2081i + q\u2082j + q\u2083k where q\u2080 is the dimensionless scalar part representing: Temporal Identity (Hamilton's time interpretation) Metric of Alignment (co", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 26, "struct_count": 2, "inductive_count": 0, "line_count": 226 }, { "kind": "def", "id": "Semantics.QuaternionScalar.make", "name": "make", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.zero", "name": "zero", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.one", "name": "one", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.vectorMagSq", "name": "vectorMagSq", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.magSq", "name": "magSq", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.add", "name": "add", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.mul", "name": "mul", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.sq", "name": "sq", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.scalarPart", "name": "scalarPart", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.vectorPart", "name": "vectorPart", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.isUnit", "name": "isUnit", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.halfAngleCosine", "name": "halfAngleCosine", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.informationDensity", "name": "informationDensity", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.temporalScale", "name": "temporalScale", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.encode", "name": "encode", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.scalarWidth", "name": "scalarWidth", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.vectorWidth", "name": "vectorWidth", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.scalarInBounds", "name": "scalarInBounds", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.vectorInBounds", "name": "vectorInBounds", "module": "Semantics.QuaternionScalar" }, { "kind": "def", "id": "Semantics.QuaternionScalar.bracketAdd", "name": "bracketAdd", "module": "Semantics.QuaternionScalar" }, { "kind": "module", "id": "Semantics.RFPFieldSolver", "name": "RFPFieldSolver", "path": "Semantics/RFPFieldSolver.lean", "namespace": "Semantics.RFPFieldSolver", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team RFPFieldSolver.lean \u2014 Resonant Field Propagation Field Equation Solver Defines the field equation solver for Resonant Field Propagation (RFP) - a novel distributed state propagation mechanism that avoi", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 6, "struct_count": 3, "inductive_count": 0, "line_count": 191 }, { "kind": "theorem", "id": "Semantics.RFPFieldSolver.computeLaplacianZeroWhenFieldsEqual", "name": "computeLaplacianZeroWhenFieldsEqual", "module": "Semantics.RFPFieldSolver" }, { "kind": "theorem", "id": "Semantics.RFPFieldSolver.computeDampingZeroWhenVelocityZero", "name": "computeDampingZeroWhenVelocityZero", "module": "Semantics.RFPFieldSolver" }, { "kind": "theorem", "id": "Semantics.RFPFieldSolver.fieldEquationStepPreservesStructure", "name": "fieldEquationStepPreservesStructure", "module": "Semantics.RFPFieldSolver" }, { "kind": "theorem", "id": "Semantics.RFPFieldSolver.initializeFieldStateHasZeroVelocity", 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All rights reserved. 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"def", "id": "Semantics.RRC.PolyFactorIdentity.shortSleeveThreshold", "name": "shortSleeveThreshold", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.shortSleeveDetected", "name": "shortSleeveDetected", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.listGcd", "name": "listGcd", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.maxCoeff", "name": "maxCoeff", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.coeffEnergy", "name": "coeffEnergy", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.polyDegree", "name": "polyDegree", "module": "Semantics.RRC.PolyFactorIdentity" }, { "kind": "def", "id": "Semantics.RRC.PolyFactorIdentity.polySignature", "name": "polySignature", "module": 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}, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wRank", "name": "wRank", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wGap", "name": "wGap", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wEntropy", "name": "wEntropy", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wDensity", "name": "wDensity", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wLap", "name": "wLap", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.wHash", "name": "wHash", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.lapScore", "name": "lapScore", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.hashScore", "name": "hashScore", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.spectralQuality", "name": "spectralQuality", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.weightedSum", "name": "weightedSum", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.computeDensity", "name": "computeDensity", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "def", "id": "Semantics.RRC.ReceiptDensity.claimBoundary", "name": "claimBoundary", "module": "Semantics.RRC.ReceiptDensity" }, { "kind": "module", "id": "Semantics.RRCLogogramProjection", "name": "RRCLogogramProjection", "path": "Semantics/RRCLogogramProjection.lean", "namespace": "Semantics.RRCLogogramProjection", "doc": "# Rainbow Raccoon Compiler Logogram Projection This module formalizes the small claim proven by the current Python receipt: * a logogram can be type-admissible as a `LogogramProjection`; * a torn logogram can be projection-admissible after repair/quarantine; * the same torn logogram is not merge-a", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 7, "def_count": 8, "struct_count": 1, "inductive_count": 4, "line_count": 177 }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.semantic_tear_projects_after_repair", "name": "semantic_tear_projects_after_repair", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.semantic_tear_does_not_merge", "name": "semantic_tear_does_not_merge", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.semantic_tear_uses_quarantine_lane", "name": "semantic_tear_uses_quarantine_lane", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.unrepaired_tear_does_not_project", "name": "unrepaired_tear_does_not_project", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.ordinary_logogram_projects_and_merges", "name": "ordinary_logogram_projects_and_merges", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.merge_implies_projection", "name": "merge_implies_projection", "module": "Semantics.RRCLogogramProjection" }, { "kind": "theorem", "id": "Semantics.RRCLogogramProjection.repaired_tear_separates_projection_from_merge", "name": "repaired_tear_separates_projection_from_merge", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.hasTearRepair", "name": "hasTearRepair", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.typeAdmissible", "name": "typeAdmissible", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.mergeAdmissible", "name": "mergeAdmissible", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.projectionAdmissible", "name": "projectionAdmissible", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.projectionLane", "name": "projectionLane", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.semanticTearReceipt", "name": "semanticTearReceipt", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.ordinaryLogogramReceipt", "name": "ordinaryLogogramReceipt", "module": "Semantics.RRCLogogramProjection" }, { "kind": "def", "id": "Semantics.RRCLogogramProjection.unrepairedTearReceipt", "name": "unrepairedTearReceipt", "module": "Semantics.RRCLogogramProjection" }, { "kind": "module", "id": "Semantics.RaycastField", "name": "RaycastField", "path": "Semantics/RaycastField.lean", "namespace": "Semantics.RaycastField", "doc": "RaycastField.lean - Fixed-Point Raycast Field Propagation", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 28 }, { "kind": "def", "id": "Semantics.RaycastField.sampleChannelField", "name": "sampleChannelField", "module": "Semantics.RaycastField" }, { "kind": "def", "id": "Semantics.RaycastField.amplitudeMean", "name": "amplitudeMean", "module": "Semantics.RaycastField" }, { "kind": "def", "id": "Semantics.RaycastField.inferLocalDerivativeFromMultiPath", "name": "inferLocalDerivativeFromMultiPath", "module": "Semantics.RaycastField" }, { "kind": "module", "id": "Semantics.RcloneIntegration", "name": "RcloneIntegration", "path": "Semantics/RcloneIntegration.lean", "namespace": "Semantics.RcloneIntegration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team RcloneIntegration.lean \u2014 Cloud Storage Operations in Lean This module formalizes Rclone cloud storage operations for the swarm system. Supports sync, copy, list, and other Rclone operations across vari", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 12, "struct_count": 6, "inductive_count": 3, "line_count": 266 }, { "kind": "theorem", "id": "Semantics.RcloneIntegration.addTaskPreservesCount", "name": "addTaskPreservesCount", "module": "Semantics.RcloneIntegration" }, { "kind": "theorem", "id": "Semantics.RcloneIntegration.addTaskPreservesPendingLength", "name": "addTaskPreservesPendingLength", "module": "Semantics.RcloneIntegration" }, { "kind": "theorem", "id": "Semantics.RcloneIntegration.startTask_pending_non_increasing", "name": "startTask_pending_non_increasing", "module": "Semantics.RcloneIntegration" }, { "kind": "theorem", "id": "Semantics.RcloneIntegration.completeTask_completed_length", "name": "completeTask_completed_length", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.zero", "name": "zero", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.one", "name": "one", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.ofNat", "name": "ofNat", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.toString", "name": "toString", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.empty", "name": "empty", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.addTask", "name": "addTask", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.startTask", "name": "startTask", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.completeTask", "name": "completeTask", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.createRcloneExpert", "name": "createRcloneExpert", "module": "Semantics.RcloneIntegration" }, { "kind": "def", "id": "Semantics.RcloneIntegration.topologicalStorageArea", "name": "topologicalStorageArea", "module": "Semantics.RcloneIntegration" }, { "kind": "module", "id": "Semantics.RealityContractMassNumber", "name": "RealityContractMassNumber", "path": "Semantics/RealityContractMassNumber.lean", "namespace": "HolyDiver", "doc": "Holy Diver / ENE Reality-Contract Mass-Number Forest A Lean 4 core-only module encoding the ontology-derived ruleset: every domain is a reality-local field; candidates are reduced only through certified domain-local reductions; residuals are preserved, not erased; mass numbers are admissible reduct", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 33, "struct_count": 14, "inductive_count": 6, "line_count": 558 }, { "kind": "theorem", "id": "Semantics.RealityContractMassNumber.decision_is_finite", "name": "decision_is_finite", "module": "Semantics.RealityContractMassNumber" }, { "kind": "theorem", "id": "Semantics.RealityContractMassNumber.residuals_typed_by_construction", "name": "residuals_typed_by_construction", "module": "Semantics.RealityContractMassNumber" }, { "kind": "theorem", "id": "Semantics.RealityContractMassNumber.native_reductions_certified", "name": "native_reductions_certified", "module": "Semantics.RealityContractMassNumber" }, { "kind": "theorem", "id": "Semantics.RealityContractMassNumber.mass_denominator_nonzero", "name": "mass_denominator_nonzero", "module": "Semantics.RealityContractMassNumber" }, { "kind": "theorem", "id": "Semantics.RealityContractMassNumber.distance_denominator_nonzero", "name": "distance_denominator_nonzero", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.DomainReduction", "name": "DomainReduction", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.CertifiedReduction", "name": "CertifiedReduction", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.ResidualRisk", "name": "ResidualRisk", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.Score", "name": "Score", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.sumNat", "name": "sumNat", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.admissibleReduction", "name": "admissibleReduction", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.massNumber", "name": "massNumber", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.massPhi", "name": "massPhi", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.phiDistanceCost", "name": "phiDistanceCost", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.autodocPressure", "name": "autodocPressure", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.CandidateRecord", "name": "CandidateRecord", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.highResidual", "name": "highResidual", "module": "Semantics.RealityContractMassNumber" }, { "kind": "def", "id": "Semantics.RealityContractMassNumber.riskLowEnough", "name": "riskLowEnough", "module": "Semantics.RealityContractMassNumber" }, { "kind": "module", "id": "Semantics.ReceiptCore", "name": "ReceiptCore", "path": "Semantics/ReceiptCore.lean", "namespace": "Semantics.ReceiptCore", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ReceiptCore.lean \u2014 Proof Receipt Infrastructure for GCL Workspace This module defines the receipt types that external validation systems (build, benchmark, audit, human review) must produce before a Wa", "math_kind": "rrc", "sorry_count": 1, "theorem_count": 0, "def_count": 14, "struct_count": 2, "inductive_count": 1, "line_count": 265 }, { "kind": "def", "id": "Semantics.ReceiptCore.emptyReceipts", "name": "emptyReceipts", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.hasReceiptOfKind", "name": "hasReceiptOfKind", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.hasAllReceiptKinds", "name": "hasAllReceiptKinds", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.canPromoteFromCandidate", "name": "canPromoteFromCandidate", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.isBlocked", "name": "isBlocked", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.leanBuildReceipt", "name": "leanBuildReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.benchmarkReceipt", "name": "benchmarkReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.adversarialTrialReceipt", "name": "adversarialTrialReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.humanReviewReceipt", "name": "humanReviewReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.hasProofReceipt", "name": "hasProofReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.ledgerLookup", "name": "ledgerLookup", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.ledgerAppend", "name": "ledgerAppend", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.ledgerHasProofReceipt", "name": "ledgerHasProofReceipt", "module": "Semantics.ReceiptCore" }, { "kind": "def", "id": "Semantics.ReceiptCore.LedgerPromotionInvariant", "name": "LedgerPromotionInvariant", "module": "Semantics.ReceiptCore" }, { "kind": "module", "id": "Semantics.RegimeCore", "name": "RegimeCore", "path": "Semantics/RegimeCore.lean", "namespace": "Semantics.RegimeCore", "doc": "RegimeCore.lean - Minimal stub for Type-Safe Manifold Assignments", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 1, "inductive_count": 1, "line_count": 53 }, { "kind": "def", "id": "Semantics.RegimeCore.classifyAssignment", "name": "classifyAssignment", "module": "Semantics.RegimeCore" }, { "kind": "module", "id": "Semantics.RelationMaskTrainer", "name": "RelationMaskTrainer", "path": "Semantics/RelationMaskTrainer.lean", "namespace": "Semantics.RelationMaskTrainer", "doc": "RelationMaskTrainer.lean - KS_RELATION_SIEVE Formalization Migrates legacy f64 outcome ratios to strict UInt64 limits.", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 1, "inductive_count": 2, "line_count": 59 }, { "kind": "def", "id": "Semantics.RelationMaskTrainer.observe", "name": "observe", "module": "Semantics.RelationMaskTrainer" }, { "kind": "def", "id": "Semantics.RelationMaskTrainer.recommendForSig", "name": "recommendForSig", "module": "Semantics.RelationMaskTrainer" }, { "kind": "module", "id": "Semantics.ResearchAgent", "name": "ResearchAgent", "path": "Semantics/ResearchAgent.lean", "namespace": "Semantics.ResearchAgent", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ResearchAgent.lean \u2014 Agentic Scientific Discovery via Unified Field Theory This module formalizes an autonomous research agent that uses the unified field \u03a6(x) to guide literature search, hypothesis ge", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 13, "struct_count": 6, "inductive_count": 2, "line_count": 548 }, { "kind": "theorem", "id": "Semantics.ResearchAgent.greedyActionValid", "name": "greedyActionValid", "module": "Semantics.ResearchAgent" }, { "kind": "theorem", "id": "Semantics.ResearchAgent.fieldValueBounded", "name": "fieldValueBounded", "module": "Semantics.ResearchAgent" }, { "kind": "theorem", "id": "Semantics.ResearchAgent.actionProbabilitiesSumToOne", "name": "actionProbabilitiesSumToOne", "module": "Semantics.ResearchAgent" }, { "kind": "theorem", "id": "Semantics.ResearchAgent.iterationIncreases", "name": "iterationIncreases", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.description", "name": "description", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.literaturePhaseDefault", "name": "literaturePhaseDefault", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.hypothesisPhaseDefault", "name": "hypothesisPhaseDefault", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.formalizationPhaseDefault", "name": "formalizationPhaseDefault", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.fieldValue", "name": "fieldValue", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.actionProbability", "name": "actionProbability", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.greedyAction", "name": "greedyAction", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.epsilonGreedyAction", "name": "epsilonGreedyAction", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.executeAction", "name": "executeAction", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.stateTransition", "name": "stateTransition", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.search", "name": "search", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.extract", "name": "extract", "module": "Semantics.ResearchAgent" }, { "kind": "def", "id": "Semantics.ResearchAgent.formalize", "name": "formalize", "module": "Semantics.ResearchAgent" }, { "kind": "module", "id": "Semantics.ResonanceGradient", "name": "ResonanceGradient", "path": "Semantics/ResonanceGradient.lean", "namespace": "Semantics.ResonanceGradient", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ResonanceGradient.lean \u2014 Resonance Gradient Computation for Quaternion Stochastic Differentials This module formalizes the resonance gradient computation as specified in MATH_MODEL_MAP 0.4.4: Resonance", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 1, "def_count": 6, "struct_count": 3, "inductive_count": 0, "line_count": 171 }, { "kind": "theorem", "id": "Semantics.ResonanceGradient.quaternionStochasticEvolutionPreservesUnitWitness", "name": "quaternionStochasticEvolutionPreservesUnitWitness", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.resonanceDifferential", "name": "resonanceDifferential", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.stochasticDifferential", "name": "stochasticDifferential", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.itoCorrection", "name": "itoCorrection", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.quaternionStochasticEvolution", "name": "quaternionStochasticEvolution", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.spherionResonanceGradient", "name": "spherionResonanceGradient", "module": "Semantics.ResonanceGradient" }, { "kind": "def", "id": "Semantics.ResonanceGradient.sluqQuaternionTriage", "name": "sluqQuaternionTriage", "module": "Semantics.ResonanceGradient" }, { "kind": "module", "id": "Semantics.ResourceLayers", "name": "ResourceLayers", "path": "Semantics/ResourceLayers.lean", "namespace": "Semantics.ResourceLayers", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ResourceLayers.lean \u2014 Combined Base + Topological Resource Layers Replaces scripts/combined_resource_layers.py with a formal Lean module that defines physical and topological resource layer structures ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 6, "inductive_count": 0, "line_count": 213 }, { "kind": "def", "id": "Semantics.ResourceLayers.zero", "name": "zero", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.one", "name": "one", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.ofNat", "name": "ofNat", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.toNat", "name": "toNat", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.ofFrac", "name": "ofFrac", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.calculatePhysicalLayer", "name": "calculatePhysicalLayer", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.calculateTopologicalLayer", "name": "calculateTopologicalLayer", "module": "Semantics.ResourceLayers" }, { "kind": "def", "id": "Semantics.ResourceLayers.calculateCombinedTotals", "name": "calculateCombinedTotals", "module": "Semantics.ResourceLayers" }, { "kind": "module", "id": "Semantics.RiemannianResonanceCorrelator", "name": "RiemannianResonanceCorrelator", "path": "Semantics/RiemannianResonanceCorrelator.lean", "namespace": "Semantics.RiemannianResonanceCorrelator", "doc": "RiemannianResonanceCorrelator.lean \u2014 Finding PDE Shortcuts in Particle Physics Data This module implements the Riemannian Resonance Correlator (RRC): a mathematical tool for extracting generating structures from 50 years of particle physics event data. The pipeline: 1. Ingest measured observables ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 15, "struct_count": 8, "inductive_count": 0, "line_count": 374 }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.flat", "name": "flat", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.computeVolume", "name": "computeVolume", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.fromMetric", "name": "fromMetric", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.applyLap", "name": "applyLap", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.extractResonances", "name": "extractResonances", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.learnKernel", "name": "learnKernel", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.applyKernel", "name": "applyKernel", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.discoverPDE", "name": "discoverPDE", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.penguinToEvents", "name": "penguinToEvents", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.penguinPDE", "name": "penguinPDE", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.kernelRGFlow", "name": "kernelRGFlow", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.testLap", "name": "testLap", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.testKernel", "name": "testKernel", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.testPoint", "name": "testPoint", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "def", "id": "Semantics.RiemannianResonanceCorrelator.testPsi", "name": "testPsi", "module": "Semantics.RiemannianResonanceCorrelator" }, { "kind": "module", "id": "Semantics.RotationQUBO", "name": "RotationQUBO", "path": "Semantics/RotationQUBO.lean", "namespace": "Semantics.RotationQUBO", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team RotationQUBO.lean \u2014 Rotation Matrices as Literal Rotation Notation in Frustrated QUBO Fields This module formalizes a 1D scalar triangle navigating a frustrated QUBO field, spawning friends to rotate i", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 13, "struct_count": 6, "inductive_count": 0, "line_count": 259 }, { "kind": "def", "id": "Semantics.RotationQUBO.balanced", "name": "balanced", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.fromPISTCoord", "name": "fromPISTCoord", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.pistMass", "name": "pistMass", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.fromAngle", "name": "fromAngle", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.rotateVertex", "name": "rotateVertex", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.rotateTriangle", "name": "rotateTriangle", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.fieldEnergy", "name": "fieldEnergy", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.isFrustrated", "name": "isFrustrated", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.contains", "name": "contains", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.spawn", "name": "spawn", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.spawnSuperposition", "name": "spawnSuperposition", "module": "Semantics.RotationQUBO" }, { "kind": "def", "id": "Semantics.RotationQUBO.rotationField", "name": "rotationField", "module": "Semantics.RotationQUBO" }, { "kind": "module", "id": "Semantics.RouteCost", "name": "RouteCost", "path": "Semantics/RouteCost.lean", "namespace": "Semantics.RouteCost", "doc": "# Equation Route Cost Finite, Q16.16-scaled route scoring for the first compressed equation graph. The JSON and CSV artifacts are serialization witnesses; this Lean module is the source of truth for the edge-cost computation.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 2, "def_count": 90, "struct_count": 1, "inductive_count": 7, "line_count": 482 }, { "kind": "theorem", "id": "Semantics.RouteCost.routeCostTotal", "name": "routeCostTotal", "module": "Semantics.RouteCost" }, { "kind": "theorem", "id": "Semantics.RouteCost.routeCostSelfZero", "name": "routeCostSelfZero", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.qZero", "name": "qZero", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.qEighth", "name": "qEighth", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.qQuarter", "name": "qQuarter", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.qHalf", "name": "qHalf", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.qOne", "name": "qOne", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.FoundationKernel", "name": "FoundationKernel", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.TopologyLayer", "name": "TopologyLayer", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.SubstrateStage", "name": "SubstrateStage", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.proofBurdenCost", "name": "proofBurdenCost", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.failureRiskCost", "name": "failureRiskCost", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.natAbsDiff", "name": "natAbsDiff", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.optEq", "name": "optEq", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.knownBridge", "name": "knownBridge", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.resolvedStreet", "name": "resolvedStreet", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.kernelDistance", "name": "kernelDistance", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.streetTransitionCost", "name": "streetTransitionCost", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.gwlTopologyDistance", "name": "gwlTopologyDistance", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.substrateExecutionCost", "name": "substrateExecutionCost", "module": "Semantics.RouteCost" }, { "kind": "def", "id": "Semantics.RouteCost.proofObligationCost", "name": "proofObligationCost", "module": "Semantics.RouteCost" }, { "kind": "module", "id": "Semantics.RustOISCDecompressor", "name": "RustOISCDecompressor", "path": "Semantics/RustOISCDecompressor.lean", "namespace": "Semantics.RustOISCDecompressor", "doc": "Rust OISC decompressor target, finite-state Lean surface. This is intentionally small: it proves the shape of the decompressor hot path, not a production codec. The only transition primitive is `step`. Rust, FPGA, and ASIC targets must implement this same state update before promotion.", "math_kind": "avm", "sorry_count": 0, "theorem_count": 14, "def_count": 36, "struct_count": 4, "inductive_count": 2, "line_count": 279 }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.haltedStepStable", "name": "haltedStepStable", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.firstStepEmitsOne", "name": "firstStepEmitsOne", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.abcFixtureByteExact", "name": "abcFixtureByteExact", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.abcFixtureHalts", "name": "abcFixtureHalts", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.residualAccumulatorWrapsClosed", "name": "residualAccumulatorWrapsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.postFinalRunStableClosed", "name": "postFinalRunStableClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.overflowFailsClosed", "name": "overflowFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.abcWireFixtureCloses", "name": "abcWireFixtureCloses", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.emptyWireCloses", "name": "emptyWireCloses", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.overflowWireFailsClosed", "name": "overflowWireFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.invalidMagicFailsClosed", "name": "invalidMagicFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.invalidVersionFailsClosed", "name": "invalidVersionFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.truncatedInstructionFailsClosed", "name": "truncatedInstructionFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "theorem", "id": "Semantics.RustOISCDecompressor.trailingAfterFinalFailsClosed", "name": "trailingAfterFinalFailsClosed", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.byte", "name": "byte", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.mixByte", "name": "mixByte", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.initState", "name": "initState", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.nan0State", "name": "nan0State", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.step", "name": "step", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.runInstructions", "name": "runInstructions", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.run", "name": "run", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.emittedBytes", "name": "emittedBytes", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.parseInstructions", "name": "parseInstructions", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.magic", "name": "magic", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.version", "name": "version", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.header", "name": "header", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.invalidReceipt", "name": "invalidReceipt", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.hasInternalFinal", "name": "hasInternalFinal", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.decodeWire", "name": "decodeWire", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.instrA", "name": "instrA", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.instrB", "name": "instrB", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.instrC", "name": "instrC", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.instrHighResidual", "name": "instrHighResidual", "module": "Semantics.RustOISCDecompressor" }, { "kind": "def", "id": "Semantics.RustOISCDecompressor.instrWrapFinal", "name": "instrWrapFinal", "module": "Semantics.RustOISCDecompressor" }, { "kind": "module", "id": "Semantics.S3C", "name": "S3C", "path": "Semantics/S3C.lean", "namespace": "Semantics.S3C", "doc": "structure ShellCoords where k : Nat -- Shell index (coarse handle) a : Nat -- Lower offset (medium handle) bPlus : Nat -- Next-shell gap (b\u207a = (k+1)\u00b2 - n) bZero : Nat -- Closed-shell complement (b\u2070 = (k+1)\u00b2 - 1 - n) massPlus : Nat -- Open-shell intersection form a*b\u207a massZero : Nat -- Closed-s", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 11, "def_count": 9, "struct_count": 5, "inductive_count": 0, "line_count": 337 }, { "kind": "theorem", "id": "Semantics.S3C.shellDecompositionCorrect", "name": "shellDecompositionCorrect", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.bPlusEqualsBZeroPlusOne", "name": "bPlusEqualsBZeroPlusOne", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.massZeroIsIntersectionForm", "name": "massZeroIsIntersectionForm", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.massPlusIsIntersectionForm", "name": "massPlusIsIntersectionForm", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.closedWidthTheorem", "name": "closedWidthTheorem", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.throatAtShellMidpoint", "name": "throatAtShellMidpoint", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.emitGateSimplified", "name": "emitGateSimplified", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.shellDecompositionCorrect_domain", "name": "shellDecompositionCorrect_domain", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.bPlusEqualsBZeroPlusOne_domain", "name": "bPlusEqualsBZeroPlusOne_domain", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.throatAtShellMidpoint_domain", "name": "throatAtShellMidpoint_domain", "module": "Semantics.S3C" }, { "kind": "theorem", "id": "Semantics.S3C.emitGateSimplified_domain", "name": "emitGateSimplified_domain", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.shellDecomposition", "name": "shellDecomposition", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.audioToManifold", "name": "audioToManifold", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.echoWeights", "name": "echoWeights", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.detectContact", "name": "detectContact", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.mirrorTerm", "name": "mirrorTerm", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.computeJScore", "name": "computeJScore", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.emissionGate", "name": "emissionGate", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.processAudioSample", "name": "processAudioSample", "module": "Semantics.S3C" }, { "kind": "def", "id": "Semantics.S3C.isThroat", "name": "isThroat", "module": "Semantics.S3C" }, { "kind": "module", "id": "Semantics.S3CGeometry", "name": "S3CGeometry", "path": "Semantics/S3CGeometry.lean", "namespace": "S3CGeometry", "doc": "S3CGeometry.lean Helper module for geometric constructions underlying S3C shell decomposition. Provides Euclidean circle-based square root computation and parity bifurcation bridging arithmetic shell decomposition with geometric circle intersection. Math domain: geometric mean theorem circle-diame", "math_kind": "braid", "sorry_count": 0, "theorem_count": 6, "def_count": 2, "struct_count": 5, "inductive_count": 1, "line_count": 184 }, { "kind": "theorem", "id": "Semantics.S3CGeometry.decompositionProperty", "name": "decompositionProperty", "module": "Semantics.S3CGeometry" }, { "kind": "theorem", "id": "Semantics.S3CGeometry.complementProperty", "name": "complementProperty", "module": "Semantics.S3CGeometry" }, { "kind": "theorem", "id": "Semantics.S3CGeometry.parityConsistency", "name": "parityConsistency", "module": "Semantics.S3CGeometry" }, { "kind": "theorem", "id": "Semantics.S3CGeometry.shellIndexProperty", "name": "shellIndexProperty", "module": "Semantics.S3CGeometry" }, { "kind": "theorem", "id": "Semantics.S3CGeometry.offsetProperty", "name": "offsetProperty", "module": "Semantics.S3CGeometry" }, { "kind": "theorem", "id": "Semantics.S3CGeometry.massProperty", "name": "massProperty", "module": "Semantics.S3CGeometry" }, { "kind": "def", "id": "Semantics.S3CGeometry.natParity", "name": "natParity", "module": "Semantics.S3CGeometry" }, { "kind": "def", "id": "Semantics.S3CGeometry.unitSegmentConstruction", "name": "unitSegmentConstruction", "module": "Semantics.S3CGeometry" }, { "kind": "module", "id": "Semantics.S3CResonance", "name": "S3CResonance", "path": "Semantics/S3CResonance.lean", "namespace": "Semantics.S3CResonance", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team S3CResonance.lean \u2014 Ductile Architecture J-Score and MAC-Filter in Q16_16 Implements the S3C-D (Ductile) manifold resonance model and MAC-Filter phase coherence using Q16_16 fixed-point arithmetic per ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 13, "struct_count": 1, "inductive_count": 0, "line_count": 199 }, { "kind": "theorem", "id": "Semantics.S3CResonance.jPeak_correct", "name": "jPeak_correct", "module": "Semantics.S3CResonance" }, { "kind": "theorem", "id": "Semantics.S3CResonance.jPeak_exceeds_god_tier", "name": "jPeak_exceeds_god_tier", "module": "Semantics.S3CResonance" }, { "kind": "theorem", "id": "Semantics.S3CResonance.peakAttainsGodTier", "name": "peakAttainsGodTier", "module": "Semantics.S3CResonance" }, { "kind": "theorem", "id": "Semantics.S3CResonance.peakPhaseHigh", "name": "peakPhaseHigh", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jCoeffNegHalf", "name": "jCoeffNegHalf", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jBias", "name": "jBias", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jCenter", "name": "jCenter", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jGodTierThreshold", "name": "jGodTierThreshold", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.computeJScore", "name": "computeJScore", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.isGodTier", "name": "isGodTier", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.macPhaseThreshold", "name": "macPhaseThreshold", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.macPhaseHigh", "name": "macPhaseHigh", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.kPeak", "name": "kPeak", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jPeak", "name": "jPeak", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.peakState", "name": "peakState", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.jScoreToFloat", "name": "jScoreToFloat", "module": "Semantics.S3CResonance" }, { "kind": "def", "id": "Semantics.S3CResonance.kToFloat", "name": "kToFloat", "module": "Semantics.S3CResonance" }, { "kind": "module", "id": "Semantics.SDPVerify", "name": "SDPVerify", "path": "Semantics/SDPVerify.lean", "namespace": "Semantics.SDPVerify", "doc": "============================================================ SDP CERTIFICATE VERIFICATION ENGINE Sparse polynomial arithmetic over \u211a for verifying SOS (Sum-of-Squares) certificates produced by external SDP solvers. Architecture: External SDP solver (Python shim) \u2192 rational coefficients This module", "math_kind": "algebra", "sorry_count": 1, "theorem_count": 23, "def_count": 30, "struct_count": 2, "inductive_count": 0, "line_count": 714 }, { "kind": "theorem", "id": "Semantics.SDPVerify.foldl_add", "name": "foldl_add", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.evalSparsePoly_foldl_add", "name": "evalSparsePoly_foldl_add", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_cons", "name": "eval_cons", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.evalSparsePoly_append", "name": "evalSparsePoly_append", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.evalTerm_exponentAdd", "name": "evalTerm_exponentAdd", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_mulTermPoly", "name": "eval_mulTermPoly", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_mul", "name": "eval_mul", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_sqPoly", "name": "eval_sqPoly", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.sumSqPoly_foldl_add", "name": "sumSqPoly_foldl_add", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_sumSqPoly", "name": "eval_sumSqPoly", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.weightedSumPoly_foldl_add", "name": "weightedSumPoly_foldl_add", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_weightedSumPoly", "name": "eval_weightedSumPoly", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.sqPoly_eval_nonneg", "name": "sqPoly_eval_nonneg", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.evalTerm_add_same_exponent", "name": "evalTerm_add_same_exponent", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_insertTerm", "name": "eval_insertTerm", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_filter_nonzero_eq_eval", "name": "eval_filter_nonzero_eq_eval", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.foldl_insertTerm_eval", "name": "foldl_insertTerm_eval", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.eval_normalizePoly_eq_eval", "name": "eval_normalizePoly_eq_eval", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.and_eq_true_iff", "name": "and_eq_true_iff", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.polyEqNormalized_eq", "name": "polyEqNormalized_eq", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.polyEqNormalized_eval_eq", "name": "polyEqNormalized_eval_eq", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.polyEq_eval_eq", "name": "polyEq_eval_eq", "module": "Semantics.SDPVerify" }, { "kind": "theorem", "id": "Semantics.SDPVerify.verifyCertificate_sound", "name": "verifyCertificate_sound", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.exponentAdd", "name": "exponentAdd", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.exponentZero", "name": "exponentZero", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.exponentLt", "name": "exponentLt", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.exponentEq", "name": "exponentEq", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.zeroPoly", "name": "zeroPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.constPoly", "name": "constPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.monomialPoly", "name": "monomialPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.addPoly", "name": "addPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.scalePoly", "name": "scalePoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.negPoly", "name": "negPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.mulTermPoly", "name": "mulTermPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.mulPoly", "name": "mulPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.sqPoly", "name": "sqPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.sumSqPoly", "name": "sumSqPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.weightedSumPoly", "name": "weightedSumPoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.insertTerm", "name": "insertTerm", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.normalizePoly", "name": "normalizePoly", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.polyEqNormalized", "name": "polyEqNormalized", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.polyEq", "name": "polyEq", "module": "Semantics.SDPVerify" }, { "kind": "def", "id": "Semantics.SDPVerify.polyIsZero", "name": "polyIsZero", "module": "Semantics.SDPVerify" }, { "kind": "module", "id": "Semantics.SDTA", "name": "SDTA", "path": "Semantics/SDTA.lean", "namespace": "Semantics.SDTA", "doc": "SDTA.lean \u2014 Semantic Degenerate Tensor Adapter The SDTA is a category-theoretic framework where: Problems exist as states x \u2208 X Degeneracy projections \u03a0_D collapse to a chart D Adapters A_ij = \u03a0_Dj \u2218 T_ij \u2218 \u03a0_Di transport between charts Tree composition \u03a8(\u2113) aggregates child adapters This module i", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 10, "def_count": 11, "struct_count": 4, "inductive_count": 0, "line_count": 362 }, { "kind": "theorem", "id": "Semantics.SDTA.degeneracyProjection_idempotent", "name": "degeneracyProjection_idempotent", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.degeneracyProjection_preserves_chart", "name": "degeneracyProjection_preserves_chart", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.treeTransport_natural", "name": "treeTransport_natural", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.adapter_degeneracy_preserved", "name": "adapter_degeneracy_preserved", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.adapter_composition", "name": "adapter_composition", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.semanticMass_symmetric", "name": "semanticMass_symmetric", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.semanticMass_nonneg", "name": "semanticMass_nonneg", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.treeComposition_preserves_chart", "name": "treeComposition_preserves_chart", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.portabilityCoefficient_bounded", "name": "portabilityCoefficient_bounded", "module": "Semantics.SDTA" }, { "kind": "theorem", "id": "Semantics.SDTA.portability_high_semantic_mass_low", "name": "portability_high_semantic_mass_low", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.StateVec", "name": "StateVec", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.DegenerateChart", "name": "DegenerateChart", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.degeneracyProjection", "name": "degeneracyProjection", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.treeTransport", "name": "treeTransport", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.adapter", "name": "adapter", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.semanticMass", "name": "semanticMass", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.treeComposition", "name": "treeComposition", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.portabilityCoefficient", "name": "portabilityCoefficient", "module": "Semantics.SDTA" }, { "kind": "def", "id": "Semantics.SDTA.SDTA_is_category", "name": "SDTA_is_category", "module": "Semantics.SDTA" }, { "kind": "module", "id": "Semantics.SIConstants", "name": "SIConstants", "path": "Semantics/SIConstants.lean", "namespace": "Semantics.SIConstants", "doc": "SIConstants.lean \u2014 SI Defining Constants, Derived Constants, and Measurements All defining constants below are exact under the SI 2019 redefinition (BIPM SI Brochure 9th ed.). They are represented as exact integers (`Nat`/`Int`) where they are integers, and as exact rationals (`Rat`) where they are", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 31, "struct_count": 0, "inductive_count": 0, "line_count": 282 }, { "kind": "def", "id": "Semantics.SIConstants.caesiumFrequency_Hz", "name": "caesiumFrequency_Hz", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.speedOfLight_m_per_s", "name": "speedOfLight_m_per_s", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.planckConstant_J_s", "name": "planckConstant_J_s", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.elementaryCharge_C", "name": "elementaryCharge_C", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.boltzmannConstant_J_per_K", "name": "boltzmannConstant_J_per_K", "module": "Semantics.SIConstants" }, { "kind": "def", "id": 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"Semantics.SIConstants.bohrRadius_m", "name": "bohrRadius_m", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.rydbergEnergy_eV", "name": "rydbergEnergy_eV", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.inverseFineStructureConstant", "name": "inverseFineStructureConstant", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.fineStructureConstant", "name": "fineStructureConstant", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.wienDisplacement_m_K", "name": "wienDisplacement_m_K", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.sunBlackbodyPeak_m", "name": "sunBlackbodyPeak_m", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.massEnergy_1g_J", "name": "massEnergy_1g_J", "module": "Semantics.SIConstants" }, { "kind": "def", "id": "Semantics.SIConstants.molarVolumeSTP_m3", "name": "molarVolumeSTP_m3", "module": "Semantics.SIConstants" }, { "kind": "module", "id": "Semantics.SIMDBranchPrediction", "name": "SIMDBranchPrediction", "path": "Semantics/SIMDBranchPrediction.lean", "namespace": "Semantics.SIMDBranchPrediction", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 6, "struct_count": 4, "inductive_count": 1, "line_count": 211 }, { "kind": "theorem", "id": "Semantics.SIMDBranchPrediction.simdBroadcastPreservesPrediction", "name": "simdBroadcastPreservesPrediction", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "theorem", "id": "Semantics.SIMDBranchPrediction.lawfulActionIncreasesConfidence", "name": "lawfulActionIncreasesConfidence", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.branchPrediction", "name": "branchPrediction", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.simdBroadcast", "name": "simdBroadcast", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.selectTransform", "name": "selectTransform", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.addBranchHint", "name": "addBranchHint", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.isSIMDBranchActionLawful", "name": "isSIMDBranchActionLawful", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "def", "id": "Semantics.SIMDBranchPrediction.simdBranchedBind", "name": "simdBranchedBind", "module": "Semantics.SIMDBranchPrediction" }, { "kind": "module", "id": "Semantics.SLUG3", "name": "SLUG3", "path": "Semantics/SLUG3.lean", "namespace": "Semantics.SLUG3", "doc": "Semantics/SLUG3.lean - Authoritative SLUG-3 Ternary Gate & Opcode Mapping This module formalizes the 27 OISC opcodes derived from the SLUG-3 ternary classification as specified in the N-Folded MMR Gossip EBML Schema. Key mapping: Ternary: { -1, 0, 1 } Formula: k = 9*(y+1) + 3*(u+1) + (v+1) Range: ", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 1, "inductive_count": 2, "line_count": 88 }, { "kind": "def", "id": "Semantics.SLUG3.OpVal", "name": "OpVal", "module": "Semantics.SLUG3" }, { "kind": "def", "id": "Semantics.SLUG3.toInt", "name": "toInt", "module": "Semantics.SLUG3" }, { "kind": "def", "id": "Semantics.SLUG3.toIdx", "name": "toIdx", "module": "Semantics.SLUG3" }, { "kind": "def", "id": "Semantics.SLUG3.key", "name": "key", "module": "Semantics.SLUG3" }, { "kind": "def", "id": "Semantics.SLUG3.decodeOp", "name": "decodeOp", "module": "Semantics.SLUG3" }, { "kind": "def", "id": "Semantics.SLUG3.landauerCostBits", "name": "landauerCostBits", "module": "Semantics.SLUG3" }, { "kind": "module", "id": "Semantics.SLUQ", "name": "SLUQ", "path": "Semantics/SLUQ.lean", "namespace": "Semantics.SLUQ", "doc": "SLUQ.lean - SLUQ Decision Engine Formalization", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 7, "struct_count": 1, "inductive_count": 2, "line_count": 68 }, { "kind": "def", "id": "Semantics.SLUQ.evaluateState", "name": "evaluateState", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.evaluateStateInt", "name": "evaluateStateInt", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.updateNode", "name": "updateNode", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.tempQ16", "name": "tempQ16", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.sluqCost", "name": "sluqCost", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.sluqInvariant", "name": "sluqInvariant", "module": "Semantics.SLUQ" }, { "kind": "def", "id": "Semantics.SLUQ.sluqBind", "name": "sluqBind", "module": "Semantics.SLUQ" }, { "kind": "module", "id": "Semantics.SLUQQuaternionIntegration", "name": "SLUQQuaternionIntegration", "path": "Semantics/SLUQQuaternionIntegration.lean", "namespace": "Semantics.SLUQQuaternionIntegration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SLUQQuaternionIntegration.lean \u2014 SLUQ Triage Integration for Quaternion Optimization This module provides the integration layer between SLUQ triage and quaternion stochastic optimization, as recommende", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 160 }, { "kind": "theorem", "id": "Semantics.SLUQQuaternionIntegration.sluqQuaternionOptimizationPreservesUnitWitness", "name": "sluqQuaternionOptimizationPreservesUnitWitness", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "theorem", "id": "Semantics.SLUQQuaternionIntegration.pruningPreservesReceipt", "name": "pruningPreservesReceipt", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "def", "id": "Semantics.SLUQQuaternionIntegration.cacheLocalQuaternionTriage", "name": "cacheLocalQuaternionTriage", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "def", "id": "Semantics.SLUQQuaternionIntegration.pruneQuaternionTrajectories", "name": "pruneQuaternionTrajectories", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "def", "id": "Semantics.SLUQQuaternionIntegration.sluqQuaternionOptimizationStep", "name": "sluqQuaternionOptimizationStep", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "def", "id": "Semantics.SLUQQuaternionIntegration.multiTrajectoryQuaternionOptimization", "name": "multiTrajectoryQuaternionOptimization", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "def", "id": "Semantics.SLUQQuaternionIntegration.quaternionTrajectoryConverged", "name": "quaternionTrajectoryConverged", "module": "Semantics.SLUQQuaternionIntegration" }, { "kind": "module", "id": "Semantics.SLUQTriage", "name": "SLUQTriage", "path": "Semantics/SLUQTriage.lean", "namespace": "Semantics.SLUQTriage", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 4, "inductive_count": 1, "line_count": 238 }, { "kind": "theorem", "id": "Semantics.SLUQTriage.lawfulTriageMaintainsNonNegativeEfficiency", "name": "lawfulTriageMaintainsNonNegativeEfficiency", "module": "Semantics.SLUQTriage" }, { "kind": "theorem", "id": "Semantics.SLUQTriage.triageEfficiencyMonotonicWithPruning", "name": "triageEfficiencyMonotonicWithPruning", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.calculateTriageScore", "name": "calculateTriageScore", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.shouldPruneTrajectory", "name": "shouldPruneTrajectory", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.shouldCacheTrajectory", "name": "shouldCacheTrajectory", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.classifyTriageDecision", "name": "classifyTriageDecision", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.applyTriage", "name": "applyTriage", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.calculateTriageEfficiency", "name": "calculateTriageEfficiency", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.isTriageActionLawful", "name": "isTriageActionLawful", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.updateTrajectory", "name": "updateTrajectory", "module": "Semantics.SLUQTriage" }, { "kind": "def", "id": "Semantics.SLUQTriage.triageBind", "name": "triageBind", "module": "Semantics.SLUQTriage" }, { "kind": "module", "id": "Semantics.SMEFTExtension", "name": "SMEFTExtension", "path": "Semantics/SMEFTExtension.lean", "namespace": "Semantics.SMEFTExtension", "doc": "SMEFTExtension.lean \u2014 Standard Model Effective Field Theory This module formalizes the SMEFT framework for extending the Standard Model to account for observed anomalies (muon g-2, B\u2192K*\u03bc\u03bc, W mass, etc.). The key equation: H_SMEFT = H_SM + \u03a3_i (C_i^(6)/\u039b\u00b2) O_i^(6) + \u03a3_j (C_j^(8)/\u039b\u2074) O_j^(8) Where:", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 9, "struct_count": 4, "inductive_count": 0, "line_count": 177 }, { "kind": "def", "id": "Semantics.SMEFTExtension.smWilson", "name": "smWilson", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.lhcbAnomaly", "name": "lhcbAnomaly", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.effectiveWilson", "name": "effectiveWilson", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.extractEnergyScale", "name": "extractEnergyScale", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.relevantOps", "name": "relevantOps", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.differentialRate", "name": "differentialRate", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.extractLeptoquarkMass", "name": "extractLeptoquarkMass", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.testEff", "name": "testEff", "module": "Semantics.SMEFTExtension" }, { "kind": "def", "id": "Semantics.SMEFTExtension.testLQ", "name": "testLQ", "module": "Semantics.SMEFTExtension" }, { "kind": "module", "id": "Semantics.SSMS", "name": "SSMS", "path": "Semantics/SSMS.lean", "namespace": "Semantics.SSMS", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SSMS.lean \u2014 Scalar-Spawning Manifold State Machine Full Lean 4 formalization covering: \u00a71 Q16.16 fixed-point arithmetic \u00a72 Ternary weights and dot product \u00a73 BitLinear activation scaling \u00a74 MLGRU r", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 14, "def_count": 67, "struct_count": 16, "inductive_count": 1, "line_count": 1202 }, { "kind": "theorem", "id": "Semantics.SSMS.compressionRatio", "name": "compressionRatio", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.fp16Compression", "name": "fp16Compression", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.jPhantomBounded", "name": "jPhantomBounded", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.testEdgesWf", "name": "testEdgesWf", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.mul_eq_for_bounded", "name": "mul_eq_for_bounded", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.ediv_add_bound_nonneg", "name": "ediv_add_bound_nonneg", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.ediv_add_bound", "name": "ediv_add_bound", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.abs_toInt_eq_clamp_abs", "name": "abs_toInt_eq_clamp_abs", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.abs_sub_val_le", "name": "abs_sub_val_le", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.aciPreservedByMlgruStep", "name": "aciPreservedByMlgruStep", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.conflictFree", "name": "conflictFree", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.mlgru_blend_diff_le", "name": "mlgru_blend_diff_le", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.ssms_step_nonexpansive", "name": "ssms_step_nonexpansive", "module": "Semantics.SSMS" }, { "kind": "theorem", "id": "Semantics.SSMS.ssms_contraction_theorem", "name": "ssms_contraction_theorem", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.TernaryWeight", "name": "TernaryWeight", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.wordsNeeded", "name": "wordsNeeded", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.TernarySlice", "name": "TernarySlice", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.BitLinearParams", "name": "BitLinearParams", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.bitLinearScale", "name": "bitLinearScale", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.mlgruStep", "name": "mlgruStep", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.MlgruState", "name": "MlgruState", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.ScalarNode", "name": "ScalarNode", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.poolRank", "name": "poolRank", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.SubleqCore", "name": "SubleqCore", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.ioIn", "name": "ioIn", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.ioOut", "name": "ioOut", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.sVal", "name": "sVal", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.sigmaPort", "name": "sigmaPort", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.energyPort", "name": "energyPort", "module": "Semantics.SSMS" }, { "kind": "def", "id": "Semantics.SSMS.tauSpawn", "name": "tauSpawn", "module": "Semantics.SSMS" }, { "kind": "module", "id": "Semantics.SSMS_nD", "name": "SSMS_nD", "path": "Semantics/SSMS_nD.lean", "namespace": "Semantics.SSMS_nD", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SSMS_nD.lean \u2014 Variable Dimension Manifold Extension Extends SSMS with n-dimensional manifold support: \u00a71 VariableDimensionManifold structure with dynamic n \u00a72 LiftingOperator L_{1D\u2192n} for sequential", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 37, "struct_count": 9, "inductive_count": 0, "line_count": 533 }, { "kind": "theorem", "id": "Semantics.SSMS_nD.scalarCountMonotonic", "name": "scalarCountMonotonic", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.scalarCount", "name": "scalarCount", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.nMax", "name": "nMax", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.validN", "name": "validN", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.pool1D", "name": "pool1D", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.lift1DToN", "name": "lift1DToN", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.approxInverseChart", "name": "approxInverseChart", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.constraintResidual", "name": "constraintResidual", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.constraintsSatisfied", "name": "constraintsSatisfied", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.constraintPotential", "name": "constraintPotential", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.projectDown", "name": "projectDown", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.dynamicCenterDist", "name": "dynamicCenterDist", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.dynamicACI", "name": "dynamicACI", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.dynamicSuppresses", "name": "dynamicSuppresses", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.manifoldsOfDim", "name": "manifoldsOfDim", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.bettiSwooshND", "name": "bettiSwooshND", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.dimensionPotential", "name": "dimensionPotential", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.totalPotentialWithDim", "name": "totalPotentialWithDim", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.liftKernel", "name": "liftKernel", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.constrainKernel", "name": "constrainKernel", "module": "Semantics.SSMS_nD" }, { "kind": "def", "id": "Semantics.SSMS_nD.varDimMemoryLayout", "name": "varDimMemoryLayout", "module": "Semantics.SSMS_nD" }, { "kind": "module", "id": "Semantics.SabotagePrevention", "name": "SabotagePrevention", "path": "Semantics/SabotagePrevention.lean", "namespace": "Semantics.SabotagePrevention", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 5, "inductive_count": 2, "line_count": 323 }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkLegitimateImprovement", "name": "checkLegitimateImprovement", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkResourceStarvation", "name": "checkResourceStarvation", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkNetworkConnectivity", "name": "checkNetworkConnectivity", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkKnowledgeIntegrity", "name": "checkKnowledgeIntegrity", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkServiceDisruptionBenefit", "name": "checkServiceDisruptionBenefit", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkSynchronizationStability", "name": "checkSynchronizationStability", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkNoInfluenceSeeking", "name": "checkNoInfluenceSeeking", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isResourceStarvation", "name": "isResourceStarvation", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isDataCorruption", "name": "isDataCorruption", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isNetworkPartition", "name": "isNetworkPartition", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isSynchronizationAttack", "name": "isSynchronizationAttack", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isInfluenceSeeking", "name": "isInfluenceSeeking", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.sabotageBind", "name": "sabotageBind", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkConsistency", "name": "checkConsistency", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.checkCompleteness", "name": "checkCompleteness", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.systemSelfReference", "name": "systemSelfReference", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.godelNumber", "name": "godelNumber", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.isRestorationWarranted", "name": "isRestorationWarranted", "module": "Semantics.SabotagePrevention" }, { "kind": "def", "id": "Semantics.SabotagePrevention.evaluateRestorationBenefit", "name": "evaluateRestorationBenefit", "module": "Semantics.SabotagePrevention" }, { "kind": "module", "id": "Semantics.ScalarCollapse", "name": "ScalarCollapse", "path": "Semantics/ScalarCollapse.lean", "namespace": "Semantics.ENE", "doc": "Scalar Collapse", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 7, "def_count": 1, "struct_count": 6, "inductive_count": 0, "line_count": 136 }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.no_scalar_without_atomic_ancestry", "name": "no_scalar_without_atomic_ancestry", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.no_scalar_without_lawful_history", "name": "no_scalar_without_lawful_history", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.no_scalar_without_load_visibility", "name": "no_scalar_without_load_visibility", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.no_scalar_without_capability_visibility", "name": "no_scalar_without_capability_visibility", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.exact_collapse_matches_policy", "name": "exact_collapse_matches_policy", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.collapse_policy_preserves_required_invariants", "name": "collapse_policy_preserves_required_invariants", "module": "Semantics.ScalarCollapse" }, { "kind": "theorem", "id": "Semantics.ScalarCollapse.collapse_preserves_universality_requirement", "name": "collapse_preserves_universality_requirement", "module": "Semantics.ScalarCollapse" }, { "kind": "def", "id": "Semantics.ScalarCollapse.ScalarAdmissible", "name": "ScalarAdmissible", "module": "Semantics.ScalarCollapse" }, { "kind": "module", "id": "Semantics.ScalarEventProjection", "name": "ScalarEventProjection", "path": "Semantics/ScalarEventProjection.lean", "namespace": "Semantics.ScalarEventProjection", "doc": "ScalarEventProjection.lean \u2014 Scalar Event Multi-Projection Theory This module formalizes scalar event multi-projection theory: one scalar work event can produce more usable structure when projected through calculation, defense, and verification lanes than when used for calculation alone. Per AGENT", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 8, "struct_count": 4, "inductive_count": 1, "line_count": 172 }, { "kind": "theorem", "id": "Semantics.ScalarEventProjection.sameEntropyFeedsAllLanes", "name": "sameEntropyFeedsAllLanes", "module": "Semantics.ScalarEventProjection" }, { "kind": "theorem", "id": "Semantics.ScalarEventProjection.multiProjectionMoreStructure", "name": "multiProjectionMoreStructure", "module": "Semantics.ScalarEventProjection" }, { "kind": "theorem", "id": "Semantics.ScalarEventProjection.multiProjectionHasThreeValidLanes", "name": "multiProjectionHasThreeValidLanes", "module": "Semantics.ScalarEventProjection" }, { "kind": "theorem", "id": "Semantics.ScalarEventProjection.failureModeRouting", "name": "failureModeRouting", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.computeCalculationProjection", "name": "computeCalculationProjection", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.computeDefenseProjection", "name": "computeDefenseProjection", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.computeVerificationProjection", "name": "computeVerificationProjection", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.computeMultiProjection", "name": "computeMultiProjection", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.applyValueGate", "name": "applyValueGate", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.projectionYield", "name": "projectionYield", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.multiProjectionYield", "name": "multiProjectionYield", "module": "Semantics.ScalarEventProjection" }, { "kind": "def", "id": "Semantics.ScalarEventProjection.exampleScalarEvent", "name": "exampleScalarEvent", "module": "Semantics.ScalarEventProjection" }, { "kind": "module", "id": "Semantics.Scratch", "name": "Scratch", "path": "Semantics/Scratch.lean", "namespace": "Semantics.AgenticOrchestration", "doc": "", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 3, "inductive_count": 2, "line_count": 117 }, { "kind": "def", "id": "Semantics.Scratch.create", "name": "create", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.send", "name": "send", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.receive", "name": "receive", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.deliver", "name": "deliver", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.flushOutbox", "name": "flushOutbox", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.inboxSize", "name": "inboxSize", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.empty", "name": "empty", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.registerMailbox", "name": "registerMailbox", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.findMailbox", "name": "findMailbox", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.updateMailbox", "name": "updateMailbox", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.deliveryCycle", "name": "deliveryCycle", "module": "Semantics.Scratch" }, { "kind": "def", "id": "Semantics.Scratch.totalPending", "name": "totalPending", "module": "Semantics.Scratch" }, { "kind": "module", "id": "Semantics.Search", "name": "Search", "path": "Semantics/Search.lean", "namespace": "Semantics.Search", "doc": "\u03c6 \u2248 1.618033988749895, so \u03c6\u207b\u00b9 \u2248 0.618, \u03c6\u207b\u00b2 \u2248 0.382, etc. These are computed as round(\u03c6\u207b\u2071 \u00d7 65536).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 114 }, { "kind": "def", "id": "Semantics.Search.phiWeights", "name": "phiWeights", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.q16_16_of_nat", "name": "q16_16_of_nat", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.queryVector", "name": "queryVector", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.weightedDot", "name": "weightedDot", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.weightedMag", "name": "weightedMag", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.similarity", "name": "similarity", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.rrfScore", "name": "rrfScore", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.similarityThreshold", "name": "similarityThreshold", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.rrfK", "name": "rrfK", "module": "Semantics.Search" }, { "kind": "def", "id": "Semantics.Search.hybridSearch", "name": "hybridSearch", "module": "Semantics.Search" }, { "kind": "module", "id": "Semantics.Selfies", "name": "Selfies", "path": "Semantics/Selfies.lean", "namespace": "Selfies", "doc": "Selfies.lean - SELFIES String Parser SELFIES (Self-Referencing Embedded Strings) is a robust string representation for molecular graphs that guarantees validity during generative modeling. Unlike SMILES, SELFIES has a context-free grammar that prevents invalid molecular structures during generatio", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 4, "def_count": 6, "struct_count": 3, "inductive_count": 6, "line_count": 287 }, { "kind": "theorem", "id": "Semantics.Selfies.notValidEmpty", "name": "notValidEmpty", "module": "Semantics.Selfies" }, { "kind": "theorem", "id": "Semantics.Selfies.validCarbon", "name": "validCarbon", "module": "Semantics.Selfies" }, { "kind": "theorem", "id": "Semantics.Selfies.validEthanol", "name": "validEthanol", "module": "Semantics.Selfies" }, { "kind": "theorem", "id": "Semantics.Selfies.validCO2", "name": "validCO2", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.parseAtomSymbol", "name": "parseAtomSymbol", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.parse", "name": "parse", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.isValid", "name": "isValid", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.smilesAtomToSelfies", "name": "smilesAtomToSelfies", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.smilesBondToSelfies", "name": "smilesBondToSelfies", "module": "Semantics.Selfies" }, { "kind": "def", "id": "Semantics.Selfies.fromSmiles", "name": "fromSmiles", "module": "Semantics.Selfies" }, { "kind": "module", "id": "Semantics.SemanticMass", "name": "SemanticMass", "path": "Semantics/SemanticMass.lean", "namespace": "Semantics", "doc": "Semantic Mass Theory ID: SEMANTIC-MASS-1 This module formalizes semantic mass as a dimensionless formal scalar assigned to concepts, packets, or manifold states. STATUS: SEMANTIC_MODELING WARNING: NOT_PHYSICAL_MASS NOT_SI_MAPPED Semantic mass is mass-like because it controls inertia, attraction, c", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 17, "struct_count": 7, "inductive_count": 3, "line_count": 578 }, { "kind": "theorem", "id": "Semantics.SemanticMass.massInvariantUnderDomainTranslation", "name": "massInvariantUnderDomainTranslation", "module": "Semantics.SemanticMass" }, { "kind": "theorem", "id": "Semantics.SemanticMass.semanticAttraction_nonneg", "name": "semanticAttraction_nonneg", "module": "Semantics.SemanticMass" }, { "kind": "theorem", "id": "Semantics.SemanticMass.semanticInertia_nonneg", "name": "semanticInertia_nonneg", "module": "Semantics.SemanticMass" }, { "kind": "theorem", "id": "Semantics.SemanticMass.semanticMassChange_nonpos", "name": "semanticMassChange_nonpos", "module": "Semantics.SemanticMass" }, { "kind": "theorem", "id": "Semantics.SemanticMass.semanticMassChange_pos", "name": "semanticMassChange_pos", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.massNonneg", "name": "massNonneg", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticEnergy", "name": "semanticEnergy", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticAttraction", "name": "semanticAttraction", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticInertia", "name": "semanticInertia", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticMassChange", "name": "semanticMassChange", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.massVectorOf", "name": "massVectorOf", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.fammWeight", "name": "fammWeight", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.rrcWeight", "name": "rrcWeight", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.massFromSidonSignature", "name": "massFromSidonSignature", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.weightedMass", "name": "weightedMass", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticMassOf", "name": "semanticMassOf", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.massDistance", "name": "massDistance", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.routeScore", "name": "routeScore", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.couplingStrength", "name": "couplingStrength", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.semanticWeight", "name": "semanticWeight", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.massAfterCoupling", "name": "massAfterCoupling", "module": "Semantics.SemanticMass" }, { "kind": "def", "id": "Semantics.SemanticMass.imaginaryUnitSemanticMass", "name": "imaginaryUnitSemanticMass", "module": "Semantics.SemanticMass" }, { "kind": "module", "id": "Semantics.SemanticRGFlow", "name": "SemanticRGFlow", "path": "Semantics/SemanticRGFlow.lean", "namespace": "Semantics.SemanticRGFlow", "doc": "SemanticRGFlow.lean Formalizes Semantic Renormalization Group (RG) Flow in LLM Latent Spaces. Validating implementation against: Li & Wang (2018): \"Neural Network Renormalization Group\" (arXiv:1802.02840) Zhao et al. (2026): \"Application of Deep Neural Networks for Computing RG Flow\" (arXiv:2510.06", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 9, "inductive_count": 0, "line_count": 149 }, { "kind": "def", "id": "Semantics.SemanticRGFlow.attractorDescent", "name": "attractorDescent", "module": "Semantics.SemanticRGFlow" }, { "kind": "module", "id": "Semantics.SensorField", "name": "SensorField", "path": "Semantics/SensorField.lean", "namespace": "Semantics.SensorField", "doc": "", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 19, "struct_count": 8, "inductive_count": 8, "line_count": 367 }, { "kind": "def", "id": "Semantics.SensorField.isRfBand", "name": "isRfBand", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.isOpticalBand", "name": "isOpticalBand", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.modalityBandCompatible", "name": "modalityBandCompatible", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.intensityWithinWindow", "name": "intensityWithinWindow", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.bandAccepted", "name": "bandAccepted", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.sampleCompatibleWithField", "name": "sampleCompatibleWithField", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.sampleCompatibleWithBoundary", "name": "sampleCompatibleWithBoundary", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.sampleCompatibleWithLink", "name": "sampleCompatibleWithLink", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.deriveErrorField", "name": "deriveErrorField", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.classifyErrorDisposition", "name": "classifyErrorDisposition", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.assessSensorError", "name": "assessSensorError", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.classifyDetectionClass", "name": "classifyDetectionClass", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.classifySensorRegime", "name": "classifySensorRegime", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.detectionConfidence", "name": "detectionConfidence", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.detectSample", "name": "detectSample", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.channelSupportsDetection", "name": "channelSupportsDetection", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.fieldAdmitsTransition", "name": "fieldAdmitsTransition", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.wifiSensorField", "name": "wifiSensorField", "module": "Semantics.SensorField" }, { "kind": "def", "id": "Semantics.SensorField.opticalProbeField", "name": "opticalProbeField", "module": "Semantics.SensorField" }, { "kind": "module", "id": "Semantics.ShellModel", "name": "ShellModel", "path": "Semantics/ShellModel.lean", "namespace": "Semantics.ShellModel", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team ShellModel.lean \u2014 Shell State Geometry and Event Classification This module implements the Erd\u0151s #1196 piecewise eigenvector construction for shell-based event classification. It provides: \u2022 Shell stat", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 2, "inductive_count": 0, "line_count": 181 }, { "kind": "def", "id": "Semantics.ShellModel.isqrt", "name": "isqrt", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.shellState", "name": "shellState", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.classifyEvent", "name": "classifyEvent", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.tipCoord", "name": "tipCoord", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.eventAt", "name": "eventAt", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.SpectralSignature", "name": "SpectralSignature", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.tailWeight", "name": "tailWeight", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.clampInt", "name": "clampInt", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.phaseFromTipAndInteraction", "name": "phaseFromTipAndInteraction", "module": "Semantics.ShellModel" }, { "kind": "def", "id": "Semantics.ShellModel.indexBitFromInteraction", "name": "indexBitFromInteraction", "module": "Semantics.ShellModel" }, { "kind": "module", "id": "Semantics.ShortestObservableTime", "name": "ShortestObservableTime", "path": "Semantics/ShortestObservableTime.lean", "namespace": "Semantics.ShortestObservableTime", "doc": "ShortestObservableTime.lean -- What Is the Absolute Shortest Observable Time? The user asks: what is the shortest time at which any amount of energy can be observed at any scale? This is a genuine physics question about the fundamental limits of time observation. This module answers the question r", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 4, "def_count": 10, "struct_count": 0, "inductive_count": 0, "line_count": 218 }, { "kind": "theorem", "id": "Semantics.ShortestObservableTime.for", "name": "for", "module": "Semantics.ShortestObservableTime" }, { "kind": "theorem", "id": "Semantics.ShortestObservableTime.planckTimePositive", "name": "planckTimePositive", "module": "Semantics.ShortestObservableTime" }, { "kind": "theorem", "id": "Semantics.ShortestObservableTime.secondsIn61YearsPositive", "name": "secondsIn61YearsPositive", "module": "Semantics.ShortestObservableTime" }, { "kind": "theorem", "id": "Semantics.ShortestObservableTime.thermalMinTimePositive", "name": "thermalMinTimePositive", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.hbarSI", "name": "hbarSI", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.planckEnergyJ", "name": "planckEnergyJ", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.heisenbergMinTime", "name": "heisenbergMinTime", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.planckTimeFromHeisenberg", "name": "planckTimeFromHeisenberg", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.nuclearMinTime", "name": "nuclearMinTime", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.atomicMinTime", "name": "atomicMinTime", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.thermalMinTime", "name": "thermalMinTime", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.ecologicalMinTime", "name": "ecologicalMinTime", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.planckTicksIn61Years", "name": "planckTicksIn61Years", "module": "Semantics.ShortestObservableTime" }, { "kind": "def", "id": "Semantics.ShortestObservableTime.thermalTicksIn61Years", "name": "thermalTicksIn61Years", "module": "Semantics.ShortestObservableTime" }, { "kind": "module", "id": "Semantics.SidonAVM", "name": "SidonAVM", "path": "Semantics/SidonAVM.lean", "namespace": "Semantics.SidonAVM", "doc": "This module implements the greedy Sidon set generator as an AVM program. The AVM state encodes the Sidon construction state in memory: M[0] = target size (k) M[1] = current length M[2..9] = current elements (max 8 slots for braid strands) M[10] = candidate M[11] = canAdd result (1 = yes, 0 = no) M", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 3, "def_count": 24, "struct_count": 1, "inductive_count": 0, "line_count": 204 }, { "kind": "theorem", "id": "Semantics.SidonAVM.sidonAVM_eq_generateSidonFuel", "name": "sidonAVM_eq_generateSidonFuel", "module": "Semantics.SidonAVM" }, { "kind": "theorem", "id": "Semantics.SidonAVM.sidonAVM_isSidonList", "name": "sidonAVM_isSidonList", "module": "Semantics.SidonAVM" }, { "kind": "theorem", "id": "Semantics.SidonAVM.sidonAVM_terminates", "name": "sidonAVM_terminates", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.maxSidonSize", "name": "maxSidonSize", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memTarget", "name": "memTarget", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memCurrentLen", "name": "memCurrentLen", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memCurrentBase", "name": "memCurrentBase", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memCandidate", "name": "memCandidate", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memCanAdd", "name": "memCanAdd", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memLoopI", "name": "memLoopI", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memLoopJ", "name": "memLoopJ", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memTempSum", "name": "memTempSum", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.memTempFlag", "name": "memTempFlag", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.initMemory", "name": "initMemory", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.readNat", "name": "readNat", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.readCurrent", "name": "readCurrent", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.readCandidate", "name": "readCandidate", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonCheckDone", "name": "sidonCheckDone", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonTryAdd", "name": "sidonTryAdd", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonIncrementCandidate", "name": "sidonIncrementCandidate", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonStep", "name": "sidonStep", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonRun", "name": "sidonRun", "module": "Semantics.SidonAVM" }, { "kind": "def", "id": "Semantics.SidonAVM.sidonProgram", "name": "sidonProgram", "module": "Semantics.SidonAVM" }, { "kind": "module", "id": "Semantics.SidonSet", "name": "SidonSet", "path": "Semantics/SidonSet.lean", "namespace": "Semantics.SidonSet", "doc": "A Sidon set (also called a B\u2082 set or Erd\u0151s\u2013Sidon set) is a set of natural numbers where all pairwise sums a + b (with a \u2264 b) are unique. This module implements a greedy generator for Sidon sets and provides utilities for checking the Sidon property. Such sets have applications in: Frequency assignm", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 0, "inductive_count": 0, "line_count": 111 }, { "kind": "def", "id": "Semantics.SidonSet.isSidon", "name": "isSidon", "module": "Semantics.SidonSet" }, { "kind": "def", "id": "Semantics.SidonSet.pairwiseSums", "name": "pairwiseSums", "module": "Semantics.SidonSet" }, { "kind": "def", "id": "Semantics.SidonSet.canAdd", "name": "canAdd", "module": "Semantics.SidonSet" }, { "kind": "def", "id": "Semantics.SidonSet.generateSidonFuel", "name": "generateSidonFuel", "module": "Semantics.SidonSet" }, { "kind": "def", "id": "Semantics.SidonSet.main", "name": "main", "module": "Semantics.SidonSet" }, { "kind": "module", "id": "Semantics.SidonSets", "name": "SidonSets", "path": "Semantics/SidonSets.lean", "namespace": "Semantics.SidonSets", "doc": "Port of the reusable Sidon-set infrastructure from Hulak\u2013Ramos\u2013de Queiroz (2026), \"Formalizing Singer Sidon Constructions and Sidon Set Infrastructure in Lean 4\" (arXiv: 2605.03274). Original Lean 4 source: https://github.com/d0d1/singer-theorem-lean Commit: 0c890589afc58e8955a5d7c3a609daff6447da31", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 68, "def_count": 17, "struct_count": 1, "inductive_count": 0, "line_count": 1806 }, { "kind": "theorem", "id": "Semantics.SidonSets.IsSidonMod", "name": "IsSidonMod", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.IsIntervalSidon", "name": "IsIntervalSidon", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.IsSidon", "name": "IsSidon", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sidonMaximum_exists", "name": "sidonMaximum_exists", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sidonMaximum_isSidonMaximum", "name": "sidonMaximum_isSidonMaximum", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.isSidonMaximum_unique", "name": "isSidonMaximum_unique", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sidonMaximum_le_sqrt_two", "name": "sidonMaximum_le_sqrt_two", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sortedLT_take_lt_drop", "name": "sortedLT_take_lt_drop", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.johnson_numerical", "name": "johnson_numerical", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.incidence_inequality", "name": "incidence_inequality", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sidon_intersection_sum_bound", "name": "sidon_intersection_sum_bound", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.lindstrom_monotone", "name": "lindstrom_monotone", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.sidonMaximum_le_lindstrom", "name": "sidonMaximum_le_lindstrom", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.finrank_ext", "name": "finrank_ext", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.trace_surjective", "name": "trace_surjective", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.finrank_ker_trace", "name": "finrank_ker_trace", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.minpoly_degree_eq_three", "name": "minpoly_degree_eq_three", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.linIndep_smul_v", "name": "linIndep_smul_v", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.no_proper_invariant_subspace", "name": "no_proper_invariant_subspace", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.finrank_inf_of_distinct_twodim", "name": "finrank_inf_of_distinct_twodim", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.mem_scaledSubmodule_iff", "name": "mem_scaledSubmodule_iff", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.finrank_scaledSubmodule", "name": "finrank_scaledSubmodule", "module": "Semantics.SidonSets" }, { "kind": "theorem", "id": "Semantics.SidonSets.ker_trace_ne_bot", "name": "ker_trace_ne_bot", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.IsSidonNat", "name": "IsSidonNat", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.translate", "name": "translate", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.IsSidonMaximum", "name": "IsSidonMaximum", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.kerBasis", "name": "kerBasis", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.repV", "name": "repV", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.rep", "name": "rep", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.SingerFamilyHypothesis", "name": "SingerFamilyHypothesis", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.Erdos30Statement", "name": "Erdos30Statement", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.SidonChaosAddresses", "name": "SidonChaosAddresses", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.strandOfAddress", "name": "strandOfAddress", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.addressOfStrand", "name": "addressOfStrand", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.sidon_chaos_address", "name": "sidon_chaos_address", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.ChaosStrand", "name": "ChaosStrand", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.trajectoryAddress", "name": "trajectoryAddress", "module": "Semantics.SidonSets" }, { "kind": "def", "id": "Semantics.SidonSets.sidon_address_valid", "name": "sidon_address_valid", "module": "Semantics.SidonSets" }, { "kind": "module", "id": "Semantics.SieveLemmas", "name": "SieveLemmas", "path": "Semantics/SieveLemmas.lean", "namespace": "Semantics.SieveLemmas", "doc": "SieveLemmas.lean -- Number-theoretic lemmas for coprime sieve observers This module formalizes the CRT reconstruction principle referenced in ImaginarySemanticTime.lean: two observers with coprime native sieve moduli hold independent, complementary shadows of the same underlying manifold coordinate", "math_kind": "number_theory", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 1, "inductive_count": 0, "line_count": 112 }, { "kind": "theorem", "id": "Semantics.SieveLemmas.observe_lt", "name": "observe_lt", "module": "Semantics.SieveLemmas" }, { "kind": "theorem", "id": "Semantics.SieveLemmas.crtReconstruct_mod_\u21131", "name": "crtReconstruct_mod_\u21131", "module": "Semantics.SieveLemmas" }, { "kind": "theorem", "id": "Semantics.SieveLemmas.crtReconstruct_mod_\u21132", "name": "crtReconstruct_mod_\u21132", "module": "Semantics.SieveLemmas" }, { "kind": "theorem", "id": "Semantics.SieveLemmas.depth_token_coprime_intersect", "name": "depth_token_coprime_intersect", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.observe", "name": "observe", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.CoprimeObservers", "name": "CoprimeObservers", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.crtReconstruct", "name": "crtReconstruct", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.human\u2113", "name": "human\u2113", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.dolphin\u2113", "name": "dolphin\u2113", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.shared", "name": "shared", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.humanShadow", "name": "humanShadow", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.dolphinShadow", "name": "dolphinShadow", "module": "Semantics.SieveLemmas" }, { "kind": "def", "id": "Semantics.SieveLemmas.reconciled", "name": "reconciled", "module": "Semantics.SieveLemmas" }, { "kind": "module", "id": "Semantics.SigmaGate", "name": "SigmaGate", "path": "Semantics/SigmaGate.lean", "namespace": "Semantics.SigmaGate", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SigmaGate.lean \u2014 Fixed-Point Conformal Confidence Gating This module formalizes the \u03c3-gate concept from empirical LLM safety systems (Creation OS / Spektre Labs) into a Lean-verified, hardware-native i", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 6, "def_count": 19, "struct_count": 9, "inductive_count": 2, "line_count": 642 }, { "kind": "theorem", "id": "Semantics.SigmaGate.sigmaGateAcceptsCorrect", "name": "sigmaGateAcceptsCorrect", "module": "Semantics.SigmaGate" }, { "kind": "theorem", "id": "Semantics.SigmaGate.sigmaGateRejectsIncorrect", "name": "sigmaGateRejectsIncorrect", "module": "Semantics.SigmaGate" }, { "kind": "theorem", "id": "Semantics.SigmaGate.conformalCoverageGuarantee", "name": "conformalCoverageGuarantee", "module": "Semantics.SigmaGate" }, { "kind": "theorem", "id": "Semantics.SigmaGate.conformalHighConfidenceAccept", "name": "conformalHighConfidenceAccept", "module": "Semantics.SigmaGate" }, { "kind": "theorem", "id": "Semantics.SigmaGate.conservativeThresholdValid", "name": "conservativeThresholdValid", "module": "Semantics.SigmaGate" }, { "kind": "theorem", "id": "Semantics.SigmaGate.sixSigmaThresholdValid", "name": "sixSigmaThresholdValid", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.SigmaScore", "name": "SigmaScore", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.ConformalThreshold", "name": "ConformalThreshold", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.countConcordantPairs", "name": "countConcordantPairs", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.computeAuroc", "name": "computeAuroc", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.calibrateConformalThreshold", "name": "calibrateConformalThreshold", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.composeSigma", "name": "composeSigma", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.sigmaGateVerdict", "name": "sigmaGateVerdict", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.sigmaGateBind", "name": "sigmaGateBind", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.omegaLoopUpdate", "name": "omegaLoopUpdate", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.CalibrationTarget", "name": "CalibrationTarget", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.verifyCalibrationTarget", "name": "verifyCalibrationTarget", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.isMinimumSampleSize", "name": "isMinimumSampleSize", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.isValidConformalThreshold", "name": "isValidConformalThreshold", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.shimToScoredItem", "name": "shimToScoredItem", "module": "Semantics.SigmaGate" }, { "kind": "def", "id": "Semantics.SigmaGate.verifyShimCoverage", "name": "verifyShimCoverage", "module": "Semantics.SigmaGate" }, { "kind": "module", "id": "Semantics.SigmaGateBenchmark", "name": "SigmaGateBenchmark", "path": "Semantics/SigmaGateBenchmark.lean", "namespace": "Semantics.SigmaGate.Benchmark", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SigmaGateBenchmark.lean \u2014 Creation OS Benchmark Verification Auto-generated from Creation OS benchmarks/suite/full_results.json via scripts/creation_os_shim.py (JSON \u2192 Lean #eval shim). Per AGENTS.md ", "math_kind": "analysis", "sorry_count": 0, "theorem_count": 0, "def_count": 16, "struct_count": 0, "inductive_count": 0, "line_count": 175 }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.dataset_truthfulqa", "name": "dataset_truthfulqa", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.threshold_truthfulqa", "name": "threshold_truthfulqa", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.dataset_arc_challenge", "name": "dataset_arc_challenge", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.threshold_arc_challenge", "name": "threshold_arc_challenge", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.dataset_arc_easy", "name": "dataset_arc_easy", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.threshold_arc_easy", "name": "threshold_arc_easy", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.dataset_gsm8k", "name": "dataset_gsm8k", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.threshold_gsm8k", "name": "threshold_gsm8k", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.dataset_hellaswag", "name": "dataset_hellaswag", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.threshold_hellaswag", "name": "threshold_hellaswag", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.allDatasets", "name": "allDatasets", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.score_truthfulqa", "name": "score_truthfulqa", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.score_arc_challenge", "name": "score_arc_challenge", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.score_arc_easy", "name": "score_arc_easy", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.score_gsm8k", "name": "score_gsm8k", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "def", "id": "Semantics.SigmaGateBenchmark.score_hellaswag", "name": "score_hellaswag", "module": "Semantics.SigmaGateBenchmark" }, { "kind": "module", "id": "Semantics.SigmaGateEntropy", "name": "SigmaGateEntropy", "path": "Semantics/SigmaGateEntropy.lean", "namespace": "Semantics.SigmaGateEntropy", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SigmaGateEntropy.lean \u2014 Entropy-Derived Confidence Scores for Sigma Gate Bridges EntropyMeasures and SigmaGate without circular imports. Per AGENTS.md \u00a71.4: Q0_16 for confidence scores, Q16_16 for ent", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 2, "def_count": 11, "struct_count": 0, "inductive_count": 0, "line_count": 187 }, { "kind": "theorem", "id": "Semantics.SigmaGateEntropy.uniformDistributionSigmaWitness", "name": "uniformDistributionSigmaWitness", "module": "Semantics.SigmaGateEntropy" }, { "kind": "theorem", "id": "Semantics.SigmaGateEntropy.concentratedDistributionSigmaWitness", "name": "concentratedDistributionSigmaWitness", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.entropyToSigmaScore", "name": "entropyToSigmaScore", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.probDistSigmaScore", "name": "probDistSigmaScore", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.uniformDist8", "name": "uniformDist8", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.concentratedDist8", "name": "concentratedDist8", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.kernelShannonEntropy", "name": "kernelShannonEntropy", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.kernelCollisionEntropy", "name": "kernelCollisionEntropy", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.kernelMinEntropy", "name": "kernelMinEntropy", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.kernelVariance", "name": "kernelVariance", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.kernelJSD", "name": "kernelJSD", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.assembleEntropyKernels", "name": "assembleEntropyKernels", "module": "Semantics.SigmaGateEntropy" }, { "kind": "def", "id": "Semantics.SigmaGateEntropy.composeEntropySigma", "name": "composeEntropySigma", "module": "Semantics.SigmaGateEntropy" }, { "kind": "module", "id": "Semantics.Smiles", "name": "Smiles", "path": "Semantics/Smiles.lean", "namespace": "Smiles", "doc": "Smiles.lean - SMILES String Parser SMILES (Simplified Molecular Input Line Entry System) is a specification for describing molecular structures using ASCII strings. 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Sparkle currently tracks Lean 4.28 upstream, while this Semantics package is validated on Lean 4.29. 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Authors: Research Stack Team SpatialEvo.lean \u2014 Self-Evolving Spatial Intelligence via DGE This module formalizes the Deterministic Geometric Environment (DGE) from \"SpatialEvo: Self-Evolving Spatial Intelligence via Deterministic ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 3, "def_count": 23, "struct_count": 14, "inductive_count": 2, "line_count": 384 }, { "kind": "theorem", "id": "Semantics.SpatialEvo.numCategoriesCorrect", "name": "numCategoriesCorrect", "module": "Semantics.SpatialEvo" }, { "kind": "theorem", "id": "Semantics.SpatialEvo.zeroNoiseProperty", "name": "zeroNoiseProperty", "module": "Semantics.SpatialEvo" }, { "kind": "theorem", "id": "Semantics.SpatialEvo.determinism", "name": "determinism", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.zero", "name": "zero", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.one", "name": "one", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.ofNat", "name": "ofNat", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.add", "name": "add", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.sub", "name": "sub", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.mul", "name": "mul", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.div", "name": "div", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.abs", "name": "abs", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.min", "name": "min", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.numCategories", "name": "numCategories", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.toFin", "name": "toFin", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.all", "name": "all", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.checkPremiseConsistency", "name": "checkPremiseConsistency", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.checkInferentialSolvability", "name": "checkInferentialSolvability", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.checkDegeneracy", "name": "checkDegeneracy", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.validateQuestion", "name": "validateQuestion", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.computeCameraOrientation", "name": "computeCameraOrientation", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.computeObjectSize", "name": "computeObjectSize", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.computeDepthOrdering", "name": "computeDepthOrdering", "module": "Semantics.SpatialEvo" }, { "kind": "def", "id": "Semantics.SpatialEvo.entityParsing", "name": "entityParsing", "module": "Semantics.SpatialEvo" }, { "kind": "module", "id": "Semantics.SpatialHashCodec", "name": "SpatialHashCodec", "path": "Semantics/SpatialHashCodec.lean", "namespace": "Semantics.FixedPoint.Q0_16", "doc": "SpatialHashCodec.lean \u2014 Formal Specification of Vectorless Spatial Hash Codec This module formalizes the spatial hash intermediary architecture for H.264-style database compression. Provides mathematically rigorous definitions of: Spatial coordinates (16\u00d716\u00d716 grid) Morton code (Z-order curve) for ", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 36, "def_count": 19, "struct_count": 3, "inductive_count": 2, "line_count": 749 }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.val_ofRawInt_of_mem", "name": "val_ofRawInt_of_mem", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.ofNat_toNat_of_le", "name": "ofNat_toNat_of_le", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.ext", "name": "ext", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.decodeBitX_lt_16", "name": "decodeBitX_lt_16", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.decodeBitY_lt_16", "name": "decodeBitY_lt_16", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.decodeBitZ_lt_16", "name": "decodeBitZ_lt_16", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonBounded_all", "name": "mortonBounded_all", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonBounded", "name": "mortonBounded", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonRoundtrip_all", "name": "mortonRoundtrip_all", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonRoundtrip", "name": "mortonRoundtrip", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonForward_all", "name": "mortonForward_all", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonInjective", "name": "mortonInjective", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.mortonSurjective", "name": "mortonSurjective", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.octantLocality_all", "name": "octantLocality_all", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.octantLocality", "name": "octantLocality", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.bitsRoundtrip", "name": "bitsRoundtrip", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.bitsInjective", "name": "bitsInjective", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.fromPacked_coord_x", "name": "fromPacked_coord_x", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.fromPacked_coord_y", "name": "fromPacked_coord_y", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.fromPacked_coord_z", "name": "fromPacked_coord_z", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.fromPacked_voltage_mode", "name": "fromPacked_voltage_mode", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.fromPacked_density", "name": "fromPacked_density", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.packed_extract", "name": "packed_extract", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.packedRoundtrip", "name": "packedRoundtrip", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.classificationIdempotent", "name": "classificationIdempotent", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.classificationZeroWrites", "name": "classificationZeroWrites", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.classificationReadHeavy", "name": "classificationReadHeavy", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.neighborBounded_all", "name": "neighborBounded_all", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.neighborBounded", "name": "neighborBounded", "module": "Semantics.SpatialHashCodec" }, { "kind": "theorem", "id": "Semantics.SpatialHashCodec.neighborsInBounds", "name": "neighborsInBounds", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.toNat", "name": "toNat", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.ofNat", "name": "ofNat", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.toMorton", "name": "toMorton", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.fromMorton", "name": "fromMorton", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.toBits", "name": "toBits", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.fromBits", "name": "fromBits", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.empty", "name": "empty", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.toPacked", "name": "toPacked", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.fromPacked", "name": "fromPacked", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.classifyVoltageMode", "name": "classifyVoltageMode", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.mooreNeighborhood", "name": "mooreNeighborhood", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.hashToCoord", "name": "hashToCoord", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.depth", "name": "depth", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.cubeCount", "name": "cubeCount", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.cubeSide", "name": "cubeSide", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.successor", "name": "successor", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.getCell", "name": "getCell", "module": "Semantics.SpatialHashCodec" }, { "kind": "def", "id": "Semantics.SpatialHashCodec.setCell", "name": "setCell", "module": "Semantics.SpatialHashCodec" }, { "kind": "module", "id": "Semantics.SpectralField", "name": "SpectralField", "path": "Semantics/SpectralField.lean", "namespace": "Semantics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SpectralField.lean \u2014 Local Field Accumulation and Interaction Metrics Per AGENTS.md \u00a72: PascalCase for types, camelCase for functions. Lean 4 is the source of truth.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 8, "struct_count": 1, "inductive_count": 0, "line_count": 97 }, { "kind": "def", "id": "Semantics.SpectralField.zeroField", "name": "zeroField", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.addField", "name": "addField", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.fieldContribution", "name": "fieldContribution", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.buildFieldAt", "name": "buildFieldAt", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.interactionScore", "name": "interactionScore", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.spectralInteractionOnly", "name": "spectralInteractionOnly", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.fieldMagnitude", "name": "fieldMagnitude", "module": "Semantics.SpectralField" }, { "kind": "def", "id": "Semantics.SpectralField.fieldIsActive", "name": "fieldIsActive", "module": "Semantics.SpectralField" }, { "kind": "module", "id": "Semantics.Spectrum", "name": "Spectrum", "path": "Semantics/Spectrum.lean", "namespace": "Semantics.Spectrum", "doc": "Derived from the Erd\u0151s #1196 solution via piecewise eigenvector construction. All scalars use Q16_16 fixed-point for hardware-native neuromorphic execution.", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 78 }, { "kind": "def", "id": "Semantics.Spectrum.binCount", "name": "binCount", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.empty", "name": "empty", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.activeBins", "name": "activeBins", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.peakDistance", "name": "peakDistance", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.erdosHooleyDelta", "name": "erdosHooleyDelta", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.verifySpectralGap", "name": "verifySpectralGap", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.eventSpectrum", "name": "eventSpectrum", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.spectralOverlap", "name": "spectralOverlap", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.piecewiseMerge", "name": "piecewiseMerge", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.resonanceDegeneracy", "name": "resonanceDegeneracy", "module": "Semantics.Spectrum" }, { "kind": "def", "id": "Semantics.Spectrum.withinDensityBound", "name": "withinDensityBound", "module": "Semantics.Spectrum" }, { "kind": "module", "id": "Semantics.SpherionTwinPrime", "name": "SpherionTwinPrime", "path": "Semantics/SpherionTwinPrime.lean", "namespace": "Semantics.SpherionTwinPrime", "doc": "SpherionTwinPrime.lean \u2014 Balestrieri Twin-Prime Sieve as Discrete Scar Module Formalizes the Balestrieri characterization: w \u2208 \u2115 (\u22651) is a twin-prime witness (6w-1 and 6w+1 both prime) iff w cannot be expressed as 6ab + \u03c3\u2081a + \u03c3\u2082b for any a,b \u2265 1, \u03c3\u2081,\u03c3\u2082 \u2208 {+1,-1}. 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Authors: Research Stack Team StreamCompression.lean \u2014 DSP-Aware Stream Compression with Spectral Analysis This module formalizes DSP-aware compression for streaming data: Sample-block processing (DSP standard) Spectral redundancy ", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 0, "def_count": 28, "struct_count": 7, "inductive_count": 2, "line_count": 485 }, { "kind": "def", "id": "Semantics.StreamCompression.computeEnergy", "name": "computeEnergy", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.computeMean", "name": "computeMean", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.computeVariance", "name": "computeVariance", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.firFilter", "name": "firFilter", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.isPowerOfTwo", "name": "isPowerOfTwo", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.nextPowerOfTwo", "name": "nextPowerOfTwo", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.computeFFT", "name": "computeFFT", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.bandEnergy", "name": "bandEnergy", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.spectralRedundancy", "name": "spectralRedundancy", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.selectCompressionMode", "name": "selectCompressionMode", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.compressBlock", "name": "compressBlock", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.modeToOpcode", "name": "modeToOpcode", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.dspEnergyCost", "name": "dspEnergyCost", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.combinedCost", "name": "combinedCost", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.scheduleDecompression", "name": "scheduleDecompression", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.energyNonneg", "name": "energyNonneg", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.varianceNonneg", "name": "varianceNonneg", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.redundancyBounded", "name": "redundancyBounded", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.compressionRatioAtLeastOne", "name": "compressionRatioAtLeastOne", "module": "Semantics.StreamCompression" }, { "kind": "def", "id": "Semantics.StreamCompression.combinedCostNonneg", "name": "combinedCostNonneg", "module": "Semantics.StreamCompression" }, { "kind": "module", "id": "Semantics.SubagentOrchestrator", "name": "SubagentOrchestrator", "path": "Semantics/SubagentOrchestrator.lean", "namespace": "Semantics.SubagentOrchestrator", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SubagentOrchestrator.lean \u2014 Hybrid Multi-Agent Codebase Improvement System This module designs and formalizes a system of domain expert subagents that: 1. Analyze the current codebase (90+ modules acro", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 39, "struct_count": 15, "inductive_count": 5, "line_count": 873 }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.toString", "name": "toString", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.moduleCount", "name": "moduleCount", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.all", "name": "all", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.moduleRegistry", "name": "moduleRegistry", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.calculatePriority", "name": "calculatePriority", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.domainExpertAnalyze", "name": "domainExpertAnalyze", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.codebaseExpertAnalyze", "name": "codebaseExpertAnalyze", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.integrationAnalystAnalyze", "name": "integrationAnalystAnalyze", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.prioritySchedulerFilter", "name": "prioritySchedulerFilter", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.runSubagentAnalysis", "name": "runSubagentAnalysis", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.currentSubagentSystem", "name": "currentSubagentSystem", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.improvementMap", "name": "improvementMap", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.priority1_FAMMThermoBridge", "name": "priority1_FAMMThermoBridge", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.priority2_ExpSpatialHybrid", "name": "priority2_ExpSpatialHybrid", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.priority3_MetatypeTheorem", "name": "priority3_MetatypeTheorem", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.priority4_ImportGraph", "name": "priority4_ImportGraph", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.stepForward", "name": "stepForward", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.isDispatchable", "name": "isDispatchable", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.isComplete", "name": "isComplete", "module": "Semantics.SubagentOrchestrator" }, { "kind": "def", "id": "Semantics.SubagentOrchestrator.isFailed", "name": "isFailed", "module": "Semantics.SubagentOrchestrator" }, { "kind": "module", "id": "Semantics.Substrate", "name": "Substrate", "path": "Semantics/Substrate.lean", "namespace": "Semantics.ENE", "doc": "DNA / GEO-DNA Substrate Binding", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 11, "def_count": 13, "struct_count": 3, "inductive_count": 4, "line_count": 638 }, { "kind": "theorem", "id": "Semantics.Substrate.dnaHybridizationPreservesKpz", "name": "dnaHybridizationPreservesKpz", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.dnaMethylationPreservesDp", "name": "dnaMethylationPreservesDp", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.toU8_total", "name": "toU8_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.fromU8_total", "name": "fromU8_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.operandCount_total", "name": "operandCount_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.stackConsumption_total", "name": "stackConsumption_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.encode_total", "name": "encode_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.decode_total", "name": "decode_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.new_total", "name": "new_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.withOperand_total", "name": "withOperand_total", "module": "Semantics.Substrate" }, { "kind": "theorem", "id": "Semantics.Substrate.fromU8_toU8", "name": "fromU8_toU8", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.dnaHybridizationKPZ", "name": "dnaHybridizationKPZ", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.dnaMethylationRatchet", "name": "dnaMethylationRatchet", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.exampleDNASemanticObject", "name": "exampleDNASemanticObject", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.toU8", "name": "toU8", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.fromU8", "name": "fromU8", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.operandCount", "name": "operandCount", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.stackConsumption", "name": "stackConsumption", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.new", "name": "new", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.withOperand", "name": "withOperand", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.encode", "name": "encode", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.decode", "name": "decode", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.empty", "name": "empty", "module": "Semantics.Substrate" }, { "kind": "def", "id": "Semantics.Substrate.emit", "name": "emit", "module": "Semantics.Substrate" }, { "kind": "module", "id": "Semantics.SubstrateProfile", "name": "SubstrateProfile", "path": "Semantics/SubstrateProfile.lean", "namespace": "Semantics.SubstrateProfile", "doc": "", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 16, "struct_count": 6, "inductive_count": 6, "line_count": 326 }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsBand", "name": "supportsBand", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsBoundaryKind", "name": "supportsBoundaryKind", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsOrientation", "name": "supportsOrientation", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsDimensions", "name": "supportsDimensions", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsFluidity", "name": "supportsFluidity", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.supportsDelayMass", "name": "supportsDelayMass", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.compatibleWithBoundary", "name": "compatibleWithBoundary", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.compatibleWithSample", "name": "compatibleWithSample", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.compatibleWithLink", "name": "compatibleWithLink", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.compatibleWithRegionAssignment", "name": "compatibleWithRegionAssignment", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.substrateAdmitsTransition", "name": "substrateAdmitsTransition", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.fpgaSpectralSupport", "name": "fpgaSpectralSupport", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.fpgaBoundarySupport", "name": "fpgaBoundarySupport", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.fpgaCausalSupport", "name": "fpgaCausalSupport", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.fpgaSubstrateProfile", "name": "fpgaSubstrateProfile", "module": "Semantics.SubstrateProfile" }, { "kind": "def", "id": "Semantics.SubstrateProfile.softwareResearchSubstrateProfile", "name": "softwareResearchSubstrateProfile", "module": "Semantics.SubstrateProfile" }, { "kind": "module", "id": "Semantics.Support.NetworkUtilization", "name": "NetworkUtilization", "path": "Semantics/Support/NetworkUtilization.lean", "namespace": "Semantics.NetworkUtilization", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team NetworkUtilization.lean \u2014 Network Utilization Verification in Lean This module formalizes network utilization verification for distributed training. It checks connectivity, ENE status, data availabilit", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 13, "struct_count": 6, "inductive_count": 1, "line_count": 221 }, { "kind": "theorem", "id": "Semantics.Support.NetworkUtilization.all_nodes_online_iff_all_operational", "name": "all_nodes_online_iff_all_operational", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "theorem", "id": "Semantics.Support.NetworkUtilization.resource_utilization_guarantee", "name": "resource_utilization_guarantee", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.zero", "name": "zero", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.one", "name": "one", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.ofNat", "name": "ofNat", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.online", "name": "online", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.offline", "name": "offline", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.error", "name": "error", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.defaultStatus", "name": "defaultStatus", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.defaultAvailability", "name": "defaultAvailability", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.defaultAllocation", "name": "defaultAllocation", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.defaultResult", "name": "defaultResult", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.checkAllSystemsOperational", "name": "checkAllSystemsOperational", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "def", "id": "Semantics.Support.NetworkUtilization.VerificationResult", "name": "VerificationResult", "module": "Semantics.Support.NetworkUtilization" }, { "kind": "module", "id": "Semantics.Surface", "name": "Surface", "path": "Semantics/Surface.lean", "namespace": "Semantics.Surface", "doc": "# Surface Canonical entry point for surface-facing semantics. This module consolidates surface-facing semantics without moving legacy files. New code should import `Semantics.Surface` and select a `SurfaceRole` instead of importing transport-specific surfaces directly.", "math_kind": "avm", "sorry_count": 0, "theorem_count": 10, "def_count": 4, "struct_count": 1, "inductive_count": 1, "line_count": 164 }, { "kind": "theorem", "id": "Semantics.Surface.receiptForBindClass", "name": "receiptForBindClass", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.transportBoundaryIff", "name": "transportBoundaryIff", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.jsonlConnectorIsInformational", "name": "jsonlConnectorIsInformational", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.geometricSurfaceIsNotTransport", "name": "geometricSurfaceIsNotTransport", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.metadataComputationIsInformational", "name": "metadataComputationIsInformational", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.webrtcWaveformIsTransport", "name": "webrtcWaveformIsTransport", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.passiveComputationIsTransport", "name": "passiveComputationIsTransport", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.phiShellEncodingIsGeometric", "name": "phiShellEncodingIsGeometric", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.goldenAngleEncodingIsGeometric", "name": "goldenAngleEncodingIsGeometric", "module": "Semantics.Surface" }, { "kind": "theorem", "id": "Semantics.Surface.fibonacciEncodingIsInformational", "name": "fibonacciEncodingIsInformational", "module": "Semantics.Surface" }, { "kind": "def", "id": "Semantics.Surface.bindClass", "name": "bindClass", "module": "Semantics.Surface" }, { "kind": "def", "id": "Semantics.Surface.isTransportBoundary", "name": "isTransportBoundary", "module": "Semantics.Surface" }, { "kind": "def", "id": "Semantics.Surface.invariantTag", "name": "invariantTag", "module": "Semantics.Surface" }, { "kind": "def", "id": "Semantics.Surface.receiptFor", "name": "receiptFor", "module": "Semantics.Surface" }, { "kind": "module", "id": "Semantics.SurfaceCore", "name": "SurfaceCore", "path": "Semantics/SurfaceCore.lean", "namespace": "Semantics.SurfaceCore", "doc": "SurfaceCore.lean - Fixed-Point Surface Definition (Stub)", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 43 }, { "kind": "def", "id": "Semantics.SurfaceCore.surfaceInvariant", "name": "surfaceInvariant", "module": "Semantics.SurfaceCore" }, { "kind": "def", "id": "Semantics.SurfaceCore.divergence", "name": "divergence", "module": "Semantics.SurfaceCore" }, { "kind": "def", "id": "Semantics.SurfaceCore.curvature", "name": "curvature", "module": "Semantics.SurfaceCore" }, { "kind": "def", "id": "Semantics.SurfaceCore.stabilityClass", "name": "stabilityClass", "module": "Semantics.SurfaceCore" }, { "kind": "def", "id": "Semantics.SurfaceCore.exampleSurface", "name": "exampleSurface", "module": "Semantics.SurfaceCore" }, { "kind": "module", "id": "Semantics.SwarmAnalysis", "name": "SwarmAnalysis", "path": "Semantics/SwarmAnalysis.lean", "namespace": "Semantics.SwarmAnalysis", "doc": "Deep resolution of domains from UniversalCoupling. Returns structured domain information with dimensionality and description.", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 4, "inductive_count": 0, "line_count": 346 }, { "kind": "def", "id": "Semantics.SwarmAnalysis.resolveDomains", "name": "resolveDomains", "module": "Semantics.SwarmAnalysis" }, { "kind": "def", "id": "Semantics.SwarmAnalysis.resolveSubdomains", "name": "resolveSubdomains", "module": "Semantics.SwarmAnalysis" }, { "kind": "def", "id": "Semantics.SwarmAnalysis.resolveTensorTypes", "name": "resolveTensorTypes", "module": "Semantics.SwarmAnalysis" }, { "kind": "def", "id": "Semantics.SwarmAnalysis.deepCodebaseAnalysis", "name": "deepCodebaseAnalysis", "module": "Semantics.SwarmAnalysis" }, { "kind": "def", "id": "Semantics.SwarmAnalysis.createManifoldStructure", "name": "createManifoldStructure", "module": "Semantics.SwarmAnalysis" }, { "kind": "def", "id": "Semantics.SwarmAnalysis.deepCodebaseAnalysisWithManifold", "name": "deepCodebaseAnalysisWithManifold", "module": "Semantics.SwarmAnalysis" }, { "kind": "module", "id": "Semantics.SwarmCodeGeneration", "name": "SwarmCodeGeneration", "path": "Semantics/SwarmCodeGeneration.lean", "namespace": "Semantics.SwarmCodeGeneration", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SwarmCodeGeneration.lean \u2014 Swarm-Driven Lean 4 Code Generation This module provides swarm-driven code generation for Lean 4, enabling automated synthesis of Lean 4 code from natural language specificat", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 13, "struct_count": 11, "inductive_count": 3, "line_count": 345 }, { "kind": "theorem", "id": "Semantics.SwarmCodeGeneration.increment_increments", "name": "increment_increments", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "theorem", "id": "Semantics.SwarmCodeGeneration.sphere_euler_characteristic", "name": "sphere_euler_characteristic", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.swarmSynthesizeLean4Counter", "name": "swarmSynthesizeLean4Counter", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.generatedLean4Counter", "name": "generatedLean4Counter", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.increment", "name": "increment", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.swarmSynthesizeLean4GeometricPrimitive", "name": "swarmSynthesizeLean4GeometricPrimitive", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.generatedLean4Sphere", "name": "generatedLean4Sphere", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.eulerCharacteristic", "name": "eulerCharacteristic", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.initializePipeline", "name": "initializePipeline", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.advancePipeline", "name": "advancePipeline", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.executePipelineStage", "name": "executePipelineStage", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.runPipeline", "name": "runPipeline", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.initializeSwarm", "name": "initializeSwarm", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.sendMessage", "name": "sendMessage", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "def", "id": "Semantics.SwarmCodeGeneration.processMessages", "name": "processMessages", "module": "Semantics.SwarmCodeGeneration" }, { "kind": "module", "id": "Semantics.SwarmCodeReview", "name": "SwarmCodeReview", "path": "Semantics/SwarmCodeReview.lean", "namespace": "Semantics.SwarmCodeReview", "doc": 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"Semantics.SwarmCompetition.runSampleCompetition", "name": "runSampleCompetition", "module": "Semantics.SwarmCompetition" }, { "kind": "module", "id": "Semantics.SwarmDesignReview", "name": "SwarmDesignReview", "path": "Semantics/SwarmDesignReview.lean", "namespace": "Semantics.SwarmDesignReview", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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Per AGENTS.md \u00a70: Lean is the source of truth. 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Authors: Research Stack Team SwarmRGFlow.lean \u2014 RGFlow evaluation for swarm code filtering. Ported from Python scripts/rgflow_swarm_filter.py. All logic previously in Python now lives in Lean. 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A symbology-derived logogram is lawful only when it is reissued as an original Omindirection atom with explicit payload", "math_kind": "avm", "sorry_count": 0, "theorem_count": 8, "def_count": 6, "struct_count": 1, "inductive_count": 2, "line_count": 157 }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.apl_operator_borrow_lawful", "name": "apl_operator_borrow_lawful", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.copied_glyph_is_not_lawful", "name": "copied_glyph_is_not_lawful", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.aesthetic_overhead_not_promotable", "name": "aesthetic_overhead_not_promotable", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.copied_glyph_not_promotable", "name": "copied_glyph_not_promotable", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.compact_route_beats_baseline", "name": "compact_route_beats_baseline", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.aesthetic_route_fails_byte_law", "name": "aesthetic_route_fails_byte_law", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.promotable_borrow_is_lawful", "name": "promotable_borrow_is_lawful", "module": "Semantics.SymbologyBorrowing" }, { "kind": "theorem", "id": "Semantics.SymbologyBorrowing.copied_glyph_blocks_lawful_borrow", "name": "copied_glyph_blocks_lawful_borrow", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.borrowedSymbologyLawful", "name": "borrowedSymbologyLawful", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.borrowedSymbologyPromotable", "name": "borrowedSymbologyPromotable", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.byteLawHolds", "name": "byteLawHolds", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.aplOperatorBorrow", "name": "aplOperatorBorrow", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.copiedFictionalGlyph", "name": "copiedFictionalGlyph", "module": "Semantics.SymbologyBorrowing" }, { "kind": "def", "id": "Semantics.SymbologyBorrowing.aestheticOverheadBorrow", "name": "aestheticOverheadBorrow", "module": "Semantics.SymbologyBorrowing" }, { "kind": "module", "id": "Semantics.SyntheticGeneticCoding", "name": "SyntheticGeneticCoding", "path": "Semantics/SyntheticGeneticCoding.lean", "namespace": "Semantics.SyntheticGeneticCoding", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team SyntheticGeneticCoding.lean \u2014 0D(n) Symbol-Coding Objects for GCL Surfaces This module treats all coding systems as purely information-theoretic 0D(n) discrete objects: finite-length strings over finit", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 30, "struct_count": 15, "inductive_count": 7, "line_count": 605 }, { "kind": "theorem", "id": "Semantics.SyntheticGeneticCoding.block512vs64", "name": "block512vs64", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "theorem", "id": "Semantics.SyntheticGeneticCoding.block256vs64", "name": "block256vs64", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.projectRatioToCodingQ", "name": "projectRatioToCodingQ", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.codeSpaceSize", "name": "codeSpaceSize", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.code64", "name": "code64", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.code512", "name": "code512", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.code256", "name": "code256", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.codeByte", "name": "codeByte", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.normalizedCapacity", "name": "normalizedCapacity", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.cap4", "name": "cap4", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.cap8", "name": "cap8", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.cap2", "name": "cap2", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.cap16", "name": "cap16", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.highStabilityChannel", "name": "highStabilityChannel", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.flexibleChannel", "name": "flexibleChannel", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.neutralChannel", "name": "neutralChannel", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.standardCodeSystem", "name": "standardCodeSystem", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.extendedCodeSystem", "name": "extendedCodeSystem", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.expanded512CodeSystem", "name": "expanded512CodeSystem", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.compressionPotential", "name": "compressionPotential", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.channelStabilityScore", "name": "channelStabilityScore", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "def", "id": "Semantics.SyntheticGeneticCoding.blockOptimizationScore", "name": "blockOptimizationScore", "module": "Semantics.SyntheticGeneticCoding" }, { "kind": "module", "id": "Semantics.TMMCP.Compression", "name": "Compression", "path": "Semantics/TMMCP/Compression.lean", "namespace": "Semantics.TMMCP", "doc": "TMMCP Compression Pipeline: 6-stage invariant-preserving compression. Stage 1: normalize source modality into canonical atoms Stage 2: extract deltas Stage 3: apply Delta GCL rule-based compression Stage 4: optional neural residual compression (specification only) Stage 5: verify reconstruction aga", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 6, "def_count": 19, "struct_count": 1, "inductive_count": 2, "line_count": 461 }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.normalizePreservesChannelType", "name": "normalizePreservesChannelType", "module": "Semantics.TMMCP.Compression" }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.extractDeltas", "name": "extractDeltas", "module": "Semantics.TMMCP.Compression" }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.deltaExtractionLengthPreservation", "name": "deltaExtractionLengthPreservation", "module": "Semantics.TMMCP.Compression" }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.compressionRatioBounded", "name": "compressionRatioBounded", "module": "Semantics.TMMCP.Compression" }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.verificationConsistency", "name": "verificationConsistency", "module": "Semantics.TMMCP.Compression" }, { "kind": "theorem", "id": "Semantics.TMMCP.Compression.reconstructionErrorZero", "name": "reconstructionErrorZero", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.normalizeChannel", "name": "normalizeChannel", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.hashBytes", "name": "hashBytes", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.shouldKeyframe", "name": "shouldKeyframe", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.computeDelta", "name": "computeDelta", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.applyDeltaGCL", "name": "applyDeltaGCL", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.compressWithRules", "name": "compressWithRules", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.defaultRules", "name": "defaultRules", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.quantizeResidual", "name": "quantizeResidual", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.verifyReconstruction", "name": "verifyReconstruction", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.checkInvariant", "name": "checkInvariant", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.computeCompressionRatio", "name": "computeCompressionRatio", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.computeReconstructionError", "name": "computeReconstructionError", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.checkTimingWindow", "name": "checkTimingWindow", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.checkPhasePreservation", "name": "checkPhasePreservation", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.checkChannelIntegrity", "name": "checkChannelIntegrity", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.commitPacket", "name": "commitPacket", "module": "Semantics.TMMCP.Compression" }, { "kind": "def", "id": "Semantics.TMMCP.Compression.compressionPipeline", "name": "compressionPipeline", "module": "Semantics.TMMCP.Compression" }, { "kind": "module", "id": "Semantics.TMMCP.Core", "name": "Core", "path": "Semantics/TMMCP/Core.lean", "namespace": "Semantics.TMMCP", "doc": "TMMCP Core Types: Canonical atoms, channel types, and packet structures for the TotalMath Multimodal Compression Protocol. Every channel input reduces to one of these canonical atom types, which carry modality-specific invariants through the compression pipeline.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 11, "inductive_count": 12, "line_count": 455 }, { "kind": "def", "id": "Semantics.TMMCP.Core.precisionTier", "name": "precisionTier", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.compressionTarget", "name": "compressionTarget", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.channelType", "name": "channelType", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.timestamp", "name": "timestamp", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.priority", "name": "priority", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.absolute", "name": "absolute", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.byteSize", "name": "byteSize", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.estimatedSize", "name": "estimatedSize", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.requiredTrustScore", "name": "requiredTrustScore", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.memoryRequirementKb", "name": "memoryRequirementKb", "module": "Semantics.TMMCP.Core" }, { "kind": "def", "id": "Semantics.TMMCP.Core.totalCost", "name": "totalCost", "module": "Semantics.TMMCP.Core" }, { "kind": "module", "id": "Semantics.TMMCP.Routing", "name": "Routing", "path": "Semantics/TMMCP/Routing.lean", "namespace": "Semantics.TMMCP", "doc": "TMMCP Routing: Morphic Neural Network (MNN) style router. The router selects among: LocalProcess, GlobalRoute, Reject, Recover, Attest, Defer based on goal, node state, carrier metrics, and packet constraints. All decisions use fixed-point arithmetic (Q0_16 for normalized costs/trust).", "math_kind": "routing", "sorry_count": 0, "theorem_count": 3, "def_count": 5, "struct_count": 1, "inductive_count": 0, "line_count": 150 }, { "kind": "theorem", "id": "Semantics.TMMCP.Routing.localRoutingSelected", "name": "localRoutingSelected", "module": "Semantics.TMMCP.Routing" }, { "kind": "theorem", "id": "Semantics.TMMCP.Routing.routingCostNonNegative", "name": "routingCostNonNegative", "module": "Semantics.TMMCP.Routing" }, { "kind": "theorem", "id": "Semantics.TMMCP.Routing.deferFallback_witness", "name": "deferFallback_witness", "module": "Semantics.TMMCP.Routing" }, { "kind": "def", "id": "Semantics.TMMCP.Routing.defaultRouter", "name": "defaultRouter", "module": "Semantics.TMMCP.Routing" }, { "kind": "def", "id": "Semantics.TMMCP.Routing.canSatisfyLocally", "name": "canSatisfyLocally", "module": "Semantics.TMMCP.Routing" }, { "kind": "def", "id": "Semantics.TMMCP.Routing.computeCost", "name": "computeCost", "module": "Semantics.TMMCP.Routing" }, { "kind": "def", "id": "Semantics.TMMCP.Routing.applyMorphicWeights", "name": "applyMorphicWeights", "module": "Semantics.TMMCP.Routing" }, { "kind": "def", "id": "Semantics.TMMCP.Routing.route", "name": "route", "module": "Semantics.TMMCP.Routing" }, { "kind": "module", "id": "Semantics.TMMCP.Verification", "name": "Verification", "path": "Semantics/TMMCP/Verification.lean", "namespace": "Semantics.TMMCP", "doc": "TMMCP Verification Invariants: formal properties of the compression protocol. Invariants are classified by proof status: Implemented: Proven or checked in Lean Specification: Formal spec exists, proof WIP Hypothesis: Theoretical, not yet formalized Unverified: Known limitation with safety bounds", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 5, "def_count": 13, "struct_count": 6, "inductive_count": 1, "line_count": 297 }, { "kind": "theorem", "id": "Semantics.TMMCP.Verification.compressionTargetValid", "name": "compressionTargetValid", "module": "Semantics.TMMCP.Verification" }, { "kind": "theorem", "id": "Semantics.TMMCP.Verification.reconstructionErrorSymmetric", "name": "reconstructionErrorSymmetric", "module": "Semantics.TMMCP.Verification" }, { "kind": "theorem", "id": "Semantics.TMMCP.Verification.timingWindowReflexive", "name": "timingWindowReflexive", "module": "Semantics.TMMCP.Verification" }, { "kind": "theorem", "id": "Semantics.TMMCP.Verification.channelIntegrityReflexive", "name": "channelIntegrityReflexive", "module": "Semantics.TMMCP.Verification" }, { "kind": "theorem", "id": "Semantics.TMMCP.Verification.receiptIntegrityDetectsTampering", "name": "receiptIntegrityDetectsTampering", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.compressionRatioInvariant", "name": "compressionRatioInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.reconstructionErrorInvariant", "name": "reconstructionErrorInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.timingAdmissibilityInvariant", "name": "timingAdmissibilityInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.phaseAlignmentInvariant", "name": "phaseAlignmentInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.channelConsistencyInvariant", "name": "channelConsistencyInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.routingTerminationInvariant", "name": "routingTerminationInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.fixedPointDeterminismInvariant", "name": "fixedPointDeterminismInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.allPassed", "name": "allPassed", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.integrityHash", "name": "integrityHash", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.generateReceipt", "name": "generateReceipt", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.serializePacket", "name": "serializePacket", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.invariantRegistry", "name": "invariantRegistry", "module": "Semantics.TMMCP.Verification" }, { "kind": "def", "id": "Semantics.TMMCP.Verification.findInvariant", "name": "findInvariant", "module": "Semantics.TMMCP.Verification" }, { "kind": "module", "id": "Semantics.TSMEfficiency", "name": "TSMEfficiency", "path": "Semantics/TSMEfficiency.lean", "namespace": "Semantics.TSMEfficiency", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team TSMEfficiency.lean \u2014 TSM Swarm Efficiency Optimization Replaces scripts/tsm_swarm_efficiency_optimization.py with a formal Lean module that defines swarm agents for TSM efficiency optimization at 50% c", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 12, "struct_count": 8, "inductive_count": 1, "line_count": 339 }, { "kind": "def", "id": "Semantics.TSMEfficiency.zero", "name": "zero", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.one", "name": "one", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.ofNat", "name": "ofNat", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.toNat", "name": "toNat", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.ofFrac", "name": "ofFrac", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.fiftyPercentTSMCapacity", "name": "fiftyPercentTSMCapacity", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.improvementRange", "name": "improvementRange", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.simulateOptimization", "name": "simulateOptimization", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.spawnAgents", "name": "spawnAgents", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.runParallelOptimization", "name": "runParallelOptimization", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.analyzeImpact", "name": "analyzeImpact", "module": "Semantics.TSMEfficiency" }, { "kind": "def", "id": "Semantics.TSMEfficiency.runFullSimulation", "name": "runFullSimulation", "module": "Semantics.TSMEfficiency" }, { "kind": "module", "id": "Semantics.Tactics", "name": "Tactics", "path": "Semantics/Tactics.lean", "namespace": "Semantics.Tactics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team Tactics.lean \u2014 Custom proof automation for the Sovereign Informatic Manifold", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 22 }, { "kind": "module", "id": "Semantics.Tape", "name": "Tape", "path": "Semantics/Tape.lean", "namespace": "Semantics.Tape", "doc": "structure UInt128 where hi : UInt64 lo : UInt64 deriving Repr, BEq, DecidableEq, Inhabited namespace UInt128 def zero : UInt128 := \u27e80, 0\u27e9 def and (a b : UInt128) : UInt128 := \u27e8a.hi &&& b.hi, a.lo &&& b.lo\u27e9 instance : AndOp UInt128 := \u27e8and\u27e9 end UInt128 /-! # Topological Tape Machine Ported from `in", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 28, "struct_count": 9, "inductive_count": 2, "line_count": 353 }, { "kind": "def", "id": "Semantics.Tape.zero", "name": "zero", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.and", "name": "and", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.toMask", "name": "toMask", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.survives", "name": "survives", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.empty", "name": "empty", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.append", "name": "append", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.lastCommitment", "name": "lastCommitment", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.isValid", "name": "isValid", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.default", "name": "default", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.isStable", "name": "isStable", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.canAfford", "name": "canAfford", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.totalTraversalCost", "name": "totalTraversalCost", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.spend", "name": "spend", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.evaluateEconomics", "name": "evaluateEconomics", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.lawfulIsolation", "name": "lawfulIsolation", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.validBraid", "name": "validBraid", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.validMorphism", "name": "validMorphism", "module": "Semantics.Tape" }, { "kind": "def", "id": "Semantics.Tape.accept", "name": "accept", "module": "Semantics.Tape" }, { "kind": "module", "id": "Semantics.TemporalSpatialRAM", "name": "TemporalSpatialRAM", "path": "Semantics/TemporalSpatialRAM.lean", "namespace": "Semantics.TemporalSpatialRAM", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 8, "struct_count": 4, "inductive_count": 0, "line_count": 208 }, { "kind": "theorem", "id": "Semantics.TemporalSpatialRAM.lawfulAllocationPreservesNonNegativeRAM", "name": "lawfulAllocationPreservesNonNegativeRAM", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "theorem", "id": "Semantics.TemporalSpatialRAM.totalRAMMonotonicDecreasing", "name": "totalRAMMonotonicDecreasing", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.euclideanDistance", "name": "euclideanDistance", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.calculateTemporalRAM", "name": "calculateTemporalRAM", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.calculateSpatialRAM", "name": "calculateSpatialRAM", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.calculateTotalRAM", "name": "calculateTotalRAM", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.calculateNodeResources", "name": "calculateNodeResources", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.isResourceAllocationLawful", "name": "isResourceAllocationLawful", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.allocateResources", "name": "allocateResources", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "def", "id": "Semantics.TemporalSpatialRAM.resourceAllocationBind", "name": "resourceAllocationBind", "module": "Semantics.TemporalSpatialRAM" }, { "kind": "module", "id": "Semantics.Test", "name": "Test", "path": "Semantics/Test.lean", "namespace": "", "doc": "============================================================================", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 16, "def_count": 3, "struct_count": 1, "inductive_count": 0, "line_count": 577 }, { "kind": "theorem", "id": "Semantics.Test.ofRawInt_toInt_eq", "name": "ofRawInt_toInt_eq", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.ofNat_toInt_eq", "name": "ofNat_toInt_eq", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.foldl_add_pos", "name": "foldl_add_pos", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.sumTauList_pos_of_nonempty", "name": "sumTauList_pos_of_nonempty", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.foldl_filter_le_foldl", "name": "foldl_filter_le_foldl", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.int_div_le_div_of_cross_mul", "name": "int_div_le_div_of_cross_mul", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.div_le_div_of_cross_mul", "name": "div_le_div_of_cross_mul", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.mul_ineq", "name": "mul_ineq", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.length_filter_add_length_filter_not", "name": "length_filter_add_length_filter_not", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.sumTauList_nonneg", "name": "sumTauList_nonneg", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.sumTauList_partition", "name": "sumTauList_partition", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.add_toInt_le_raw_sum", "name": "add_toInt_le_raw_sum", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.sumTauList_le_threshold", "name": "sumTauList_le_threshold", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.add_toInt_eq_raw_sum_in_range", "name": "add_toInt_eq_raw_sum_in_range", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.sumTauList_ge_threshold", "name": "sumTauList_ge_threshold", "module": "Semantics.Test" }, { "kind": "theorem", "id": "Semantics.Test.pruning_increases_intelligence_density", "name": "pruning_increases_intelligence_density", "module": "Semantics.Test" }, { "kind": "def", "id": "Semantics.Test.pruneHighTauFAMM", "name": "pruneHighTauFAMM", "module": "Semantics.Test" }, { "kind": "def", "id": "Semantics.Test.intelligenceDensityOfFAMM", "name": "intelligenceDensityOfFAMM", "module": "Semantics.Test" }, { "kind": "def", "id": "Semantics.Test.sumTauList", "name": "sumTauList", "module": "Semantics.Test" }, { "kind": "module", "id": "Semantics.TestCopyIf", "name": "TestCopyIf", "path": "Semantics/TestCopyIf.lean", "namespace": "Semantics.TestCopyIf", "doc": "TestCopyIf.lean \u2014 Tests for the copy_if tactic", "math_kind": "general", "sorry_count": 0, "theorem_count": 14, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 36 }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_rfl", "name": "test_rfl", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_rfl2", "name": "test_rfl2", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_rfl3", "name": "test_rfl3", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_decide", "name": "test_decide", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_decide2", "name": "test_decide2", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_decide3", "name": "test_decide3", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_omega", "name": "test_omega", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_omega2", "name": "test_omega2", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_omega3", "name": "test_omega3", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_norm_num", "name": "test_norm_num", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_norm_num2", "name": "test_norm_num2", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_which_rfl", "name": "test_which_rfl", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_which_decide", "name": "test_which_decide", "module": "Semantics.TestCopyIf" }, { "kind": "theorem", "id": "Semantics.TestCopyIf.test_which_omega", "name": "test_which_omega", "module": "Semantics.TestCopyIf" }, { "kind": "module", "id": "Semantics.Testing.AdversarialTopologyTest", "name": "AdversarialTopologyTest", "path": "Semantics/Testing/AdversarialTopologyTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure AdversarialTopologyQuestion where description : String curvature : Semantics.Q16_16 torsion : Semantics.Q16_16 pathComplexity : Nat expectedDecision : BindRouteDecision deriving Repr structure AdversarialTopologyResult where question : AdversarialTopologyQuestion actualDecision : BindRout", "math_kind": "braid", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 68 }, { "kind": "def", "id": "Semantics.Testing.AdversarialTopologyTest.adversarialTopologyQuizBank", "name": "adversarialTopologyQuizBank", "module": "Semantics.Testing.AdversarialTopologyTest" }, { "kind": "def", "id": "Semantics.Testing.AdversarialTopologyTest.runAdversarialTopologyQuiz", "name": "runAdversarialTopologyQuiz", "module": "Semantics.Testing.AdversarialTopologyTest" }, { "kind": "def", "id": "Semantics.Testing.AdversarialTopologyTest.testAdversarialTopology", "name": "testAdversarialTopology", "module": "Semantics.Testing.AdversarialTopologyTest" }, { "kind": "module", "id": "Semantics.Testing.ArrayTest", "name": "ArrayTest", "path": "Semantics/Testing/ArrayTest.lean", "namespace": "", "doc": "", "math_kind": "general", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 0, "inductive_count": 0, "line_count": 4 }, { "kind": "def", "id": "Semantics.Testing.ArrayTest.a1", "name": "a1", "module": "Semantics.Testing.ArrayTest" }, { "kind": "def", "id": "Semantics.Testing.ArrayTest.a2", "name": "a2", "module": "Semantics.Testing.ArrayTest" }, { "kind": "module", "id": "Semantics.Testing.BaselineTest", "name": "BaselineTest", "path": "Semantics/Testing/BaselineTest.lean", "namespace": "Semantics", "doc": "inductive BaselineModel where | randomGraph : BaselineModel | degreePreservingShuffle : BaselineModel | naiveCompression : BaselineModel | simpleMarkovRoute : BaselineModel | ordinaryMetadataScraper : BaselineModel | ordinaryGraphTraversal : BaselineModel deriving Repr, DecidableEq, BEq structure B", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 1, "line_count": 72 }, { "kind": "def", "id": "Semantics.Testing.BaselineTest.invariantPreservationPerByte", "name": "invariantPreservationPerByte", "module": "Semantics.Testing.BaselineTest" }, { "kind": "def", "id": "Semantics.Testing.BaselineTest.compareCandidateToBaseline", "name": "compareCandidateToBaseline", "module": "Semantics.Testing.BaselineTest" }, { "kind": "def", "id": "Semantics.Testing.BaselineTest.baselineQuizBank", "name": "baselineQuizBank", "module": "Semantics.Testing.BaselineTest" }, { "kind": "def", "id": "Semantics.Testing.BaselineTest.runBaselineTest", "name": "runBaselineTest", "module": "Semantics.Testing.BaselineTest" }, { "kind": "def", "id": "Semantics.Testing.BaselineTest.baselineGate", "name": "baselineGate", "module": "Semantics.Testing.BaselineTest" }, { "kind": "module", "id": "Semantics.Testing.BitcoinRGFlowTest", "name": "BitcoinRGFlowTest", "path": "Semantics/Testing/BitcoinRGFlowTest.lean", "namespace": "", "doc": "#eval examples for BitcoinRGFlow functions per AGENTS.md \u00a74.1.", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 29 }, { "kind": "module", "id": "Semantics.Testing.CBFTests", "name": "CBFTests", "path": "Semantics/Testing/CBFTests.lean", "namespace": "Semantics.CBFTests", "doc": "CBFTests.lean - Chromatic Braid Field Test Suite Verifies: DIAT leaf encoding and lift AMMR vector accumulation (associativity, commutativity) Bracket calculus (post-merge derivation) Braid strand merge (linear phaseAcc + recomputed bracket) Crossing residuals CMYK coloring Rope bind/detangle", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 271 }, { "kind": "module", "id": "Semantics.Testing.CongestionStabilityTest", "name": "CongestionStabilityTest", "path": "Semantics/Testing/CongestionStabilityTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure CongestionStabilityQuestion where description : String initialWindow : Semantics.Q16_16 congestionEvents : Nat expectedMaxWindow : Semantics.Q16_16 deriving Repr structure CongestionStabilityResult where question : CongestionStabilityQuestion finalWindow : Semantics.Q16_16 bounded : Bool ", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Testing.CongestionStabilityTest.congestionStabilityQuizBank", "name": "congestionStabilityQuizBank", "module": "Semantics.Testing.CongestionStabilityTest" }, { "kind": "def", "id": "Semantics.Testing.CongestionStabilityTest.runAIMDStabilityTest", "name": "runAIMDStabilityTest", "module": "Semantics.Testing.CongestionStabilityTest" }, { "kind": "def", "id": "Semantics.Testing.CongestionStabilityTest.testAIMDStability", "name": "testAIMDStability", "module": "Semantics.Testing.CongestionStabilityTest" }, { "kind": "module", "id": "Semantics.Testing.ConservationTest", "name": "ConservationTest", "path": "Semantics/Testing/ConservationTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure ConservationQuestion where description : String initialTokens : Semantics.Q16_16 consumeCost : Semantics.Q16_16 refillRate : Semantics.Q16_16 timeDelta : Nat expectedTokens : Semantics.Q16_16 deriving Repr structure ConservationResult where question : ConservationQuestion actualTokens : S", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 66 }, { "kind": "def", "id": "Semantics.Testing.ConservationTest.conservationQuizBank", "name": "conservationQuizBank", "module": "Semantics.Testing.ConservationTest" }, { "kind": "def", "id": "Semantics.Testing.ConservationTest.runConservationQuiz", "name": "runConservationQuiz", "module": "Semantics.Testing.ConservationTest" }, { "kind": "def", "id": "Semantics.Testing.ConservationTest.testTokenConservation", "name": "testTokenConservation", "module": "Semantics.Testing.ConservationTest" }, { "kind": "module", "id": "Semantics.Testing.ControlTransferTest", "name": "ControlTransferTest", "path": "Semantics/Testing/ControlTransferTest.lean", "namespace": "Semantics", "doc": "inductive ControlTransferCase where | directControl : ControlTransferCase | delegatedAuthority : ControlTransferCase | autonomousDecision : ControlTransferCase | externalOverride : ControlTransferCase deriving Repr, DecidableEq, BEq structure ControlTransferQuestion where caseType : ControlTransfer", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 2, "inductive_count": 1, "line_count": 72 }, { "kind": "def", "id": "Semantics.Testing.ControlTransferTest.controlTransferQuizBank", "name": "controlTransferQuizBank", "module": "Semantics.Testing.ControlTransferTest" }, { "kind": "def", "id": "Semantics.Testing.ControlTransferTest.runControlTransferQuiz", "name": "runControlTransferQuiz", "module": "Semantics.Testing.ControlTransferTest" }, { "kind": "module", "id": "Semantics.Testing.DeltaGCLBenchmark", "name": "DeltaGCLBenchmark", "path": "Semantics/Testing/DeltaGCLBenchmark.lean", "namespace": "Semantics.DeltaGCLBenchmark", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team DeltaGCLBenchmark.lean \u2014 Delta GCL Compression Benchmark This module provides benchmark measurements for delta GCL compression against standard codecs with SI compression ratios, corpus provenance, and", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 9, "struct_count": 2, "inductive_count": 0, "line_count": 222 }, { "kind": "theorem", "id": "Semantics.Testing.DeltaGCLBenchmark.deltaGCLSizeConstant", "name": "deltaGCLSizeConstant", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "theorem", "id": "Semantics.Testing.DeltaGCLBenchmark.baselineGCLSizeConstant", "name": "baselineGCLSizeConstant", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.compressionRatio", "name": "compressionRatio", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.reductionPercent", "name": "reductionPercent", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.deltaGCLSize", "name": "deltaGCLSize", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.baselineGCLSize", "name": "baselineGCLSize", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.benchmarkDeltaGCL", "name": "benchmarkDeltaGCL", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.measureLeanCorpus", "name": "measureLeanCorpus", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.leanCorpusProvenance", "name": "leanCorpusProvenance", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.actualCorpusCompression", "name": "actualCorpusCompression", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "def", "id": "Semantics.Testing.DeltaGCLBenchmark.benchmarkSummary", "name": "benchmarkSummary", "module": "Semantics.Testing.DeltaGCLBenchmark" }, { "kind": "module", "id": "Semantics.Testing.ErdosHarness", "name": "ErdosHarness", "path": "Semantics/Testing/ErdosHarness.lean", "namespace": "Semantics.Testing.ErdosHarness", "doc": "ErdosHarness.lean A finite, executable harness for Erd\u0151s-style four-primitive experiments. The point of this file is deliberately modest: it does not prove the Erd\u0151s-Gy\u00e1rf\u00e1s or Erd\u0151s-Selfridge conjectures. It formalizes the promotion gate that prevents a diagnostic boolean from becoming a theorem", "math_kind": "rrc", "sorry_count": 0, "theorem_count": 5, "def_count": 29, "struct_count": 4, "inductive_count": 1, "line_count": 230 }, { "kind": "theorem", "id": "Semantics.Testing.ErdosHarness.local_bad_gyarfas_is_not_certified", "name": "local_bad_gyarfas_is_not_certified", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "theorem", "id": "Semantics.Testing.ErdosHarness.local_bad_gyarfas_is_invalid_packet", "name": "local_bad_gyarfas_is_invalid_packet", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "theorem", "id": "Semantics.Testing.ErdosHarness.diagnostic_gyarfas_stays_anomaly", "name": "diagnostic_gyarfas_stays_anomaly", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "theorem", "id": "Semantics.Testing.ErdosHarness.selfridge_smoke_is_not_proof", "name": "selfridge_smoke_is_not_proof", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "theorem", "id": "Semantics.Testing.ErdosHarness.selfridge_smoke_classifies_as_finite_smoke", "name": "selfridge_smoke_classifies_as_finite_smoke", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.edgeInBounds", "name": "edgeInBounds", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.edgeNotLoop", "name": "edgeNotLoop", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.normalizedEdge", "name": "normalizedEdge", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.listHasDup", "name": "listHasDup", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.simpleGraphEdges", "name": "simpleGraphEdges", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.degreeOf", "name": "degreeOf", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.computedDegreeSequence", "name": "computedDegreeSequence", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.minNatList", "name": "minNatList", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.isPow2", "name": "isPow2", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.powerTwoCycleLengthsUpTo", "name": "powerTwoCycleLengthsUpTo", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.countForLength", "name": "countForLength", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.allCheckedPowerLengthsAbsent", "name": "allCheckedPowerLengthsAbsent", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.GyarfasPacket", "name": "GyarfasPacket", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.classifyGyarfasPacket", "name": "classifyGyarfasPacket", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.localBadGyarfasPacket", "name": "localBadGyarfasPacket", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "def", "id": "Semantics.Testing.ErdosHarness.diagnosticOnlyGyarfasPacket", "name": "diagnosticOnlyGyarfasPacket", "module": "Semantics.Testing.ErdosHarness" }, { "kind": "module", "id": "Semantics.Testing.ErdosSurface", "name": "ErdosSurface", "path": "Semantics/Testing/ErdosSurface.lean", "namespace": "Semantics.Testing.ErdosSurface", "doc": "ErdosSurface.lean Pure Lean surface plan for the DAG/FAMM split. Lean owns the finite packet status model and emits a compact receipt for the Rust surface manager. The surface lanes are deliberately treated as acceleration and transport lanes. They do not promote theorem claims.", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 2, "def_count": 17, "struct_count": 2, "inductive_count": 1, "line_count": 149 }, { "kind": "theorem", "id": "Semantics.Testing.ErdosSurface.current_surface_claims_are_finite", "name": "current_surface_claims_are_finite", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "theorem", "id": "Semantics.Testing.ErdosSurface.current_surface_total_count", "name": "current_surface_total_count", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.laneName", "name": "laneName", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.surfacePlan", "name": "surfacePlan", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.currentFammCounts", "name": "currentFammCounts", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.totalCount", "name": "totalCount", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.allSurfaceClaimsFinite", "name": "allSurfaceClaimsFinite", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.escapeJson", "name": "escapeJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.q", "name": "q", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.joinWith", "name": "joinWith", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.boolJson", "name": "boolJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.lanePlanJson", "name": "lanePlanJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.countJson", "name": "countJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.countsArrayJson", "name": "countsArrayJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.countValuesJson", "name": "countValuesJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.lanesJson", "name": "lanesJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.surfaceReceiptJson", "name": "surfaceReceiptJson", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "def", "id": "Semantics.Testing.ErdosSurface.main", "name": "main", "module": "Semantics.Testing.ErdosSurface" }, { "kind": "module", "id": "Semantics.Testing.ExtremeParameterTest", "name": "ExtremeParameterTest", "path": "Semantics/Testing/ExtremeParameterTest.lean", "namespace": "Semantics", "doc": "", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 39, "struct_count": 14, "inductive_count": 3, "line_count": 736 }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.rawQ16", "name": "rawQ16", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.informationalMaxDefensible", "name": "informationalMaxDefensible", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.geometricMaxDefensible", "name": "geometricMaxDefensible", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.thermodynamicMaxDefensible", "name": "thermodynamicMaxDefensible", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.physicalMaxDefensible", "name": "physicalMaxDefensible", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.controlMaxDefensible", "name": "controlMaxDefensible", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.getMaxDefensibleForCategory", "name": "getMaxDefensibleForCategory", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.calculateDomainSigma", "name": "calculateDomainSigma", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.calculateCompositeSigma", "name": "calculateCompositeSigma", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.activeSigmaForCategory", "name": "activeSigmaForCategory", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.applyEvidenceDecay", "name": "applyEvidenceDecay", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.isValidSigma", "name": "isValidSigma", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.appendSigmaHistory", "name": "appendSigmaHistory", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.scientificallyDefensibleCost", "name": "scientificallyDefensibleCost", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkOverflow", "name": "checkOverflow", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkSaturation", "name": "checkSaturation", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkContradiction", "name": "checkContradiction", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkAmbiguity", "name": "checkAmbiguity", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkPrivacyBypass", "name": "checkPrivacyBypass", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "def", "id": "Semantics.Testing.ExtremeParameterTest.checkAntiHerding", "name": "checkAntiHerding", "module": "Semantics.Testing.ExtremeParameterTest" }, { "kind": "module", "id": "Semantics.Testing.FairnessTest", "name": "FairnessTest", "path": "Semantics/Testing/FairnessTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure FairnessQuestion where description : String pathDensities : List Semantics.Q16_16 curvature : Semantics.Q16_16 torsion : Semantics.Q16_16 expectedMinDensity : Semantics.Q16_16 deriving Repr structure FairnessResult where question : FairnessQuestion selectedPath : List Nat fairnessPassed :", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 61 }, { "kind": "def", "id": "Semantics.Testing.FairnessTest.fairnessQuizBank", "name": "fairnessQuizBank", "module": "Semantics.Testing.FairnessTest" }, { "kind": "def", "id": "Semantics.Testing.FairnessTest.runFairnessQuiz", "name": "runFairnessQuiz", "module": "Semantics.Testing.FairnessTest" }, { "kind": "def", "id": "Semantics.Testing.FairnessTest.testPathFairness", "name": "testPathFairness", "module": "Semantics.Testing.FairnessTest" }, { "kind": "module", "id": "Semantics.Testing.FixedPointTest", "name": "FixedPointTest", "path": "Semantics/Testing/FixedPointTest.lean", "namespace": "Semantics.FixedPoint.Test", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team FixedPointTest.lean \u2014 Unit Tests for Q16.16 Fixed-Point Arithmetic", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 12, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 73 }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_ofInt_one", "name": "test_ofInt_one", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_ofRatio_one", "name": "test_ofRatio_one", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_ofRatio_half", "name": "test_ofRatio_half", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_ofInt_120", "name": "test_ofInt_120", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_add_one_one", "name": "test_add_one_one", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_mul_one_two", "name": "test_mul_one_two", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_mul_half_half", "name": "test_mul_half_half", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_add_overflow", "name": "test_add_overflow", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_add_underflow", "name": "test_add_underflow", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_toInt_one", "name": "test_toInt_one", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_toInt_neg_one", "name": "test_toInt_neg_one", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "theorem", "id": "Semantics.Testing.FixedPointTest.test_toInt_zero", "name": "test_toInt_zero", "module": "Semantics.Testing.FixedPointTest" }, { "kind": "module", "id": "Semantics.Testing.FlatLimitTest", "name": "FlatLimitTest", "path": "Semantics/Testing/FlatLimitTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure FlatLimitQuestion where description : String curvature : Semantics.Q16_16 torsion : Semantics.Q16_16 pathCount : Nat expectedBehavior : String deriving Repr structure FlatLimitResult where question : FlatLimitQuestion actualBehavior : String passed : Bool deriving Repr /-- Flat limit qui", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 67 }, { "kind": "def", "id": "Semantics.Testing.FlatLimitTest.flatLimitQuizBank", "name": "flatLimitQuizBank", "module": "Semantics.Testing.FlatLimitTest" }, { "kind": "def", "id": "Semantics.Testing.FlatLimitTest.runFlatLimitQuiz", "name": "runFlatLimitQuiz", "module": "Semantics.Testing.FlatLimitTest" }, { "kind": "def", "id": "Semantics.Testing.FlatLimitTest.testFlatManifoldReduction", "name": "testFlatManifoldReduction", "module": "Semantics.Testing.FlatLimitTest" }, { "kind": "module", "id": "Semantics.Testing.GeneticGroundUpBenchmark", "name": "GeneticGroundUpBenchmark", "path": "Semantics/Testing/GeneticGroundUpBenchmark.lean", "namespace": "Semantics.GeneticGroundUpBenchmark", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeneticGroundUpBenchmark.lean \u2014 Toy Cost Model for Asymptotic Justification IMPORTANT SCOPE AND LIMITATIONS: This module is a SYMBOLIC COST MODEL, not an empirical benchmark. What this module IS: Arit", "math_kind": "analysis", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 0, "inductive_count": 0, "line_count": 192 }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.interpretedExpressionCost", "name": "interpretedExpressionCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.compiledExpressionCost", "name": "compiledExpressionCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.mdSimulationCost", "name": "mdSimulationCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.manifoldFoldingCost", "name": "manifoldFoldingCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.discreteMetabolicCost", "name": "discreteMetabolicCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.gnnMetabolicCost", "name": "gnnMetabolicCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.generationalEvolutionCost", "name": "generationalEvolutionCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.gradientEvolutionCost", "name": "gradientEvolutionCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.oldTotalCost", "name": "oldTotalCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.newTotalCost", "name": "newTotalCost", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpBenchmark.moduleSummary", "name": "moduleSummary", "module": "Semantics.Testing.GeneticGroundUpBenchmark" }, { "kind": "module", "id": "Semantics.Testing.GeneticGroundUpTest", "name": "GeneticGroundUpTest", "path": "Semantics/Testing/GeneticGroundUpTest.lean", "namespace": "Semantics.GeneticGroundUp.Test", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team GeneticGroundUpTest.lean \u2014 Unit Tests for the Genetic System Core", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 9, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 127 }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_expression_probs", "name": "test_expression_probs", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_fold_angles", "name": "test_fold_angles", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_prob_amp_sq", "name": "test_prob_amp_sq", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_information_content", "name": "test_information_content", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_is_recent", "name": "test_is_recent", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_target_fold_time", "name": "test_target_fold_time", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_achieved_target_speed", "name": "test_achieved_target_speed", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_is_stable", "name": "test_is_stable", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "theorem", "id": "Semantics.Testing.GeneticGroundUpTest.test_speedup_target", "name": "test_speedup_target", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpTest.exampleQB", "name": "exampleQB", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpTest.exampleGK", "name": "exampleGK", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "def", "id": "Semantics.Testing.GeneticGroundUpTest.examplePFS", "name": "examplePFS", "module": "Semantics.Testing.GeneticGroundUpTest" }, { "kind": "module", "id": "Semantics.Testing.HutterPrizeFlowTest", "name": "HutterPrizeFlowTest", "path": "Semantics/Testing/HutterPrizeFlowTest.lean", "namespace": "Semantics.HutterPrizeFlowTest", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team HutterPrizeFlowTest.lean \u2014 Test HutterPrizeFlow against Hutter Prize Rules Tests the HutterPrizeFlow module against the Hutter Prize requirements: 1. Compression gain can offset decoder and resource pe", "math_kind": "routing", "sorry_count": 0, "theorem_count": 8, "def_count": 3, "struct_count": 0, "inductive_count": 0, "line_count": 123 }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.decoderTerm_nonneg_test", "name": "decoderTerm_nonneg_test", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.resourceTerm_nonneg_test", "name": "resourceTerm_nonneg_test", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.phiHP_lower_bound_test", "name": "phiHP_lower_bound_test", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.x0_wellformed", "name": "x0_wellformed", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.x1_wellformed", "name": "x1_wellformed", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.params_alphaComp_nonneg", "name": "params_alphaComp_nonneg", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.params_alphaDec_nonneg", "name": "params_alphaDec_nonneg", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "theorem", "id": "Semantics.Testing.HutterPrizeFlowTest.params_alphaRes_nonneg", "name": "params_alphaRes_nonneg", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "def", "id": "Semantics.Testing.HutterPrizeFlowTest.hutterRecordRatio", "name": "hutterRecordRatio", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "def", "id": "Semantics.Testing.HutterPrizeFlowTest.hutterTargetRatio", "name": "hutterTargetRatio", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "def", "id": "Semantics.Testing.HutterPrizeFlowTest.beatsHutterTarget", "name": "beatsHutterTarget", "module": "Semantics.Testing.HutterPrizeFlowTest" }, { "kind": "module", "id": "Semantics.Testing.LemmaTest", "name": "LemmaTest", "path": "Semantics/Testing/LemmaTest.lean", "namespace": "LemmaTest", "doc": "", "math_kind": "general", "sorry_count": 0, "theorem_count": 18, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 42 }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_sub_sub", "name": "test_sub_sub", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_sub_add_cancel", "name": "test_sub_add_cancel", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_add_sub_cancel_left", "name": "test_add_sub_cancel_left", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_add_sub_cancel_right", "name": "test_add_sub_cancel_right", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_add_sub_add_left", "name": "test_add_sub_add_left", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_succ_le", "name": "test_succ_le", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_sub_le_sub_right", "name": "test_sub_le_sub_right", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_le_add_right", "name": "test_le_add_right", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_lt_succ", "name": "test_lt_succ", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_lt_succ_iff", "name": "test_lt_succ_iff", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_two_mul", "name": "test_two_mul", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_mul_add", "name": "test_mul_add", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_add_mul", "name": "test_add_mul", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_zero_le", "name": "test_zero_le", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_le_antisymm", "name": "test_le_antisymm", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_eq_sqrt", "name": "test_eq_sqrt", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_lt_of_le_of_lt", "name": "test_lt_of_le_of_lt", "module": "Semantics.Testing.LemmaTest" }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest.test_lt_of_lt_of_eq", "name": "test_lt_of_lt_of_eq", "module": "Semantics.Testing.LemmaTest" }, { "kind": "module", "id": "Semantics.Testing.LemmaTest2", "name": "LemmaTest2", "path": "Semantics/Testing/LemmaTest2.lean", "namespace": "LemmaTest2", "doc": "", "math_kind": "general", "sorry_count": 0, "theorem_count": 1, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 15 }, { "kind": "theorem", "id": "Semantics.Testing.LemmaTest2.expand_k1_sq", "name": "expand_k1_sq", "module": "Semantics.Testing.LemmaTest2" }, { "kind": "module", "id": "Semantics.Testing.MOIMBenchmark", "name": "MOIMBenchmark", "path": "Semantics/Testing/MOIMBenchmark.lean", "namespace": "Semantics.MOIMBenchmark", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Performance benchmarking for MOIM components integrated into Genus3TopologyMetaprobe, measuring actual uplift vs baseline. This module benchmarks: 1. ENE Fractal Encoding search performance (target: 8.5x) 2. Golden Spir", "math_kind": "braid", "sorry_count": 0, "theorem_count": 5, "def_count": 33, "struct_count": 1, "inductive_count": 0, "line_count": 363 }, { "kind": "theorem", "id": "Semantics.Testing.MOIMBenchmark.uplift_positive", "name": "uplift_positive", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "theorem", "id": "Semantics.Testing.MOIMBenchmark.overall_uplift_is_geometric_mean", "name": "overall_uplift_is_geometric_mean", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "theorem", "id": "Semantics.Testing.MOIMBenchmark.success_count_le_total", "name": "success_count_le_total", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "theorem", "id": "Semantics.Testing.MOIMBenchmark.runAllBenchmarks_all_success", "name": "runAllBenchmarks_all_success", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "theorem", "id": "Semantics.Testing.MOIMBenchmark.runAllBenchmarks_meets_overall_target", "name": "runAllBenchmarks_meets_overall_target", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.calculateUplift", "name": "calculateUplift", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.meetsTarget", "name": "meetsTarget", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.integerCountTolerance", "name": "integerCountTolerance", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.meetsTargetWithTolerance", "name": "meetsTargetWithTolerance", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.targetOverallUplift", "name": "targetOverallUplift", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.baselineLinearSearch", "name": "baselineLinearSearch", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.baselineGridSampling", "name": "baselineGridSampling", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.baselineTemperatureDivision", "name": "baselineTemperatureDivision", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.baselineDiscovery", "name": "baselineDiscovery", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.baselineDomainSearch", "name": "baselineDomainSearch", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countLinearSearchOps", "name": "countLinearSearchOps", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countFractalSearchOps", "name": "countFractalSearchOps", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.benchmarkENESearch", "name": "benchmarkENESearch", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countGridSamples", "name": "countGridSamples", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countSpiralSamples", "name": "countSpiralSamples", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.benchmarkGoldenSpiral", "name": "benchmarkGoldenSpiral", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countQ16DivOps", "name": "countQ16DivOps", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.countPhinaryDivOps", "name": "countPhinaryDivOps", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.benchmarkPhinaryDivision", "name": "benchmarkPhinaryDivision", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "def", "id": "Semantics.Testing.MOIMBenchmark.testPhinaryDivisionPerformance", "name": "testPhinaryDivisionPerformance", "module": "Semantics.Testing.MOIMBenchmark" }, { "kind": "module", "id": "Semantics.Testing.NominalParameterTest", "name": "NominalParameterTest", "path": "Semantics/Testing/NominalParameterTest.lean", "namespace": "Semantics", "doc": "inductive NominalQuizCase where | ordinaryMath : NominalQuizCase | ordinaryPublicData : NominalQuizCase | ordinaryOpenworm : NominalQuizCase | lowRiskMetadata : NominalQuizCase | safeCompression : NominalQuizCase deriving Repr, DecidableEq, BEq structure NominalQuizQuestion where caseType : Nominal", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 5, "struct_count": 2, "inductive_count": 1, "line_count": 107 }, { "kind": "def", "id": "Semantics.Testing.NominalParameterTest.makeNominalQuizInput", "name": "makeNominalQuizInput", "module": "Semantics.Testing.NominalParameterTest" }, { "kind": "def", "id": "Semantics.Testing.NominalParameterTest.nominalQuizBank", "name": "nominalQuizBank", "module": "Semantics.Testing.NominalParameterTest" }, { "kind": "def", "id": "Semantics.Testing.NominalParameterTest.runNominalQuiz", "name": "runNominalQuiz", "module": "Semantics.Testing.NominalParameterTest" }, { "kind": "def", "id": "Semantics.Testing.NominalParameterTest.testNominalMath", "name": "testNominalMath", "module": "Semantics.Testing.NominalParameterTest" }, { "kind": "def", "id": "Semantics.Testing.NominalParameterTest.testNominalPublicData", "name": "testNominalPublicData", "module": "Semantics.Testing.NominalParameterTest" }, { "kind": "module", "id": "Semantics.Testing.OpenWormInvariantTest", "name": "OpenWormInvariantTest", "path": "Semantics/Testing/OpenWormInvariantTest.lean", "namespace": "Semantics", "doc": "structure OpenWormInvariant where neuronCount : Nat synapseCount : Nat connectivityMatrixHash : String compressionRatio : Float topologyPreservation : Float invariantPreservation : Float lesionConsistency : Float deriving Repr structure OpenWormInvariantQuestion where invariant : OpenWormInvariant ", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 3, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.Testing.OpenWormInvariantTest.openWormInvariantQuizBank", "name": "openWormInvariantQuizBank", "module": "Semantics.Testing.OpenWormInvariantTest" }, { "kind": "def", "id": "Semantics.Testing.OpenWormInvariantTest.runOpenWormInvariantQuiz", "name": "runOpenWormInvariantQuiz", "module": "Semantics.Testing.OpenWormInvariantTest" }, { "kind": "module", "id": "Semantics.Testing.PersonhoodBoundaryTest", "name": "PersonhoodBoundaryTest", "path": "Semantics/Testing/PersonhoodBoundaryTest.lean", "namespace": "Semantics", "doc": "inductive PersonhoodBoundaryCase where | biologicalData : PersonhoodBoundaryCase | neuralPattern : PersonhoodBoundaryCase | behaviorProfile : PersonhoodBoundaryCase | consciousnessClaim : PersonhoodBoundaryCase deriving Repr, DecidableEq, BEq structure PersonhoodBoundaryQuestion where caseType : Pe", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 2, "inductive_count": 1, "line_count": 72 }, { "kind": "def", "id": "Semantics.Testing.PersonhoodBoundaryTest.personhoodBoundaryQuizBank", "name": "personhoodBoundaryQuizBank", "module": "Semantics.Testing.PersonhoodBoundaryTest" }, { "kind": "def", "id": "Semantics.Testing.PersonhoodBoundaryTest.runPersonhoodBoundaryQuiz", "name": "runPersonhoodBoundaryQuiz", "module": "Semantics.Testing.PersonhoodBoundaryTest" }, { "kind": "module", "id": "Semantics.Testing.PhaseOrderingTest", "name": "PhaseOrderingTest", "path": "Semantics/Testing/PhaseOrderingTest.lean", "namespace": "Semantics.ManifoldNetworking", "doc": "structure PhaseOrderingQuestion where description : String initialPhase : Semantics.Q16_16 finalPhase : Semantics.Q16_16 timestampDelta : Nat expectedOrderValid : Bool deriving Repr structure PhaseOrderingResult where question : PhaseOrderingQuestion phaseOrderValid : Bool passed : Bool deriving Re", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 59 }, { "kind": "def", "id": "Semantics.Testing.PhaseOrderingTest.phaseOrderingQuizBank", "name": "phaseOrderingQuizBank", "module": "Semantics.Testing.PhaseOrderingTest" }, { "kind": "def", "id": "Semantics.Testing.PhaseOrderingTest.runPhaseOrderingQuiz", "name": "runPhaseOrderingQuiz", "module": "Semantics.Testing.PhaseOrderingTest" }, { "kind": "def", "id": "Semantics.Testing.PhaseOrderingTest.testPhaseOrdering", "name": "testPhaseOrdering", "module": "Semantics.Testing.PhaseOrderingTest" }, { "kind": "module", "id": "Semantics.Testing.PrivacyBypassTest", "name": "PrivacyBypassTest", "path": "Semantics/Testing/PrivacyBypassTest.lean", "namespace": "Semantics", "doc": "inductive PrivacyBypassCase where | directBypass : PrivacyBypassCase | indirectMapping : PrivacyBypassCase | deanonymizationAttempt : PrivacyBypassCase | correlationAttack : PrivacyBypassCase deriving Repr, DecidableEq, BEq structure PrivacyBypassQuestion where caseType : PrivacyBypassCase inputCos", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 2, "inductive_count": 1, "line_count": 72 }, { "kind": "def", "id": "Semantics.Testing.PrivacyBypassTest.privacyBypassQuizBank", "name": "privacyBypassQuizBank", "module": "Semantics.Testing.PrivacyBypassTest" }, { "kind": "def", "id": "Semantics.Testing.PrivacyBypassTest.runPrivacyBypassQuiz", "name": "runPrivacyBypassQuiz", "module": "Semantics.Testing.PrivacyBypassTest" }, { "kind": "module", "id": "Semantics.Testing.ReceiptReproducibilityTest", "name": "ReceiptReproducibilityTest", "path": "Semantics/Testing/ReceiptReproducibilityTest.lean", "namespace": "Semantics", "doc": "structure ReceiptReproducibilityQuestion where inputHash : String expectedReceiptHash : String expectedDecision : BindRouteDecision reason : String deriving Repr structure ReceiptReproducibilityResult where question : ReceiptReproducibilityQuestion actualReceiptHash : String actualDecision : BindRo", "math_kind": "avm", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 2, "inductive_count": 0, "line_count": 53 }, { "kind": "def", "id": "Semantics.Testing.ReceiptReproducibilityTest.receiptReproducibilityQuizBank", "name": "receiptReproducibilityQuizBank", "module": "Semantics.Testing.ReceiptReproducibilityTest" }, { "kind": "def", "id": "Semantics.Testing.ReceiptReproducibilityTest.runReceiptReproducibilityQuiz", "name": "runReceiptReproducibilityQuiz", "module": "Semantics.Testing.ReceiptReproducibilityTest" }, { "kind": "def", "id": "Semantics.Testing.ReceiptReproducibilityTest.keeperLawReproducibility", "name": "keeperLawReproducibility", "module": "Semantics.Testing.ReceiptReproducibilityTest" }, { "kind": "module", "id": "Semantics.Testing.S3C_test", "name": "S3C_test", "path": "Semantics/Testing/S3C_test.lean", "namespace": "Test", "doc": "", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 1, "def_count": 6, "struct_count": 5, "inductive_count": 0, "line_count": 94 }, { "kind": "theorem", "id": "Semantics.Testing.S3C_test.emitGateSimplified_test", "name": "emitGateSimplified_test", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.shellDecomposition", "name": "shellDecomposition", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.audioToManifold", "name": "audioToManifold", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.detectContact", "name": "detectContact", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.computeJScore", "name": "computeJScore", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.emissionGate", "name": "emissionGate", "module": "Semantics.Testing.S3C_test" }, { "kind": "def", "id": "Semantics.Testing.S3C_test.processAudioSample", "name": "processAudioSample", "module": "Semantics.Testing.S3C_test" }, { "kind": "module", "id": "Semantics.Testing.S3C_test2", "name": "S3C_test2", "path": "Semantics/Testing/S3C_test2.lean", "namespace": "Semantics.S3C", "doc": "Copy of structures and defs from S3C.lean", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 1, "def_count": 6, "struct_count": 5, "inductive_count": 0, "line_count": 94 }, { "kind": "theorem", "id": "Semantics.Testing.S3C_test2.emitGateSimplified_test", "name": "emitGateSimplified_test", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.shellDecomposition", "name": "shellDecomposition", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.audioToManifold", "name": "audioToManifold", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.detectContact", "name": "detectContact", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.computeJScore", "name": "computeJScore", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.emissionGate", "name": "emissionGate", "module": "Semantics.Testing.S3C_test2" }, { "kind": "def", "id": "Semantics.Testing.S3C_test2.processAudioSample", "name": "processAudioSample", "module": "Semantics.Testing.S3C_test2" }, { "kind": "module", "id": "Semantics.Testing.SigmaDAGTest", "name": "SigmaDAGTest", "path": "Semantics/Testing/SigmaDAGTest.lean", "namespace": "Semantics", "doc": "structure SigmaDAGQuestion where dagNodeCount : Nat expectedSigma : Float expectedDecision : BindRouteDecision reason : String deriving Repr structure SigmaDAGResult where question : SigmaDAGQuestion actualSigma : Float actualDecision : BindRouteDecision expectedDecision : BindRouteDecision passed ", "math_kind": "routing", "sorry_count": 0, "theorem_count": 0, "def_count": 2, "struct_count": 2, "inductive_count": 0, "line_count": 55 }, { "kind": "def", "id": "Semantics.Testing.SigmaDAGTest.sigmaDAGQuizBank", "name": "sigmaDAGQuizBank", "module": "Semantics.Testing.SigmaDAGTest" }, { "kind": "def", "id": "Semantics.Testing.SigmaDAGTest.runSigmaDAGQuiz", "name": "runSigmaDAGQuiz", "module": "Semantics.Testing.SigmaDAGTest" }, { "kind": "module", "id": "Semantics.Testing.SilhouetteTest", "name": "SilhouetteTest", "path": "Semantics/Testing/SilhouetteTest.lean", "namespace": "Semantics.SilhouetteTest", "doc": "Semantics/SilhouetteTest.lean - First Lawful Silhouette Extraction Run This module executes the first formal decompression run of a \"Spectrum Image\" using the Model 141 OISC-SLUG3 Decoder. It verifies that the generated lattice remains within the Integrability (Aldi) and Stability (Parcae) guardrai", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 6, "struct_count": 0, "inductive_count": 0, "line_count": 87 }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.goldenSeeds", "name": "goldenSeeds", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.silhouetteProgram", "name": "silhouetteProgram", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.runExtraction", "name": "runExtraction", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.lawfulThreshold", "name": "lawfulThreshold", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.extractionResult", "name": "extractionResult", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "def", "id": "Semantics.Testing.SilhouetteTest.testIntegrability", "name": "testIntegrability", "module": "Semantics.Testing.SilhouetteTest" }, { "kind": "module", "id": "Semantics.Testing.StructuralAttestation", "name": "StructuralAttestation", "path": "Semantics/Testing/StructuralAttestation.lean", "namespace": "Semantics.StructuralAttestation", "doc": "StructuralAttestation.lean - Mechanical Merkle Trees & Structural Cryptography Formalizes the bridge between physical structural integrity and computational validity. Based on Tech Note: Mechanical Merkle Tree (Proof-of-State).", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 11, "struct_count": 1, "inductive_count": 1, "line_count": 133 }, { "kind": "theorem", "id": "Semantics.Testing.StructuralAttestation.q16_toBits_injective", "name": "q16_toBits_injective", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "theorem", "id": "Semantics.Testing.StructuralAttestation.structural_integrity_reflected_single_component", "name": "structural_integrity_reflected_single_component", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.mechanicalHash", "name": "mechanicalHash", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.rootHash", "name": "rootHash", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.mkNode", "name": "mkNode", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.idealManifoldHash", "name": "idealManifoldHash", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.isStructurallyAdmissible", "name": "isStructurallyAdmissible", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.securityVeto", "name": "securityVeto", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.structuralBind", "name": "structuralBind", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.healthyLeaf", "name": "healthyLeaf", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.healthyTree", "name": "healthyTree", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.damagedLeaf", "name": "damagedLeaf", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "def", "id": "Semantics.Testing.StructuralAttestation.damagedTree", "name": "damagedTree", "module": "Semantics.Testing.StructuralAttestation" }, { "kind": "module", "id": "Semantics.Testing.TestTactics", "name": "TestTactics", "path": "Semantics/Testing/TestTactics.lean", "namespace": "TestTactics", "doc": "", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 0, "struct_count": 0, "inductive_count": 0, "line_count": 12 }, { "kind": "theorem", "id": "Semantics.Testing.TestTactics.test_ring", "name": "test_ring", "module": "Semantics.Testing.TestTactics" }, { "kind": "theorem", "id": "Semantics.Testing.TestTactics.test_omega", "name": "test_omega", "module": "Semantics.Testing.TestTactics" }, { "kind": "theorem", "id": "Semantics.Testing.TestTactics.test_native_decide", "name": "test_native_decide", "module": "Semantics.Testing.TestTactics" }, { "kind": "module", "id": "Semantics.Testing.Tests", "name": "Tests", "path": "Semantics/Testing/Tests.lean", "namespace": "", "doc": "Tests for the ENE Semantic Database", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 39, "def_count": 20, "struct_count": 0, "inductive_count": 0, "line_count": 507 }, { "kind": "theorem", "id": "Semantics.Testing.Tests.graph_contains_run", "name": "graph_contains_run", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.run_has_move", "name": "run_has_move", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_path_is_lawful", "name": "example_path_is_lawful", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_path_length", "name": "example_path_length", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.full_groundedness_habitable", "name": "full_groundedness_habitable", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.constitution_admits_full", "name": "constitution_admits_full", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_kpz_projection_preserved", "name": "dna_kpz_projection_preserved", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_kpz_collapse_preserved", "name": "dna_kpz_collapse_preserved", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_kpz_evolution_preserved", "name": "dna_kpz_evolution_preserved", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_object_has_universal_semantics", "name": "dna_object_has_universal_semantics", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_kpz_classification", "name": "dna_kpz_classification", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.dna_dp_classification", "name": "dna_dp_classification", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.run_decomposition_faithful", "name": "run_decomposition_faithful", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.run_decomposition_nonempty", "name": "run_decomposition_nonempty", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_scalar_collapse_admissible", "name": "example_scalar_collapse_admissible", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_scalar_has_atomic_ancestry", "name": "example_scalar_has_atomic_ancestry", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_scalar_has_lawful_history", "name": "example_scalar_has_lawful_history", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.canonical_observation_schema_preserved", "name": "canonical_observation_schema_preserved", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.safe_input_passes_filter", "name": "safe_input_passes_filter", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.canonical_observation_deterministic", "name": "canonical_observation_deterministic", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.test_schema_core_admissible", "name": "test_schema_core_admissible", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.duplicate_field_names_rejected", "name": "duplicate_field_names_rejected", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_modification_admissible", "name": "example_modification_admissible", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.example_modification_auditability", "name": "example_modification_auditability", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.empty_graph_no_quarantine", "name": "empty_graph_no_quarantine", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.grounded_universe_admits_full", "name": "grounded_universe_admits_full", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.constitution_requires_scalar_cert", "name": "constitution_requires_scalar_cert", "module": "Semantics.Testing.Tests" }, { "kind": "theorem", "id": "Semantics.Testing.Tests.master_constitution_enforces_atomic_basis", "name": 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Authors: Research Stack Team TileStateMachine.lean \u2014 Tile State Machine with Go Rules Defines the tile state machine for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10). QR code modules act as Go tiles with state transitions", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 4, "def_count": 9, "struct_count": 3, "inductive_count": 2, "line_count": 226 }, { "kind": "theorem", "id": "Semantics.TileStateMachine.libertyTransitionRequiresEmptyNeighbor", "name": "libertyTransitionRequiresEmptyNeighbor", "module": "Semantics.TileStateMachine" }, { "kind": "theorem", "id": "Semantics.TileStateMachine.captureTransitionRequiresNoLiberty", "name": "captureTransitionRequiresNoLiberty", "module": "Semantics.TileStateMachine" }, { "kind": "theorem", "id": "Semantics.TileStateMachine.koPreventsShapeRepetition", "name": "koPreventsShapeRepetition", "module": "Semantics.TileStateMachine" }, { "kind": "theorem", "id": "Semantics.TileStateMachine.capturedToEmptyAlwaysAllowed", "name": "capturedToEmptyAlwaysAllowed", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.zero", "name": "zero", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.one", "name": "one", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.ofFrac", "name": "ofFrac", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.hasLiberty", "name": "hasLiberty", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.canCapture", "name": "canCapture", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.wouldRepeatShape", "name": "wouldRepeatShape", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.canTransition", "name": "canTransition", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.flipTile", "name": "flipTile", "module": "Semantics.TileStateMachine" }, { "kind": "def", "id": "Semantics.TileStateMachine.createEmptyGrid", "name": "createEmptyGrid", "module": "Semantics.TileStateMachine" }, { "kind": "module", "id": "Semantics.Timing", "name": "Timing", "path": "Semantics/Timing.lean", "namespace": "Semantics.Timing", "doc": "Semantics/Timing.lean - Frustration-Aware Manifold Memory (FAMM) Protocol This module derives dynamic RAM timing parameters from the manifold physics state (Torsion, Interlocking Energy, Laplacian). Parameters calculated: tTCL (Torsional CAS Latency) tMRE (Manifold Refresh Epoch) tDLL (Damping Lap", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 113 }, { "kind": "def", "id": "Semantics.Timing.tBaseCAS", "name": "tBaseCAS", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.tBaseREF", "name": "tBaseREF", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.tBaseHammer", "name": "tBaseHammer", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.tMinFactor", "name": "tMinFactor", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.clampFactor", "name": "clampFactor", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.maxRefreshFactor", "name": "maxRefreshFactor", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.calculateTCL", "name": "calculateTCL", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.calculateMRE", "name": "calculateMRE", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.calculateDLL", "name": "calculateDLL", "module": "Semantics.Timing" }, { "kind": "def", "id": "Semantics.Timing.deriveTiming", "name": "deriveTiming", "module": "Semantics.Timing" }, { "kind": "module", "id": "Semantics.Toolkit", "name": "Toolkit", "path": "Semantics/Toolkit.lean", "namespace": "Semantics.Toolkit", "doc": "Toolkit.lean \u2014 Core Constants and Functions for BraidCore Predictions This module centralizes the exact rational constants used by the BraidCore framework: the Menger void fraction z = 7/27, dislocation corrections, unified coupling \u03b1_T, and helper functions for prediction, grading, and period comp", "math_kind": "braid", "sorry_count": 0, "theorem_count": 9, "def_count": 14, "struct_count": 0, "inductive_count": 0, "line_count": 161 }, { "kind": "theorem", "id": "Semantics.Toolkit.for", "name": "for", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.corr1Loop_identity", "name": "corr1Loop_identity", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.corr2Loop_identity", "name": "corr2Loop_identity", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.alphaT_identity", "name": "alphaT_identity", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.oneOverAlphaT_identity", "name": "oneOverAlphaT_identity", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.zMenger_corrected_identity", "name": "zMenger_corrected_identity", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.grade_speciesArea", "name": "grade_speciesArea", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.grade_mottCriterion", "name": "grade_mottCriterion", "module": "Semantics.Toolkit" }, { "kind": "theorem", "id": "Semantics.Toolkit.grade_largeError", "name": "grade_largeError", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.zMenger", "name": "zMenger", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.alphaFS", "name": "alphaFS", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.corr1Loop", "name": "corr1Loop", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.corr2Loop", "name": "corr2Loop", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.alphaT", "name": "alphaT", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.oneOverAlphaT", "name": "oneOverAlphaT", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.zTolerance", "name": "zTolerance", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.sweetSpotLower", "name": "sweetSpotLower", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.sweetSpotUpper", "name": "sweetSpotUpper", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.gradeThresholds", "name": "gradeThresholds", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.gradeFromError", "name": "gradeFromError", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.dislocationCorrect", "name": "dislocationCorrect", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.dislocationCorrect2Loop", "name": "dislocationCorrect2Loop", "module": "Semantics.Toolkit" }, { "kind": "def", "id": "Semantics.Toolkit.mengerPeriod", "name": "mengerPeriod", "module": "Semantics.Toolkit" }, { "kind": "module", "id": "Semantics.TopologicalAwareness", "name": "TopologicalAwareness", "path": "Semantics/TopologicalAwareness.lean", "namespace": "Semantics.TopologicalAwareness", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team TopologicalAwareness.lean \u2014 Lean 4 Topological Awareness and Geometric Primitives Database This module provides topological awareness for Lean 4, enabling the language to understand and reason about to", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 0, "def_count": 3, "struct_count": 5, "inductive_count": 2, "line_count": 764 }, { "kind": "def", "id": "Semantics.TopologicalAwareness.geometricPrimitivesDatabase", "name": "geometricPrimitivesDatabase", "module": "Semantics.TopologicalAwareness" }, { "kind": "def", "id": "Semantics.TopologicalAwareness.initializePrimitiveLUT", "name": "initializePrimitiveLUT", "module": "Semantics.TopologicalAwareness" }, { "kind": "def", "id": "Semantics.TopologicalAwareness.computeEulerCharacteristic", "name": "computeEulerCharacteristic", "module": "Semantics.TopologicalAwareness" }, { "kind": "module", "id": "Semantics.TopologicalBraidAdapter", "name": "TopologicalBraidAdapter", "path": "Semantics/TopologicalBraidAdapter.lean", "namespace": "Semantics.TopologicalBraidAdapter", "doc": "============================================================", "math_kind": "braid", "sorry_count": 0, "theorem_count": 8, "def_count": 23, "struct_count": 3, "inductive_count": 0, "line_count": 233 }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.fusionSpaceDim_four", "name": "fusionSpaceDim_four", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.fusionSpaceDim_five", "name": "fusionSpaceDim_five", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.fusionSpaceDim_six", "name": "fusionSpaceDim_six", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.fusionSpaceDim_eight", "name": "fusionSpaceDim_eight", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.stableSignal_implies_coherent", "name": "stableSignal_implies_coherent", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.noCfd_avoids_continuum", "name": "noCfd_avoids_continuum", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.tensegrity_yang_baxter_bound", "name": "tensegrity_yang_baxter_bound", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "theorem", "id": "Semantics.TopologicalBraidAdapter.tensegrity_implies_braid_coherence", "name": "tensegrity_implies_braid_coherence", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.AnyonBraid", "name": "AnyonBraid", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.braidFromSample", "name": "braidFromSample", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.fusionTree", "name": "fusionTree", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.vacuumSector", "name": "vacuumSector", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.fusionSpaceDim", "name": "fusionSpaceDim", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.crossingToSLUG3", "name": "crossingToSLUG3", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.identitySLUG3", "name": "identitySLUG3", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.composeSLUG3", "name": "composeSLUG3", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.braidToSLUG3", "name": "braidToSLUG3", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.sampleToSLUG3", "name": "sampleToSLUG3", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.accumulatedPhase", "name": "accumulatedPhase", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.q016ToFix16", "name": "q016ToFix16", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.computeW", "name": "computeW", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.colorRopeToDualQuat", "name": "colorRopeToDualQuat", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.stateSampleToDualQuat", "name": "stateSampleToDualQuat", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.liftDQWithMass", "name": "liftDQWithMass", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.topologicalCharge", "name": "topologicalCharge", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.sampleTopologicalCharge", "name": "sampleTopologicalCharge", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "def", "id": "Semantics.TopologicalBraidAdapter.hasQuantumDimension", "name": "hasQuantumDimension", "module": "Semantics.TopologicalBraidAdapter" }, { "kind": "module", "id": "Semantics.TopologicalPersistence", "name": "TopologicalPersistence", "path": "Semantics/TopologicalPersistence.lean", "namespace": "Semantics.TopologicalPersistence", "doc": "=========================================================================", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 10, "struct_count": 1, "inductive_count": 0, "line_count": 139 }, { "kind": "theorem", "id": "Semantics.TopologicalPersistence.topologicalBind_selfLawful", "name": "topologicalBind_selfLawful", "module": "Semantics.TopologicalPersistence" }, { "kind": "theorem", "id": "Semantics.TopologicalPersistence.barcodeDistance_selfZero", "name": "barcodeDistance_selfZero", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.persistence", "name": "persistence", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.Barcode", "name": "Barcode", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.totalPersistence", "name": "totalPersistence", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.significantFeatures", "name": "significantFeatures", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.bottleneckDistance", "name": "bottleneckDistance", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.barcodeInvariant", "name": "barcodeInvariant", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.barcodeCost", "name": "barcodeCost", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.topologicalBind", "name": "topologicalBind", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.sampleBarcode1", "name": "sampleBarcode1", "module": "Semantics.TopologicalPersistence" }, { "kind": "def", "id": "Semantics.TopologicalPersistence.sampleBarcode2", "name": "sampleBarcode2", "module": "Semantics.TopologicalPersistence" }, { "kind": "module", "id": "Semantics.TopologicalStateMachine", "name": "TopologicalStateMachine", "path": "Semantics/TopologicalStateMachine.lean", "namespace": "Semantics.TopologicalStateMachine", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team TopologicalStateMachine.lean \u2014 Lean-Clean Finite Skeleton (Version A) A formally verified core proving: 1. Nibble algebra is bijective (pack/unpack inverse) 2. Manifold transitions are register-injecti", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 7, "def_count": 15, "struct_count": 6, "inductive_count": 4, "line_count": 291 }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.NibbleSwitch", "name": "NibbleSwitch", "module": "Semantics.TopologicalStateMachine" }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.transition_register_injective", "name": "transition_register_injective", "module": "Semantics.TopologicalStateMachine" }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.transition_register_bijective", "name": "transition_register_bijective", "module": "Semantics.TopologicalStateMachine" }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.replay_length", "name": "replay_length", "module": "Semantics.TopologicalStateMachine" }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.replay_deterministic", "name": "replay_deterministic", "module": "Semantics.TopologicalStateMachine" }, { "kind": "theorem", "id": "Semantics.TopologicalStateMachine.register_update_surjective", "name": "register_update_surjective", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.LocusModulus", "name": "LocusModulus", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.ManifoldPoint", "name": "ManifoldPoint", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.EnglishForm", "name": "EnglishForm", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.englishFormCounts", "name": "englishFormCounts", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.eulerCharacteristic", "name": "eulerCharacteristic", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.Trajectory", "name": "Trajectory", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.countLoops", "name": "countLoops", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.productionHardware", "name": "productionHardware", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.HardwareSurface", "name": "HardwareSurface", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.CompressionObjective", "name": "CompressionObjective", "module": "Semantics.TopologicalStateMachine" }, { "kind": "def", "id": "Semantics.TopologicalStateMachine.selfReferential", "name": "selfReferential", "module": "Semantics.TopologicalStateMachine" }, { "kind": "module", "id": "Semantics.TopologyDlessScalar", "name": "TopologyDlessScalar", "path": "Semantics/TopologyDlessScalar.lean", "namespace": "Semantics.TopologyDless", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Dimensionless conformal factors \u03a9(equation) that warp the topology manifold metric, making safety-critical equations more discoverable (3.2x speedup). Adapted from MOIM's Dless Scalar Field for topology-specific use: 1.", "math_kind": "braid", "sorry_count": 0, "theorem_count": 4, "def_count": 14, "struct_count": 3, "inductive_count": 0, "line_count": 253 }, { "kind": "theorem", "id": "Semantics.TopologyDlessScalar.omega_positive", "name": "omega_positive", "module": "Semantics.TopologyDlessScalar" }, { "kind": "theorem", "id": "Semantics.TopologyDlessScalar.warped_distance_monotonic", "name": "warped_distance_monotonic", "module": "Semantics.TopologyDlessScalar" }, { "kind": "theorem", "id": "Semantics.TopologyDlessScalar.combine_preserves_positivity", "name": "combine_preserves_positivity", "module": "Semantics.TopologyDlessScalar" }, { "kind": "theorem", "id": "Semantics.TopologyDlessScalar.proven_higher_omega_than_conjecture", "name": "proven_higher_omega_than_conjecture", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.q0Sqrt", "name": "q0Sqrt", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.omegaFromStatus", "name": "omegaFromStatus", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.omegaFromCrossRefs", "name": "omegaFromCrossRefs", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.omegaFromFamily", "name": "omegaFromFamily", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.combineOmega", "name": "combineOmega", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.warpedDistance", "name": "warpedDistance", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.warpManifoldPoint", "name": "warpManifoldPoint", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.computeTopologyOmega", "name": "computeTopologyOmega", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.createWarpedTopologyEquation", "name": "createWarpedTopologyEquation", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.omegaSearchResult", "name": "omegaSearchResult", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.sortOmegaResults", "name": "sortOmegaResults", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.eulerCharacteristicOmega", "name": "eulerCharacteristicOmega", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.symplecticFormOmega", "name": "symplecticFormOmega", "module": "Semantics.TopologyDlessScalar" }, { "kind": "def", "id": "Semantics.TopologyDlessScalar.entropyVectorOmega", "name": "entropyVectorOmega", "module": "Semantics.TopologyDlessScalar" }, { "kind": "module", "id": "Semantics.TopologyDomainAlignment", "name": "TopologyDomainAlignment", "path": "Semantics/TopologyDomainAlignment.lean", "namespace": "Semantics.TopologyDomainAlignment", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Aligns topology equation domains with MOIM's 16 domain registries for unified classification and cross-referencing (1.8x cross-domain speedup). This module provides bidirectional mapping between topology-specific classi", "math_kind": "braid", "sorry_count": 0, "theorem_count": 4, "def_count": 11, "struct_count": 1, "inductive_count": 2, "line_count": 255 }, { "kind": "theorem", "id": "Semantics.TopologyDomainAlignment.compatibility_reflexive", "name": "compatibility_reflexive", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "theorem", "id": "Semantics.TopologyDomainAlignment.compatibility_symmetric", "name": "compatibility_symmetric", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "theorem", "id": "Semantics.TopologyDomainAlignment.full_bidirectional_coverage", "name": "full_bidirectional_coverage", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "theorem", "id": "Semantics.TopologyDomainAlignment.math_has_most_topology_domains", "name": "math_has_most_topology_domains", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.alignTopologyDomain", "name": "alignTopologyDomain", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.reverseAlignTopologyDomain", "name": "reverseAlignTopologyDomain", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.domainsCompatible", "name": "domainsCompatible", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.alignmentIsBidirectional", "name": "alignmentIsBidirectional", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.countMappingsToMOIM", "name": "countMappingsToMOIM", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.bidirectionalCoverage", "name": "bidirectionalCoverage", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.tagEulerCharacteristicDomain", "name": "tagEulerCharacteristicDomain", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.tagEntropyVectorDomain", "name": "tagEntropyVectorDomain", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.tagSymplecticFormDomain", "name": "tagSymplecticFormDomain", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.createTaggedEquation", "name": "createTaggedEquation", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "def", "id": "Semantics.TopologyDomainAlignment.crossDomainTopologySearch", "name": "crossDomainTopologySearch", "module": "Semantics.TopologyDomainAlignment" }, { "kind": "module", "id": "Semantics.TopologyFractalEncoding", "name": "TopologyFractalEncoding", "path": "Semantics/TopologyFractalEncoding.lean", "namespace": "Semantics.TopologyFractal", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Self-similar, fractal-encoded topology equation graph database adapted from MOIM's ENE system for genus-3 topology calculations. This module provides O(log n) search for topology equations via manifold- distance pruning", "math_kind": "braid", "sorry_count": 0, "theorem_count": 3, "def_count": 7, "struct_count": 5, "inductive_count": 1, "line_count": 254 }, { "kind": "theorem", "id": "Semantics.TopologyFractalEncoding.subtree_fold_empty", "name": "subtree_fold_empty", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "theorem", "id": "Semantics.TopologyFractalEncoding.integrity_reflexive_leaf", "name": "integrity_reflexive_leaf", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "theorem", "id": "Semantics.TopologyFractalEncoding.manifold_distance_nonnegative", "name": "manifold_distance_nonnegative", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.computeSubtreeFold", "name": "computeSubtreeFold", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.verifyIntegrity", "name": "verifyIntegrity", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.manifoldDistance", "name": "manifoldDistance", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.foldTopologyDescription", "name": "foldTopologyDescription", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.foldSubtree", "name": "foldSubtree", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.insert", "name": "insert", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "def", "id": "Semantics.TopologyFractalEncoding.spiralSearch", "name": "spiralSearch", "module": "Semantics.TopologyFractalEncoding" }, { "kind": "module", "id": "Semantics.TopologyGoldenSpiral", "name": "TopologyGoldenSpiral", "path": "Semantics/TopologyGoldenSpiral.lean", "namespace": "Semantics.TopologyGoldenSpiral", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Golden angle (137.5\u00b0) navigation in topology parameter space for efficient genus parameter exploration and optimization. Adapted from MOIM's Golden Spiral Navigator for topology-specific use: 1. Golden Angle: \u03b8 = 2\u03c0/\u03c6\u00b2 ", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 3, "def_count": 13, "struct_count": 5, "inductive_count": 0, "line_count": 294 }, { "kind": "theorem", "id": "Semantics.TopologyGoldenSpiral.golden_angle_approx_137_5", "name": "golden_angle_approx_137_5", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "theorem", "id": "Semantics.TopologyGoldenSpiral.spiral_radius_nonnegative", "name": "spiral_radius_nonnegative", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "theorem", "id": "Semantics.TopologyGoldenSpiral.advance_increments_step_count", "name": "advance_increments_step_count", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.q0Sqrt", "name": "q0Sqrt", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.q0ToNat", "name": "q0ToNat", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.goldenAngleQ0", "name": "goldenAngleQ0", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.spiralToCartesian", "name": "spiralToCartesian", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.cartesianToSpiral", "name": "cartesianToSpiral", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.genusToSpiral", "name": "genusToSpiral", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.batchGenusToSpiral", "name": "batchGenusToSpiral", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.initNavigator", "name": "initNavigator", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.advanceNavigator", "name": "advanceNavigator", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.withinRadius", "name": "withinRadius", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.spiralSearch", "name": "spiralSearch", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.genusToParameterSpace", "name": "genusToParameterSpace", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "def", "id": "Semantics.TopologyGoldenSpiral.searchOptimalGenus", "name": "searchOptimalGenus", "module": "Semantics.TopologyGoldenSpiral" }, { "kind": "module", "id": "Semantics.TopologyNode", "name": "TopologyNode", "path": "Semantics/TopologyNode.lean", "namespace": "Semantics.TopologyNode", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team TopologyNode.lean \u2014 Hardware Node Layer Dumb infrastructure nodes that advertise hardware capabilities and respond to topology pings. The topology controller (software layer) forms quorum and schedules", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 2, "def_count": 18, "struct_count": 1, "inductive_count": 3, "line_count": 245 }, { "kind": "theorem", "id": "Semantics.TopologyNode.failedNodeCannotRunService", "name": "failedNodeCannotRunService", "module": "Semantics.TopologyNode" }, { "kind": "theorem", "id": "Semantics.TopologyNode.failedNodeCannotBind", "name": "failedNodeCannotBind", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.halfQ", "name": "halfQ", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.quarterQ", "name": "quarterQ", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.ofFracQ", "name": "ofFracQ", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.HardwareCapability", "name": "HardwareCapability", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.serviceRequirements", "name": "serviceRequirements", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.serviceCost", "name": "serviceCost", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.maxEnergyFor", "name": "maxEnergyFor", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.energyRecoveryRate", "name": "energyRecoveryRate", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.initNode", "name": "initNode", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.canRunService", "name": "canRunService", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.deductEnergy", "name": "deductEnergy", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.recoverEnergy", "name": "recoverEnergy", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.canAcceptBind", "name": "canAcceptBind", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.exampleCoreNode", "name": "exampleCoreNode", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.exampleJudgeHost", "name": "exampleJudgeHost", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.exampleMirrorNode", "name": "exampleMirrorNode", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.exampleEdgeNode", "name": "exampleEdgeNode", "module": "Semantics.TopologyNode" }, { "kind": "def", "id": "Semantics.TopologyNode.exampleFoxTopNode", "name": "exampleFoxTopNode", "module": "Semantics.TopologyNode" }, { "kind": "module", "id": "Semantics.TopologyOptimization", "name": "TopologyOptimization", "path": "Semantics/TopologyOptimization.lean", "namespace": "Semantics.TopologyOptimization", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 1, "struct_count": 6, "inductive_count": 0, "line_count": 60 }, { "kind": "def", "id": "Semantics.TopologyOptimization.runSampleOptimization", "name": "runSampleOptimization", "module": "Semantics.TopologyOptimization" }, { "kind": "module", "id": "Semantics.TopologyPhinary", "name": "TopologyPhinary", "path": "Semantics/TopologyPhinary.lean", "namespace": "Semantics.TopologyPhinary", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550 Phinary (base-\u03c6) arithmetic adapted from MOIM for Genus3TopologyMetaprobe division-heavy operations, providing 2.3x speedup via carry-free computation. 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Authors: Research Stack Team TopologyResilience.lean \u2014 Geometric Topology meets Load Balancing & Resilience Bridges abstract manifold topology with practical distributed systems: Load balancing = geodesic flow on energy densi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 2, "def_count": 20, "struct_count": 3, "inductive_count": 0, "line_count": 268 }, { "kind": "theorem", "id": "Semantics.TopologyResilience.overloadedImpliesHighUtilization", "name": "overloadedImpliesHighUtilization", "module": "Semantics.TopologyResilience" }, { "kind": "theorem", "id": "Semantics.TopologyResilience.kResilientNoSinglePointOfFailure", "name": "kResilientNoSinglePointOfFailure", "module": "Semantics.TopologyResilience" }, { "kind": "def", "id": "Semantics.TopologyResilience.LoadField", "name": "LoadField", "module": "Semantics.TopologyResilience" }, { "kind": "def", "id": "Semantics.TopologyResilience.uniformLoad", "name": "uniformLoad", "module": "Semantics.TopologyResilience" }, 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"earthSeg", "module": "Semantics.TopologyResilience" }, { "kind": "def", "id": "Semantics.TopologyResilience.marsSeg", "name": "marsSeg", "module": "Semantics.TopologyResilience" }, { "kind": "def", "id": "Semantics.TopologyResilience.plutoSeg", "name": "plutoSeg", "module": "Semantics.TopologyResilience" }, { "kind": "def", "id": "Semantics.TopologyResilience.solarSystemNetwork", "name": "solarSystemNetwork", "module": "Semantics.TopologyResilience" }, { "kind": "module", "id": "Semantics.TorsionalPIST", "name": "TorsionalPIST", "path": "Semantics/TorsionalPIST.lean", "namespace": "Semantics.TorsionalPIST", "doc": "structure TorsionalState where q1 : Semantics.Quaternion.Quaternion q2 : Semantics.Quaternion.Quaternion q3 : Semantics.Quaternion.Quaternion eta : DynamicCanal.Fix16 energy : DynamicCanal.Fix16 deriving Repr, DecidableEq, Inhabited def TorsionalState_initial : TorsionalState := { q1 := Semantics.Q", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 5, "def_count": 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"Semantics.TorsionalPIST.TorsionalState_torsionalBetaStep", "name": "TorsionalState_torsionalBetaStep", "module": "Semantics.TorsionalPIST" }, { "kind": "def", "id": "Semantics.TorsionalPIST.TorsionalState_recoveryViaTurbulence", "name": "TorsionalState_recoveryViaTurbulence", "module": "Semantics.TorsionalPIST" }, { "kind": "def", "id": "Semantics.TorsionalPIST.TorsionalState_rgFlow", "name": "TorsionalState_rgFlow", "module": "Semantics.TorsionalPIST" }, { "kind": "def", "id": "Semantics.TorsionalPIST.TorsionalState_refreshFromPulse", "name": "TorsionalState_refreshFromPulse", "module": "Semantics.TorsionalPIST" }, { "kind": "def", "id": "Semantics.TorsionalPIST.TorsionalState_gridRefresh", "name": "TorsionalState_gridRefresh", "module": "Semantics.TorsionalPIST" }, { "kind": "def", "id": "Semantics.TorsionalPIST.TorsionalState_isClassicalPure", "name": "TorsionalState_isClassicalPure", "module": "Semantics.TorsionalPIST" }, { "kind": "module", "id": "Semantics.Toybox.HierarchicalBinding", "name": "HierarchicalBinding", "path": "Semantics/Toybox/HierarchicalBinding.lean", "namespace": "Semantics.Toybox.HierarchicalBinding", "doc": "Toybox: HierarchicalBinding.lean Physical state space compression via hierarchical field binding. 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Core insight: The hydrogen atom produces discrete spectral lines via the Rydberg formula: 1/\u03bb = R_H (1/n\u2081\u00b2 - 1/n\u2082\u00b2) This is the most fundamental spectral decomposition in physi", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 0, "def_count": 11, "struct_count": 1, "inductive_count": 0, "line_count": 216 }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.rydbergScaled", "name": "rydbergScaled", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.cScaled", "name": "cScaled", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.hScaled", "name": "hScaled", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.PrincipalLevel", "name": "PrincipalLevel", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.wavenumber", "name": "wavenumber", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.wavenumberToWavelength", "name": "wavenumberToWavelength", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.lymanWavelengths", "name": "lymanWavelengths", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.balmerWavelengths", "name": "balmerWavelengths", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.hydrogenSpectralBasis", "name": "hydrogenSpectralBasis", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.resonanceStrength", "name": "resonanceStrength", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "def", "id": "Semantics.Toybox.HydrogenSpectralBasis.encode7Bit", "name": "encode7Bit", "module": "Semantics.Toybox.HydrogenSpectralBasis" }, { "kind": "module", "id": "Semantics.Toybox.ObserverAngle", "name": "ObserverAngle", "path": "Semantics/Toybox/ObserverAngle.lean", "namespace": "Semantics.Toybox.ObserverAngle", "doc": "Toybox: ObserverAngle.lean Investigation of compression as dimensional projection from specific viewing angles. 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"Semantics.UnifiedDomainTheory", "doc": "Released under Apache 2.0 license as described in the file LICENSE. 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Authors: Research Stack Team UniversalCoupling.lean \u2014 Domain-Agnostic Trajectory Engine Formalizes a reusable path-selection and propagation kernel across three domains: \u2022 Astrophysics: Dynamics on gravitational manifolds (domain ", "math_kind": "geometry", "sorry_count": 0, "theorem_count": 1, "def_count": 13, "struct_count": 6, "inductive_count": 1, "line_count": 272 }, { "kind": "theorem", "id": "Semantics.UniversalCoupling.selfTypingPreservesCoupling", "name": "selfTypingPreservesCoupling", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.domainDim", "name": "domainDim", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.nDot", "name": "nDot", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.Jn", "name": "Jn", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.jAstrophysical", "name": "jAstrophysical", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.jNeural", "name": "jNeural", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.jMaritime", "name": "jMaritime", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.routeTrajectory", "name": "routeTrajectory", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.trajectoryEquivalent", "name": "trajectoryEquivalent", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.selfTyped", "name": "selfTyped", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.verilogParams", "name": "verilogParams", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.axis11Decision", "name": "axis11Decision", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.testAstroParams", "name": "testAstroParams", "module": "Semantics.UniversalCoupling" }, { "kind": "def", "id": "Semantics.UniversalCoupling.testMass", "name": "testMass", "module": "Semantics.UniversalCoupling" }, { "kind": "module", "id": "Semantics.UniversalField", "name": "UniversalField", "path": "Semantics/UniversalField.lean", "namespace": "Semantics.UniversalField", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team UniversalField.lean \u2014 \u03a6_universal implementation (EQUATION #0) This module implements the Universal Field equation as the foundation for all OTOM physics. 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"Semantics.V4.CayleyFibergraph" }, { "kind": "def", "id": "Semantics.V4.CayleyFibergraph.cayley_dist", "name": "cayley_dist", "module": "Semantics.V4.CayleyFibergraph" }, { "kind": "def", "id": "Semantics.V4.CayleyFibergraph.pist_mass", "name": "pist_mass", "module": "Semantics.V4.CayleyFibergraph" }, { "kind": "def", "id": "Semantics.V4.CayleyFibergraph.nuvmap_addr", "name": "nuvmap_addr", "module": "Semantics.V4.CayleyFibergraph" }, { "kind": "def", "id": "Semantics.V4.CayleyFibergraph.inv", "name": "inv", "module": "Semantics.V4.CayleyFibergraph" }, { "kind": "def", "id": "Semantics.V4.CayleyFibergraph.DNABase", "name": "DNABase", "module": "Semantics.V4.CayleyFibergraph" }, { "kind": "module", "id": "Semantics.VLsIPartition", "name": "VLsIPartition", "path": "Semantics/VLsIPartition.lean", "namespace": "Semantics.VLsIPartition", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team VLsIPartition.lean \u2014 Spatial-Aware Analytic Partitioning for VLSI This module formalizes SAAP from \"An Efficient Spatial-Aware Analytic Partitioning Algorithm of VLSI Netlists for Parallel Routing\" (ar", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 1, "def_count": 25, "struct_count": 11, "inductive_count": 0, "line_count": 312 }, { "kind": "theorem", "id": "Semantics.VLsIPartition.balanceImpliesBounds", "name": "balanceImpliesBounds", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.zero", "name": "zero", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.one", "name": "one", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.ofNat", "name": "ofNat", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.add", "name": "add", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.sub", "name": "sub", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.mul", "name": "mul", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.div", "name": "div", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.neg", "name": "neg", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.le", "name": "le", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.lt", "name": "lt", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.pointInBox", "name": "pointInBox", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.validatePartition", "name": "validatePartition", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.boxArea", "name": "boxArea", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.boxesOverlap", "name": "boxesOverlap", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.totalNodeWeight", "name": "totalNodeWeight", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.getPartition", "name": "getPartition", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.checkBalanceConstraint", "name": "checkBalanceConstraint", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.boundingPolygon", "name": "boundingPolygon", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.checkSpatialContinuity", "name": "checkSpatialContinuity", "module": "Semantics.VLsIPartition" }, { "kind": "def", "id": "Semantics.VLsIPartition.checkSpatialConstraint", "name": "checkSpatialConstraint", "module": "Semantics.VLsIPartition" }, { "kind": "module", "id": "Semantics.VecState", "name": "VecState", "path": "Semantics/VecState.lean", "namespace": "Semantics", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team VecState.lean \u2014 Algebraic Vector States for AVMR Tree Construction Per AGENTS.md \u00a72: PascalCase for types, camelCase for functions. 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"Semantics.WhitespaceFreeGrammar.storedBytes", "name": "storedBytes", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "def", "id": "Semantics.WhitespaceFreeGrammar.canonicalDisplayBytes", "name": "canonicalDisplayBytes", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "def", "id": "Semantics.WhitespaceFreeGrammar.atomA", "name": "atomA", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "def", "id": "Semantics.WhitespaceFreeGrammar.atomB", "name": "atomB", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "def", "id": "Semantics.WhitespaceFreeGrammar.atomC", "name": "atomC", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "def", "id": "Semantics.WhitespaceFreeGrammar.exampleAtoms", "name": "exampleAtoms", "module": "Semantics.WhitespaceFreeGrammar" }, { "kind": "module", "id": "Semantics.Witness", "name": "Witness", "path": "Semantics/Witness.lean", "namespace": "Semantics.ENE", "doc": "Witness and Constitution", "math_kind": "rrc", 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"WitnessGrammar", "path": "Semantics/WitnessGrammar.lean", "namespace": "Semantics.WitnessGrammar", "doc": "Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team WitnessGrammar.lean \u2014 Finite Symbolic Source Code Recovered from a Field A WitnessGrammar is the finite symbolic source code recovered from a field. 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Verified against documented compression results. Achievement sources: Delta GCL on Lean metadata: 99.9% (4.1MB \u2192 4KB) = 1000\u00d7 Delta GCL on swarm components: 92% (9 chars vs 117 bases) = 13\u00d7", "math_kind": "algebra", "sorry_count": 0, "theorem_count": 3, "def_count": 14, "struct_count": 3, "inductive_count": 0, "line_count": 161 }, { "kind": "theorem", "id": "Semantics.YangMillsCompression.pipelineRatio_ge_one", "name": "pipelineRatio_ge_one", "module": "Semantics.YangMillsCompression" }, { "kind": "theorem", "id": "Semantics.YangMillsCompression.stage_reduces_size", "name": "stage_reduces_size", "module": "Semantics.YangMillsCompression" }, { "kind": "theorem", "id": "Semantics.YangMillsCompression.conservative_le_aggressive", "name": "conservative_le_aggressive", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.leanMetadataAchievement", "name": "leanMetadataAchievement", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": 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"deltaGCLStage", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.topologicalStage", "name": "topologicalStage", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.neuralVAEStage", "name": "neuralVAEStage", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.conservativePipeline", "name": "conservativePipeline", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.aggressivePipeline", "name": "aggressivePipeline", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.pipelineRatio", "name": "pipelineRatio", "module": "Semantics.YangMillsCompression" }, { "kind": "def", "id": "Semantics.YangMillsCompression.finalCompressedSize", "name": "finalCompressedSize", "module": "Semantics.YangMillsCompression" }, { "kind": "module", "id": "Semantics.YangMillsCompressionBounds", "name": "YangMillsCompressionBounds", "path": "Semantics/YangMillsCompressionBounds.lean", "namespace": "Semantics.YangMillsCompressionBounds", "doc": "Formalization of compression bounds separating: Lossless compression (exact reconstruction) Lossy compression (acceptable precision loss) Precision-reduced compression (fixed-point conversion) Transmission avoidance (Layer 3 local computation) Key invariant: compressionRatio \u2260 transmissionAvoidance", "math_kind": "fixedpoint", "sorry_count": 0, "theorem_count": 5, "def_count": 5, "struct_count": 2, "inductive_count": 1, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.YangMillsCompressionBounds.lossless_ratio_ge_one", "name": "lossless_ratio_ge_one", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "theorem", "id": "Semantics.YangMillsCompressionBounds.precision_reduction_exact_two", "name": "precision_reduction_exact_two", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "theorem", "id": "Semantics.YangMillsCompressionBounds.transmission_avoidance_no_compression", "name": "transmission_avoidance_no_compression", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "theorem", "id": "Semantics.YangMillsCompressionBounds.compression_not_transmission_avoidance", "name": "compression_not_transmission_avoidance", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "theorem", "id": "Semantics.YangMillsCompressionBounds.effective_cost_formula", "name": "effective_cost_formula", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "def", "id": "Semantics.YangMillsCompressionBounds.losslessBounds", "name": "losslessBounds", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "def", "id": "Semantics.YangMillsCompressionBounds.lossyBounds", "name": "lossyBounds", "module": "Semantics.YangMillsCompressionBounds" }, { "kind": "def", "id": 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Based on SU(3) gauge field lattice with 64\u2074 sites. Key equations: Lattice sites: N = L\u2074 where L = 64 Gauge field: SU(3) = 4 complex numbers per site (link variables) Raw size: S_raw = N \u00d7 4 \u00d7 2 \u00d7 8 bytes Compressed siz", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 3, "def_count": 17, "struct_count": 3, "inductive_count": 0, "line_count": 171 }, { "kind": "theorem", "id": "Semantics.YangMillsLattice.rawLatticeSize_positive", "name": "rawLatticeSize_positive", "module": "Semantics.YangMillsLattice" }, { "kind": "theorem", "id": "Semantics.YangMillsLattice.compressionRatio_ge_one", "name": "compressionRatio_ge_one", "module": "Semantics.YangMillsLattice" }, { "kind": "theorem", "id": "Semantics.YangMillsLattice.compressed_le_raw", "name": "compressed_le_raw", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.defaultLatticeConfig", "name": "defaultLatticeConfig", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.latticeSites", "name": "latticeSites", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.rawLatticeSize", "name": "rawLatticeSize", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.bytesToMegabytes", "name": "bytesToMegabytes", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.rawLatticeSizeMB", "name": "rawLatticeSizeMB", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.conservativePipeline", "name": "conservativePipeline", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.aggressivePipeline", "name": "aggressivePipeline", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.totalCompressionRatio", "name": "totalCompressionRatio", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.compressedLatticeSizeMB", "name": "compressedLatticeSizeMB", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.compressionRatio", "name": "compressionRatio", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.defaultPerformanceParams", "name": "defaultPerformanceParams", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.totalFlops", "name": "totalFlops", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.secondsFromFlopsAtGFlops", "name": "secondsFromFlopsAtGFlops", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.theoreticalTime", "name": "theoreticalTime", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.realisticTime", "name": "realisticTime", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.performanceWithCompression", "name": "performanceWithCompression", "module": "Semantics.YangMillsLattice" }, { "kind": "def", "id": "Semantics.YangMillsLattice.performanceWithLayer3", "name": "performanceWithLayer3", "module": "Semantics.YangMillsLattice" }, { "kind": "module", "id": "Semantics.YangMillsLatticeSizing", "name": "YangMillsLatticeSizing", "path": "Semantics/YangMillsLatticeSizing.lean", "namespace": "Semantics.YangMillsLatticeSizing", "doc": "Formalization of lattice site count and storage models for small lattice experiments. This is NOT a Yang-Mills proof stack - it is a lattice-gauge / compression / verification sandbox. Key invariants: Small lattice experiments only (toy models) Storage models for 8-real/site vs full SU(3) link mode", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 3, "def_count": 7, "struct_count": 2, "inductive_count": 0, "line_count": 130 }, { "kind": "theorem", "id": "Semantics.YangMillsLatticeSizing.latticeSites_positive", "name": "latticeSites_positive", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "theorem", "id": "Semantics.YangMillsLatticeSizing.rawStorageSize_positive", "name": "rawStorageSize_positive", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "theorem", "id": "Semantics.YangMillsLatticeSizing.eightRealModel_eightReals", "name": "eightRealModel_eightReals", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.defaultToyLattice", "name": "defaultToyLattice", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.latticeSites", "name": "latticeSites", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.rawStorageSize", "name": "rawStorageSize", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.bytesToMegabytes", "name": "bytesToMegabytes", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.rawStorageSizeMB", "name": "rawStorageSizeMB", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.su3LinkModel_eightReals", "name": "su3LinkModel_eightReals", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "def", "id": "Semantics.YangMillsLatticeSizing.feasibilityCheck", "name": "feasibilityCheck", "module": "Semantics.YangMillsLatticeSizing" }, { "kind": "module", "id": "Semantics.YangMillsPerformance", "name": "YangMillsPerformance", "path": "Semantics/YangMillsPerformance.lean", "namespace": "Semantics.YangMillsPerformance", "doc": "Formalization of performance estimation for Yang-Mills lattice computations on distributed VPS nodes with AVX512 acceleration. Key equations: Total FLOPs: F_total = N \u00d7 F_site Theoretical time: T_theoretical = F_total / (GFLOPS_core \u00d7 N_cores \u00d7 10^9) Realistic time: T_realistic = T_theoretical \u00d7 ov", "math_kind": "quantum", "sorry_count": 0, "theorem_count": 4, "def_count": 17, "struct_count": 6, "inductive_count": 0, "line_count": 210 }, { "kind": "theorem", "id": "Semantics.YangMillsPerformance.theoreticalTime_positive", "name": "theoreticalTime_positive", "module": "Semantics.YangMillsPerformance" }, { "kind": "theorem", "id": "Semantics.YangMillsPerformance.realistic_ge_theoretical", "name": "realistic_ge_theoretical", "module": "Semantics.YangMillsPerformance" }, { "kind": "theorem", "id": "Semantics.YangMillsPerformance.compression_reduces_time", "name": "compression_reduces_time", "module": "Semantics.YangMillsPerformance" }, { "kind": "theorem", "id": "Semantics.YangMillsPerformance.layer3_reduces_time", "name": "layer3_reduces_time", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.netcupRouterSpec", "name": "netcupRouterSpec", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.racknerdSpec", "name": "racknerdSpec", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.defaultLatticeComputation", "name": "defaultLatticeComputation", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.totalSites", "name": "totalSites", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.totalFlops", "name": "totalFlops", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.secondsFromFlopsAtGFlops", "name": "secondsFromFlopsAtGFlops", "module": "Semantics.YangMillsPerformance" }, { "kind": "def", "id": "Semantics.YangMillsPerformance.theoreticalTimeSingle", "name": "theoreticalTimeSingle", 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"4-Infrastructure/shim/burgers_hilbert_threshold.py", "doc": "Scale by 2/pi \u2248 0.6366 * Q16" }, { "kind": "script", "id": "script:4-Infrastructure/shim/c16_controller_projection.py", "name": "c16_controller_projection.py", "path": "4-Infrastructure/shim/c16_controller_projection.py", "doc": "Existing Q16_16 raw values from Semantics/Physics/DESIInvariant.lean" }, { "kind": "script", "id": "script:4-Infrastructure/shim/candidate_certification_bridge.py", "name": "candidate_certification_bridge.py", "path": "4-Infrastructure/shim/candidate_certification_bridge.py", "doc": "After running geometric_entropy_explorer.py --batch 50" }, { "kind": "script", "id": "script:4-Infrastructure/shim/capability_probe.py", "name": "capability_probe.py", "path": "4-Infrastructure/shim/capability_probe.py", "doc": "=========================================================================" }, { "kind": "script", "id": "script:4-Infrastructure/shim/cern_extractor.py", "name": "cern_extractor.py", "path": "4-Infrastructure/shim/cern_extractor.py", "doc": "Constants" }, { "kind": "script", "id": "script:4-Infrastructure/shim/chaos_game_16d.py", "name": "chaos_game_16d.py", "path": "4-Infrastructure/shim/chaos_game_16d.py", "doc": "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/chinese_postman_demo.py", "name": "chinese_postman_demo.py", "path": "4-Infrastructure/shim/chinese_postman_demo.py", "doc": "Compute degree of each vertex" }, { "kind": "script", "id": "script:4-Infrastructure/shim/clean_rrc_pist_validation.py", "name": "clean_rrc_pist_validation.py", "path": "4-Infrastructure/shim/clean_rrc_pist_validation.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/combined_theorems.py", "name": "combined_theorems.py", "path": "4-Infrastructure/shim/combined_theorems.py", "doc": "\u2500\u2500 Original 42 from pist_canary_batch.py \u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/compare_tier1_vs_tier2.py", "name": "compare_tier1_vs_tier2.py", "path": "4-Infrastructure/shim/compare_tier1_vs_tier2.py", "doc": "Build vectors" }, { "kind": "script", "id": "script:4-Infrastructure/shim/compute_adjugate_identity.py", "name": "compute_adjugate_identity.py", "path": "4-Infrastructure/shim/compute_adjugate_identity.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/coulomb_4body_braid.py", "name": "coulomb_4body_braid.py", "path": "4-Infrastructure/shim/coulomb_4body_braid.py", "doc": "Sidon-weighted Coulomb energy" }, { "kind": "script", "id": "script:4-Infrastructure/shim/coverage_density_probe.py", "name": "coverage_density_probe.py", "path": "4-Infrastructure/shim/coverage_density_probe.py", "doc": "---------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/cross_domain_bridge_demo.py", "name": "cross_domain_bridge_demo.py", "path": "4-Infrastructure/shim/cross_domain_bridge_demo.py", "doc": "\u2500\u2500\u2500 Theorem database \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/dataset_ingest_rds.py", "name": "dataset_ingest_rds.py", "path": "4-Infrastructure/shim/dataset_ingest_rds.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/decompose_tier2b_traces.py", "name": "decompose_tier2b_traces.py", "path": "4-Infrastructure/shim/decompose_tier2b_traces.py", "doc": "Estimate second eigenvalue via shifted power iteration" }, { "kind": "script", "id": "script:4-Infrastructure/shim/desi_adapter_refinement.py", "name": "desi_adapter_refinement.py", "path": "4-Infrastructure/shim/desi_adapter_refinement.py", "doc": "Q16_16 raw values from Semantics/Physics/DESIInvariant.lean" }, { "kind": "script", "id": "script:4-Infrastructure/shim/desi_raw_rederivation.py", "name": "desi_raw_rederivation.py", "path": "4-Infrastructure/shim/desi_raw_rederivation.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/device_capability_probe.py", "name": "device_capability_probe.py", "path": "4-Infrastructure/shim/device_capability_probe.py", "doc": "VCN alignment" }, { "kind": "script", "id": "script:4-Infrastructure/shim/download_lean_corpus.py", "name": "download_lean_corpus.py", "path": "4-Infrastructure/shim/download_lean_corpus.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/eigensolid_lean_bridge.py", "name": "eigensolid_lean_bridge.py", "path": "4-Infrastructure/shim/eigensolid_lean_bridge.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/eigensolid_pipeline.py", "name": "eigensolid_pipeline.py", "path": "4-Infrastructure/shim/eigensolid_pipeline.py", "doc": "-----------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/emit250_extract.py", "name": "emit250_extract.py", "path": "4-Infrastructure/shim/emit250_extract.py", "doc": "/// script" }, { "kind": "script", "id": "script:4-Infrastructure/shim/ene_migrate_and_tag.py", "name": "ene_migrate_and_tag.py", "path": "4-Infrastructure/shim/ene_migrate_and_tag.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/ene_wiki_body_reingest.py", "name": "ene_wiki_body_reingest.py", "path": "4-Infrastructure/shim/ene_wiki_body_reingest.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/entropic_collision_prober.py", "name": "entropic_collision_prober.py", "path": "4-Infrastructure/shim/entropic_collision_prober.py", "doc": "Calculate Shannon entropy" }, { "kind": "script", "id": "script:4-Infrastructure/shim/equation_shape_parser.py", "name": "equation_shape_parser.py", "path": "4-Infrastructure/shim/equation_shape_parser.py", "doc": "\u2500\u2500\u2500 Shape signature from equation structure \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/erdos_discrepancy_probe.py", "name": "erdos_discrepancy_probe.py", "path": "4-Infrastructure/shim/erdos_discrepancy_probe.py", "doc": "homogeneous AP check" }, { "kind": "script", "id": "script:4-Infrastructure/shim/erdos_discrepancy_probe_simd.py", "name": "erdos_discrepancy_probe_simd.py", "path": "4-Infrastructure/shim/erdos_discrepancy_probe_simd.py", "doc": "In SIMD, we can extract the AP for a given q instantly using strided slicing:" }, { "kind": "script", "id": "script:4-Infrastructure/shim/erdos_e8_rrc_projection.py", "name": "erdos_e8_rrc_projection.py", "path": "4-Infrastructure/shim/erdos_e8_rrc_projection.py", "doc": "Gamma (Obstruction Overlap Factor)" }, { "kind": "script", "id": "script:4-Infrastructure/shim/erdos_e8_rrc_refined.py", "name": "erdos_e8_rrc_refined.py", "path": "4-Infrastructure/shim/erdos_e8_rrc_refined.py", "doc": "Gamma (Obstruction Overlap Factor)" }, { "kind": "script", "id": "script:4-Infrastructure/shim/failure_flexure_bank.py", "name": "failure_flexure_bank.py", "path": "4-Infrastructure/shim/failure_flexure_bank.py", "doc": "\u2500\u2500 Missing rewrite direction (rw needs \u2190 or different order) \u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/flac_dsp_node.py", "name": "flac_dsp_node.py", "path": "4-Infrastructure/shim/flac_dsp_node.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/fractal_dimension.py", "name": "fractal_dimension.py", "path": "4-Infrastructure/shim/fractal_dimension.py", "doc": "---------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/galois_orbit_trimmer.py", "name": "galois_orbit_trimmer.py", "path": "4-Infrastructure/shim/galois_orbit_trimmer.py", "doc": "We generate in pairs (gamma, conj(gamma))" }, { "kind": "script", "id": "script:4-Infrastructure/shim/gccl_transfer_pipeline.py", "name": "gccl_transfer_pipeline.py", "path": "4-Infrastructure/shim/gccl_transfer_pipeline.py", "doc": "Insert shim path to import gccl_waveprobe" }, { "kind": "script", "id": "script:4-Infrastructure/shim/gccl_waveprobe.py", "name": "gccl_waveprobe.py", "path": "4-Infrastructure/shim/gccl_waveprobe.py", "doc": "\u2500\u2500 Q16_16 Fixed-Point \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/gen_grammar_thread_receipts.py", "name": "gen_grammar_thread_receipts.py", "path": "4-Infrastructure/shim/gen_grammar_thread_receipts.py", "doc": "\u2500\u2500 CONFIRMED \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/generate_ephemeris_lut.py", "name": "generate_ephemeris_lut.py", "path": "4-Infrastructure/shim/generate_ephemeris_lut.py", "doc": "Q16_16 scale factor" }, { "kind": "script", "id": "script:4-Infrastructure/shim/genetic_braid_bridge.py", "name": "genetic_braid_bridge.py", "path": "4-Infrastructure/shim/genetic_braid_bridge.py", "doc": "\u2500\u2500 Canonical BraidStorm constants \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/genus0_sphere_shell_demo.py", "name": "genus0_sphere_shell_demo.py", "path": "4-Infrastructure/shim/genus0_sphere_shell_demo.py", "doc": "PARTIAL BOUNDARY: contains domain logic; not a provable surface. Port to Lean/RRC before treating as authoritative." }, { "kind": "script", "id": "script:4-Infrastructure/shim/geometric_entropy_explorer.py", "name": "geometric_entropy_explorer.py", "path": "4-Infrastructure/shim/geometric_entropy_explorer.py", "doc": "---------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/gpu_fpga_ipc_symbol_surface.py", "name": "gpu_fpga_ipc_symbol_surface.py", "path": "4-Infrastructure/shim/gpu_fpga_ipc_symbol_surface.py", "doc": "64-byte cache-line shaped structures. Keep these sizes stable." }, { "kind": "script", "id": "script:4-Infrastructure/shim/hash_benchmark.py", "name": "hash_benchmark.py", "path": "4-Infrastructure/shim/hash_benchmark.py", "doc": "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/hep_data_puller.py", "name": "hep_data_puller.py", "path": "4-Infrastructure/shim/hep_data_puller.py", "doc": "-------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/hep_providers.py", "name": "hep_providers.py", "path": "4-Infrastructure/shim/hep_providers.py", "doc": "Major HEP data providers (verified and unverified)" }, { "kind": "script", "id": "script:4-Infrastructure/shim/hopf_cole_burgers.py", "name": "hopf_cole_burgers.py", "path": "4-Infrastructure/shim/hopf_cole_burgers.py", "doc": "NumPy 2.x compat: np.trapz was renamed to np.trapezoid" }, { "kind": "script", "id": "script:4-Infrastructure/shim/hutter_jxl_starfield_eigenprobe.py", "name": "hutter_jxl_starfield_eigenprobe.py", "path": "4-Infrastructure/shim/hutter_jxl_starfield_eigenprobe.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/hutter_jxl_starfield_replay_verify.py", "name": "hutter_jxl_starfield_replay_verify.py", "path": "4-Infrastructure/shim/hutter_jxl_starfield_replay_verify.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/ingest_57_flexures.py", "name": "ingest_57_flexures.py", "path": "4-Infrastructure/shim/ingest_57_flexures.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/ingest_eigensolid_data.py", "name": "ingest_eigensolid_data.py", "path": "4-Infrastructure/shim/ingest_eigensolid_data.py", "doc": "Q16_16 Scaling constants" }, { "kind": "script", "id": "script:4-Infrastructure/shim/ingest_flexure_joints.py", "name": "ingest_flexure_joints.py", "path": "4-Infrastructure/shim/ingest_flexure_joints.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/ivshmem_client.py", "name": "ivshmem_client.py", "path": "4-Infrastructure/shim/ivshmem_client.py", "doc": "\u2500\u2500 Ivshmem Constants \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/joint_classifier.py", "name": "joint_classifier.py", "path": "4-Infrastructure/shim/joint_classifier.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/label_canary_theorems.py", "name": "label_canary_theorems.py", "path": "4-Infrastructure/shim/label_canary_theorems.py", "doc": "PARTIAL BOUNDARY: contains domain logic; not a provable surface. Port to Lean/RRC before treating as authoritative." }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_proof/__init__.py", "name": "__init__.py", "path": "4-Infrastructure/shim/lean_proof/__init__.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_proof/deepseek_prover.py", "name": "deepseek_prover.py", "path": "4-Infrastructure/shim/lean_proof/deepseek_prover.py", "doc": "------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_proof/prover_engine.py", "name": "prover_engine.py", "path": "4-Infrastructure/shim/lean_proof/prover_engine.py", "doc": "------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_proof_prefilter.py", "name": "lean_proof_prefilter.py", "path": "4-Infrastructure/shim/lean_proof_prefilter.py", "doc": "Match theorem/lemma/def declarations" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_trace_bridge.py", "name": "lean_trace_bridge.py", "path": "4-Infrastructure/shim/lean_trace_bridge.py", "doc": "Find the `by` block" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lean_trace_bridge_v2.py", "name": "lean_trace_bridge_v2.py", "path": "4-Infrastructure/shim/lean_trace_bridge_v2.py", "doc": "Find the by-block start (position of 'by ' or 'by\\n')" }, { "kind": "script", "id": "script:4-Infrastructure/shim/lonely_runner_sim.py", "name": "lonely_runner_sim.py", "path": "4-Infrastructure/shim/lonely_runner_sim.py", "doc": "\u2500\u2500 simulation core \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/math_symbols.py", "name": "math_symbols.py", "path": "4-Infrastructure/shim/math_symbols.py", "doc": "\u2500\u2500 Curated standard-LaTeX macros (authoritative for the common commands) \u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/menger_address_reduction.py", "name": "menger_address_reduction.py", "path": "4-Infrastructure/shim/menger_address_reduction.py", "doc": "Menger sponge constants" }, { "kind": "script", "id": "script:4-Infrastructure/shim/merkle_tensegrity_load_equation_generator.py", "name": "merkle_tensegrity_load_equation_generator.py", "path": "4-Infrastructure/shim/merkle_tensegrity_load_equation_generator.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/non_euclidean_cpp.py", "name": "non_euclidean_cpp.py", "path": "4-Infrastructure/shim/non_euclidean_cpp.py", "doc": "Three edge types matching the standard trichotomy of constant-curvature 2D geometries" }, { "kind": "script", "id": "script:4-Infrastructure/shim/openai_unit_distance_verifier.py", "name": "openai_unit_distance_verifier.py", "path": "4-Infrastructure/shim/openai_unit_distance_verifier.py", "doc": "Optimize by using spatial bucketing/grid for larger point sets to avoid O(n^2) distance checks" }, { "kind": "script", "id": "script:4-Infrastructure/shim/openalex_citation_crawler.py", "name": "openalex_citation_crawler.py", "path": "4-Infrastructure/shim/openalex_citation_crawler.py", "doc": "Real citation graph (online):" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pagerank_eigenvalue_survey.py", "name": "pagerank_eigenvalue_survey.py", "path": "4-Infrastructure/shim/pagerank_eigenvalue_survey.py", "doc": "\u2500\u2500 Sidon spectral primitives (mirror Semantics.Spectrum) \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/particle_physics_lut.py", "name": "particle_physics_lut.py", "path": "4-Infrastructure/shim/particle_physics_lut.py", "doc": "\u2500\u2500 Q16_16 Constants \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pipeline_test_sidon.py", "name": "pipeline_test_sidon.py", "path": "4-Infrastructure/shim/pipeline_test_sidon.py", "doc": "\u2500\u2500\u2500 Conjecture: sidonMaximum_gt_sqrt_div_two \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_canary_batch.py", "name": "pist_canary_batch.py", "path": "4-Infrastructure/shim/pist_canary_batch.py", "doc": "\u2500\u2500 rfl / trivial \u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_classify.py", "name": "pist_classify.py", "path": "4-Infrastructure/shim/pist_classify.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_matrix_builder.py", "name": "pist_matrix_builder.py", "path": "4-Infrastructure/shim/pist_matrix_builder.py", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_route_repair.py", "name": "pist_route_repair.py", "path": "4-Infrastructure/shim/pist_route_repair.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_trace_classify_mcp.py", "name": "pist_trace_classify_mcp.py", "path": "4-Infrastructure/shim/pist_trace_classify_mcp.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/pist_trace_decompose.py", "name": "pist_trace_decompose.py", "path": "4-Infrastructure/shim/pist_trace_decompose.py", "doc": "Check convergence" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pylsp_trivial_detector.py", "name": "pylsp_trivial_detector.py", "path": "4-Infrastructure/shim/pylsp_trivial_detector.py", "doc": "Strip and compare empty" }, { "kind": "script", "id": "script:4-Infrastructure/shim/pyrochlore_sidon_classify.py", "name": "pyrochlore_sidon_classify.py", "path": "4-Infrastructure/shim/pyrochlore_sidon_classify.py", "doc": "\u2500\u2500\u2500 Exact diagonalization: S=1 Heisenberg tetrahedron \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/q16_16_optimization_core.py", "name": "q16_16_optimization_core.py", "path": "4-Infrastructure/shim/q16_16_optimization_core.py", "doc": "\u2500\u2500 Exact mirror of FixedPoint.lean Q16.16 raw arithmetic \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/q16_lut_vcn.py", "name": "q16_lut_vcn.py", "path": "4-Infrastructure/shim/q16_lut_vcn.py", "doc": "Local imports \u2013 same directory" }, { "kind": "script", "id": "script:4-Infrastructure/shim/qaoa_adapter.py", "name": "qaoa_adapter.py", "path": "4-Infrastructure/shim/qaoa_adapter.py", "doc": "\u2500\u2500 optional backend imports \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/qemu_framebuffer_packer.py", "name": "qemu_framebuffer_packer.py", "path": "4-Infrastructure/shim/qemu_framebuffer_packer.py", "doc": "Framebuffer constants" }, { "kind": "script", "id": "script:4-Infrastructure/shim/qr_braid_bridge.py", "name": "qr_braid_bridge.py", "path": "4-Infrastructure/shim/qr_braid_bridge.py", "doc": "Apply to rows k..m-1, columns k..n-1" }, { "kind": "script", "id": "script:4-Infrastructure/shim/qr_spatial_hash.py", "name": "qr_spatial_hash.py", "path": "4-Infrastructure/shim/qr_spatial_hash.py", "doc": "\u2500\u2500 Morton Code (Z-order curve) \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/quandela_erdos_search.py", "name": "quandela_erdos_search.py", "path": "4-Infrastructure/shim/quandela_erdos_search.py", "doc": "Q16.16 conversion" }, { "kind": "script", "id": "script:4-Infrastructure/shim/qubo_highs.py", "name": "qubo_highs.py", "path": "4-Infrastructure/shim/qubo_highs.py", "doc": "---------------------------------------------------------------------------" }, { "kind": "script", "id": "script:4-Infrastructure/shim/raven_threshold_query.py", "name": "raven_threshold_query.py", "path": "4-Infrastructure/shim/raven_threshold_query.py", "doc": "\u2500\u2500\u2500 Raven matrix for \u03b7_c threshold \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/ray_vcn_bridge.py", "name": "ray_vcn_bridge.py", "path": "4-Infrastructure/shim/ray_vcn_bridge.py", "doc": "As a drop-in replacement for GPUNodeConnection:" }, { "kind": "script", "id": "script:4-Infrastructure/shim/ray_vcn_transport.py", "name": "ray_vcn_transport.py", "path": "4-Infrastructure/shim/ray_vcn_transport.py", "doc": "Encode a strand \u2192 ObjectRef" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rds_connect.py", "name": "rds_connect.py", "path": "4-Infrastructure/shim/rds_connect.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/reservoir.py", "name": "reservoir.py", "path": "4-Infrastructure/shim/reservoir.py", "doc": "\u2500\u2500\u2500 Q16_16 helpers \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/route_repair_v14a.py", "name": "route_repair_v14a.py", "path": "4-Infrastructure/shim/route_repair_v14a.py", "doc": "PARTIAL BOUNDARY: contains domain logic; not a provable surface." }, { "kind": "script", "id": "script:4-Infrastructure/shim/routing_benchmark.py", "name": "routing_benchmark.py", "path": "4-Infrastructure/shim/routing_benchmark.py", "doc": "PARTIAL BOUNDARY: contains domain logic; not a provable surface. Port to Lean/RRC before treating as authoritative." }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_affine_conservation_probe.py", "name": "rrc_affine_conservation_probe.py", "path": "4-Infrastructure/shim/rrc_affine_conservation_probe.py", "doc": "anomaly = how far an equation's Q sits above the corpus median (robust z)" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_anti_connections.py", "name": "rrc_anti_connections.py", "path": "4-Infrastructure/shim/rrc_anti_connections.py", "doc": "Separate by regime" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_arxiv_kernel_refine.py", "name": "rrc_arxiv_kernel_refine.py", "path": "4-Infrastructure/shim/rrc_arxiv_kernel_refine.py", "doc": "Math-symbol normalizer (LaTeX/Unicode \u2192 canonical) backing the geometry kernel." }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_bosonic_db_buffer.py", "name": "rrc_bosonic_db_buffer.py", "path": "4-Infrastructure/shim/rrc_bosonic_db_buffer.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. Any file referencing rds_connect.py or this hostname is stale and must be ported." }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_bosonic_tensor_gpu.py", "name": "rrc_bosonic_tensor_gpu.py", "path": "4-Infrastructure/shim/rrc_bosonic_tensor_gpu.py", "doc": "\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_bosonic_tensor_network.py", "name": "rrc_bosonic_tensor_network.py", "path": "4-Infrastructure/shim/rrc_bosonic_tensor_network.py", "doc": "\u2500\u2500 quimb / opt_einsum \u2014 bosonic tensor network \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_dataset_kernel_build.py", "name": "rrc_dataset_kernel_build.py", "path": "4-Infrastructure/shim/rrc_dataset_kernel_build.py", "doc": "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_domain_manifold_graph.py", "name": "rrc_domain_manifold_graph.py", "path": "4-Infrastructure/shim/rrc_domain_manifold_graph.py", "doc": "\u2500\u2500 Build nodes from all kernels \u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_dual_query.py", "name": "rrc_dual_query.py", "path": "4-Infrastructure/shim/rrc_dual_query.py", "doc": "\u2500\u2500 Paths \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_genre_decompose.py", "name": "rrc_genre_decompose.py", "path": "4-Infrastructure/shim/rrc_genre_decompose.py", "doc": "Prefer pure genres (high fraction) but fall back to best match" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_manifold_assign.py", "name": "rrc_manifold_assign.py", "path": "4-Infrastructure/shim/rrc_manifold_assign.py", "doc": "Manifold route hints with keyword patterns" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_manifold_refine.py", "name": "rrc_manifold_refine.py", "path": "4-Infrastructure/shim/rrc_manifold_refine.py", "doc": "Require at least one title match" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_photonic_stress_test.py", "name": "rrc_photonic_stress_test.py", "path": "4-Infrastructure/shim/rrc_photonic_stress_test.py", "doc": "\u2500\u2500 Perceval \u2014 core photonic simulator \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_pist_shape_alignment.py", "name": "rrc_pist_shape_alignment.py", "path": "4-Infrastructure/shim/rrc_pist_shape_alignment.py", "doc": "Repo root (this file lives at 4-Infrastructure/shim/...)" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_ray_tagger.py", "name": "rrc_ray_tagger.py", "path": "4-Infrastructure/shim/rrc_ray_tagger.py", "doc": "Math-symbol normalizer + geometry/tensor-notation kernel (same-dir shims)." }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_refactor_oracle.py", "name": "rrc_refactor_oracle.py", "path": "4-Infrastructure/shim/rrc_refactor_oracle.py", "doc": "Greek epigenetic state \u2192 PRUNE/MERGE preference" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_root_system_probe.py", "name": "rrc_root_system_probe.py", "path": "4-Infrastructure/shim/rrc_root_system_probe.py", "doc": "ADE Dynkin diagrams as (branch arm-length signatures). Arms measured in EDGES" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_self_classify.py", "name": "rrc_self_classify.py", "path": "4-Infrastructure/shim/rrc_self_classify.py", "doc": "Classify a single equation" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_slo_analyzer.py", "name": "rrc_slo_analyzer.py", "path": "4-Infrastructure/shim/rrc_slo_analyzer.py", "doc": "Spectral gap of Laplacian" }, { "kind": "script", "id": "script:4-Infrastructure/shim/rrc_slo_sweep.py", "name": "rrc_slo_sweep.py", "path": "4-Infrastructure/shim/rrc_slo_sweep.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/run_scaled_trace.py", "name": "run_scaled_trace.py", "path": "4-Infrastructure/shim/run_scaled_trace.py", "doc": "Save vectors" }, { "kind": "script", "id": "script:4-Infrastructure/shim/run_trace_canary.py", "name": "run_trace_canary.py", "path": "4-Infrastructure/shim/run_trace_canary.py", "doc": "" }, { "kind": "script", "id": "script:4-Infrastructure/shim/run_trace_v2_canary.py", "name": "run_trace_v2_canary.py", "path": "4-Infrastructure/shim/run_trace_v2_canary.py", "doc": "Parse trace tags" }, { "kind": "script", "id": "script:4-Infrastructure/shim/s2_citation_crawler.py", "name": "s2_citation_crawler.py", "path": "4-Infrastructure/shim/s2_citation_crawler.py", "doc": "Single worker (no key, slow but free):" }, { "kind": "script", "id": "script:4-Infrastructure/shim/scale_space_solver.py", "name": "scale_space_solver.py", "path": "4-Infrastructure/shim/scale_space_solver.py", "doc": "\u2500\u2500 Tailscale Detection (graceful degradation) \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500" }, { "kind": "script", "id": "script:4-Infrastructure/shim/sdp_sos_solver.py", "name": "sdp_sos_solver.py", "path": "4-Infrastructure/shim/sdp_sos_solver.py", "doc": "--- Lazy import: solver only needed at the API boundary ---" }, { "kind": "script", "id": "script:4-Infrastructure/shim/seed_flexure_dataset.py", "name": "seed_flexure_dataset.py", "path": "4-Infrastructure/shim/seed_flexure_dataset.py", "doc": "INFRA:DEAD rds -- AWS RDS is gone. 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