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Research-Stack/0-Core-Formalism/lean/Semantics
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Brandon Schneider 8b9359394f formalize: 4-primitive framework for Erdős–Rényi random graphs in Lean 
Formalized the 4-primitive framework applied to Erdős–Rényi random graphs
G(n,p) in Lean.

Lean file: 0-Core-Formalism/lean/Semantics/ExtensionScaffold/Math/FourPrimitiveErdosRenyi.lean

Formalization includes:
- Field primitive (ρ(x⃗)): edge density field
- Shear primitive (G = AᵀA): Laplacian deformation metric
- Packet primitive (Γᵢ): adjacency matrix encoding
- Spectral primitive (C = UΛUᵀ): eigenbasis decomposition

Definitions:
- FieldPrimitive: edge density
- ShearPrimitive: Gram matrix AᵀA
- PacketPrimitive: adjacency matrix
- SpectralPrimitive: eigen decomposition
- spectralRadius, spectralGap, algebraicConnectivity
- Laplacian matrix
- connectivityThreshold, giantComponentThreshold
- detectPhaseTransition

Theorems (schematic):
- FourPrimitiveFramework_Validation
- SpectralPrimitive_PhaseTransition
- FieldPrimitive_Density
- ShearPrimitive_Deformation
- PacketPrimitive_Encoding

Canonical statement included: The compactified core reduces the stack to
four mutually orthogonal primitives: field state, shear metric, packet
witness, and spectral basis.
2026-05-08 14:50:02 -05:00
..
.github/workflows initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
blackboard initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
build-static initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
Core Address fixed-point review findings 2026-05-05 21:26:18 -05:00
ExtensionScaffold formalize: 4-primitive framework for Erdős–Rényi random graphs in Lean 2026-05-08 14:50:02 -05:00
legacy initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
OpenWormKernelFieldBenchmark initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
Quarantine initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
scripts initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
Semantics collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
.gitignore initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
AdaptivePrecision.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
AdaptivePrecision.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
AdaptivePrecision.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
BindServer.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
BindServer.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
BindServer.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
CombinatorialPrecision.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
CombinatorialPrecision.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
CombinatorialPrecision.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
debug_eval.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
EQUATIONS_EXTRACTION.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
ExtensionScaffold.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
EXTERNAL_REVIEW_REQUIREMENTS.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
ExtremeParameterTestEval.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
ExtremeParameterTestEval.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
ExtremeParameterTestEval.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
ExtremeParameterTestEval_output.txt initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
F01_Q16_16_FixedPoint.lean collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
F01_Q16_16_FixedPoint.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
F01_Q16_16_FixedPoint.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
FPGAExtraction.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
FPGAExtraction.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
FPGAExtraction.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
GenerateLUTMain.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
GenerateSparklePhiS3C.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
GenerateSparklePhiS3C.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
GenerateSparklePhiS3C.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
lake-manifest.json Consolidate research stack updates 2026-05-05 21:09:48 -05:00
lakefile.toml Consolidate research stack updates 2026-05-05 21:09:48 -05:00
lean-toolchain Consolidate research stack updates 2026-05-05 21:09:48 -05:00
Main.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
Main.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
Main.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MANIFOLD_NETWORKING_V0.1_ACCEPTANCE.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
ManifoldCompressionAgnostic.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
ManifoldCompressionAgnostic.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
ManifoldCompressionAgnostic.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MATH_MODEL_MAP.tsv initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
MetadataOverheadBudget.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
MetadataOverheadBudget.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MetadataOverheadBudget.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MetaManifoldLanguageMerging.lean Consolidate research stack updates 2026-05-05 21:09:48 -05:00
MetaManifoldLanguageMerging.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MetaManifoldLanguageMerging.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MinimumNeuralCompression.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
MinimumNeuralCompression.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MinimumNeuralCompression.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MOIMBenchmarkMain.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
MOIMBenchmarkMain.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
MOIMBenchmarkMain.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
NominalParameterTestEval.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
NominalParameterTestEval.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
NominalParameterTestEval.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
OpenWormBenchmark.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
OpenWormBenchmark.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
OpenWormBenchmark.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
OriginProtocol.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
OriginProtocol.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
OriginProtocol.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
PHASE_COMPLETION_SUMMARY.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
PUBLIC_BENCHMARK_RELEASE.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
PUBLIC_THEORY_RELEASE.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
PurifyMain.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
QuizTest.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
QuizTest.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
QuizTest.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
README.md initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
SearchServer.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
SearchServer.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
SearchServer.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
Semantics.lean Consolidate research stack updates 2026-05-05 21:09:48 -05:00
Semantics.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
Semantics.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
TangNano9KEmitter.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00
TangNano9KEmitter.lean.pist collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
TangNano9KEmitter.lean.pist.meta collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
test.lean initial: sovereign research stack (consolidated, weightless, and lfs-optimized) 2026-05-04 18:11:36 -05:00

README.md

Semantics