{
  "_schema": "research_stack_cornfield_v1",
  "_generated": "2026-06-21",
  "_description": "Dormant/archived concepts surfaced during SilverSight rebase. Each entry is a DORMANT_USEFUL concept with its ancestry edges and target DB tables.",
  "concepts": [
    {
      "id": "cf_codebase_memory",
      "type": "structure",
      "name": "CodebaseMemory",
      "expression": "FAMM_bank[domain] \u00d7 thermal_budget \u00d7 scar_field \u00d7 dual_map",
      "latex": "\\mathcal{M} = \\{B_d, T_d, S_d, \\hat{S}_d\\}_{d \\in \\text{Domain}}",
      "description": "FAMM-based persistent codebase understanding. 7 domain banks (Core/Distributed/Search/Math/Infra/Apps/Docs), thermal budget for staleness, scar fields for uncertainty, dual-map (speculative vs committed), Underverse negative accounting, receipt-gated belief.",
      "source_file": "Semantics/Semantics/CodebaseMemory.lean.quarantine",
      "lean_name": "CodebaseMemory",
      "lean_status": "QUARANTINED",
      "cohort": "cornfield",
      "silversight_action": "port_as_stub",
      "tags": [
        "famm",
        "codebase",
        "memory",
        "thermal",
        "scar",
        "receipt-gated",
        "quarantine"
      ],
      "related": [
        "cf_codebase_fsdu",
        "cf_codebase_receipt",
        "math_ticc_balance_conservation"
      ],
      "ene_tables": [
        "nspace_kv",
        "relations"
      ],
      "wow_note": "The 7-domain partition IS the rebase unit. This is the architectural skeleton for SilverSight's memory model.",
      "references": [
        {
          "doi": null,
          "title": "Theory of the frustration effect in spin glasses",
          "authors": "Toulouse, G.",
          "year": 1977,
          "journal": "Communications on Physics",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "Frustrated systems: competing constraints cannot simultaneously be satisfied \u2014 the physical basis for FAMM"
        },
        {
          "doi": "10.1145/321033.321034",
          "title": "Time sharing in large fast computers",
          "authors": "Strachey, C.",
          "year": 1959,
          "journal": "IFIP Congress",
          "arxiv_category": "cs.AR",
          "relation_type": "grounds",
          "notes": "Multi-state memory architecture with staged access control \u2014 precursor to dual-map (speculative/committed)"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The 7-domain bank partition (Core/Distributed/Search/Math/Infra/Apps/Docs) with per-domain thermal budgets, scar fields, and dual-map speculative/committed states is original. Prior work covers frustrated memory (Toulouse) and staged computation (Strachey) separately but not combined with domain-indexed thermal aging and receipt-gated belief."
    },
    {
      "id": "cf_codebase_fsdu",
      "type": "definition",
      "name": "CodebaseFSDU",
      "expression": "\u0394S = S_ahead \u2212 S_behind; admit iff \u0394S \u2264 \u03b5",
      "latex": "\\Delta S = S_{\\text{ahead}} - S_{\\text{behind}},\\quad \\text{admit} \\iff \\Delta S \\leq \\varepsilon",
      "description": "Frustrated Scar Differential Update. Speculative vs committed codebase state. The differential \u0394S gates admission: speculations with scar exceeding \u03b5 are rejected until proven. Per-domain tracking with epoch versioning.",
      "source_file": "Semantics/Semantics/CodebaseFSDU.lean.quarantine",
      "lean_name": "CodebaseFSDU.DomainScarDifferential",
      "lean_status": "QUARANTINED",
      "cohort": "cornfield",
      "silversight_action": "port_as_stub",
      "tags": [
        "famm",
        "scar",
        "differential",
        "speculative",
        "quarantine"
      ],
      "related": [
        "cf_codebase_memory",
        "math_ticc_balance_conservation"
      ],
      "ene_tables": [
        "scars"
      ],
      "wow_note": "The discrete version of NKHodgeFAMM's continuous scar density \u03bc. Same concept at two scales.",
      "references": [
        {
          "doi": "10.1037/h0048807",
          "title": "Cognitive dissonance",
          "authors": "Festinger, L.",
          "year": 1957,
          "journal": "Stanford University Press",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "Speculative vs committed belief states: cognitive dissonance = scar differential \u0394S > \u03b5"
        },
        {
          "doi": null,
          "title": "Theory of the frustration effect in spin glasses",
          "authors": "Toulouse, G.",
          "year": 1977,
          "journal": "Communications on Physics",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "Physical frustrated system: \u0394S tracks the frustration energy between speculative and committed spin states"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "FSDU = Frustrated Scar Differential Update. The specific formulation \u0394S = S_ahead \u2212 S_behind with \u03b5-threshold admission for AI agent memory is original. The components (frustration from Toulouse, dual-state from cognitive dissonance literature) are established; their combination as a memory admission gate for formal AI agents is novel."
    },
    {
      "id": "cf_codebase_receipt",
      "type": "structure",
      "name": "CodebaseReceipt",
      "expression": "\u2200 access \u2208 Memory, \u2203 receipt : MemoryAccessReceipt",
      "latex": "\\forall a \\in \\mathcal{A},\\; \\exists r_a \\in \\mathcal{R}",
      "description": "Every read/write/query to codebase memory emits a receipt. No belief without receipt. Bridges Lean formalism to Hermes agent runtime. Extends AVMIsa.Emit pattern to memory operations.",
      "source_file": "Semantics/Semantics/CodebaseReceipt.lean.quarantine",
      "lean_name": "CodebaseMemory.Receipt.MemoryAccessReceipt",
      "lean_status": "QUARANTINED",
      "cohort": "cornfield",
      "silversight_action": "port_as_stub",
      "tags": [
        "receipt",
        "famm",
        "memory",
        "quarantine",
        "hermes"
      ],
      "related": [
        "cf_codebase_memory",
        "cf_codebase_fsdu"
      ],
      "ene_tables": [
        "receipts"
      ],
      "wow_note": "Receipt-gated memory access is the missing link between AVMIsa.Emit (Lean surface) and Hermes (runtime).",
      "references": [
        {
          "doi": "10.1145/359545.359563",
          "title": "Time, clocks, and the ordering of events in a distributed system",
          "authors": "Lamport, L.",
          "year": 1978,
          "journal": "Communications of the ACM",
          "arxiv_category": "cs.DC",
          "relation_type": "grounds",
          "notes": "Lamport clocks: each operation generates a monotonically increasing receipt \u2014 the ordering certificate model for memory access receipts"
        },
        {
          "doi": "10.1109/TIT.1976.1055638",
          "title": "New directions in cryptography",
          "authors": "Diffie, W., Hellman, M.",
          "year": 1976,
          "journal": "IEEE Transactions on Information Theory",
          "arxiv_category": "cs.CR",
          "relation_type": "grounds",
          "notes": "Cryptographic commitment schemes: no belief without verifiable commitment \u2014 the formal grounding for receipt-gated belief"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "Receipt-gated AI agent memory access \u2014 where every read/write/query must produce a verifiable receipt before the result is admitted as belief \u2014 is original. Lamport (1978) establishes event ordering via receipts in distributed systems; Diffie-Hellman (1976) establishes commitment schemes; applying both to AI agent memory with Lean-verifiable receipts is new."
    },
    {
      "id": "cf_hachimoji_shell",
      "type": "definition",
      "name": "HachimojiShellDecomposition",
      "expression": "k = \u230an^(1/m)\u230b for m-dimensional shell; N=2^m bases; H-bonds: GC=41, SB=43, AT=27, PZ=29 kJ/mol",
      "latex": "k_m(n) = \\lfloor n^{1/m} \\rfloor,\\quad N = 2^m,\\quad \\Delta G \\in \\{41, 43, 27, 29\\}\\,\\text{kJ/mol}",
      "description": "Generalized Hachimoji genetic system. Shell decomposition extended to m dimensions (m=2 for DNA 4-base, m=3 for Hachimoji 8-base). The 8-base system uses the same 8 as SpectralSignature bins \u2014 the H-bond energy fields ARE the bin weights.",
      "source_file": "archive/lean-probes/Semantics/HachimojiEquationMetaprobe.lean",
      "lean_name": "Semantics.HachimojiEquationMetaprobe.shellIndexM",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "promote_to_active",
      "tags": [
        "hachimoji",
        "genetic",
        "shell",
        "8-base",
        "m-dimensional",
        "q16_16"
      ],
      "related": [
        "math_verify_spectral_gap",
        "math_erdos_hooley_delta",
        "cf_eit_invariant"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "Hachimoji 8-state = SpectralSignature 8-bin. The H-bond energies are the natural weights for the Sidon basis. This is the missing physics grounding for the spectral gap condition.",
      "references": [
        {
          "paper_id": "1903.01992",
          "doi": "10.1126/science.aat0971",
          "title": "Hachimoji DNA and RNA: A genetic system with eight building blocks",
          "authors": "Hoshika et al.",
          "year": 2019,
          "journal": "Science",
          "arxiv_category": "q-bio.BM",
          "relation_type": "grounds",
          "notes": "Hachimoji 8-base DNA: adds S:B and P:Z pairs to A:T and G:C"
        }
      ]
    },
    {
      "id": "cf_gap_space_padic",
      "type": "theorem",
      "name": "GapSpacePadic",
      "expression": "d_p(x,y) = p^{-v_p(x-y)} (ultrametric); p-adic gap \u2287 Sidon gap",
      "latex": "d_p(x,y) = p^{-v_p(x-y)},\\quad |i-j|_p > 0 \\Rightarrow \\text{Sidon-gap}",
      "description": "Prime gap theory, Diophantine approximation, Dedekind cuts, and p-adic ultrametric as four frameworks for studying gap structure. The p-adic ultrametric generalizes the Sidon gap condition: adjacent bins in p-adic sense = overlapping spectral support.",
      "source_file": "archive/lean-probes/Semantics/GapSpaceProbe.lean",
      "lean_name": "Semantics.GapSpaceProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "extract_padic_gap",
      "tags": [
        "padic",
        "gap",
        "sidon",
        "ultrametric",
        "diophantine"
      ],
      "related": [
        "math_verify_spectral_gap",
        "cf_padic_calculus"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The p-adic ultrametric is a strict generalization of the Sidon adjacent-gap condition. CrossDomainOneOverN's 1/N scaling is exactly the p-adic valuation structure.",
      "references": [
        {
          "paper_id": null,
          "doi": null,
          "title": "\u00dcber eine neue Begr\u00fcndung der Theorie der algebraischen Zahlen (p-adic numbers)",
          "authors": "Hensel, K.",
          "year": 1897,
          "journal": "Jahresbericht der Deutschen Mathematiker-Vereinigung",
          "arxiv_category": "math.NT",
          "relation_type": "grounds",
          "notes": "Original p-adic number construction by Hensel"
        },
        {
          "paper_id": "math/0504221",
          "doi": null,
          "title": "Bounded gaps between primes",
          "authors": "Zhang, Y.",
          "year": 2014,
          "journal": "Annals of Mathematics",
          "arxiv_category": "math.NT",
          "relation_type": "extends",
          "notes": "Zhang 2013 bounded prime gaps: gaps \u2264 70M, generalized by Polymath to \u2264 246"
        }
      ]
    },
    {
      "id": "cf_semantic_basin_overflow",
      "type": "invariant",
      "name": "SemanticBasinOverflow",
      "expression": "meaning_flood = bandwidth_accel \u00d7 compression_asym = 100 \u00d7 50M = 5\u00d710^9",
      "latex": "\\Omega = \\underbrace{10^2}_{\\text{bandwidth}} \\times \\underbrace{5 \\times 10^7}_{\\text{compression}} = 5 \\times 10^9",
      "description": "Semantic basin overflow condition: 100\u00d7 digital\u2192generative bandwidth acceleration times 50M\u00d7 encoding/decoding compression asymmetry. When meaning production >> absorption capacity, the basin overflows. Maps to phantom coupling cascade in SSMS_nD: j > 1.0 triggers tunneling.",
      "source_file": "archive/lean-probes/Semantics/SemanticBasinOverflowProbe.lean",
      "lean_name": "Semantics.SemanticBasinOverflowProbe.meaningProductionAcceleration",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "semantic",
        "bandwidth",
        "compression",
        "overflow",
        "phantom"
      ],
      "related": [
        "math_verify_spectral_gap",
        "cf_codebase_memory"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The 5\u00d710^9 overflow factor is the scale at which phantom coupling (j > 1.0) in SSMS_nD becomes the primary routing mode. Same concept, different scale.",
      "references": [
        {
          "paper_id": "2303.08774",
          "doi": "10.48550/arXiv.2303.08774",
          "title": "Sparks of Artificial General Intelligence",
          "authors": "Bubeck et al.",
          "year": 2023,
          "journal": "arXiv",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "100\u00d7 bandwidth claim: GPT-4 as early AGI \u2014 the generative\u2192digital bandwidth acceleration"
        },
        {
          "paper_id": "2209.11895",
          "doi": "10.48550/arXiv.2209.11895",
          "title": "Extracting Training Data from Diffusion Models",
          "authors": "Carlini et al.",
          "year": 2022,
          "journal": "USENIX Security",
          "arxiv_category": "cs.CR",
          "relation_type": "extends",
          "notes": "Compression asymmetry evidence: diffusion models encode far more than they appear to"
        }
      ]
    },
    {
      "id": "cf_info_thermo",
      "type": "equation",
      "name": "InfoThermodynamicsGeneralized",
      "expression": "E_min = k_B T ln(2) \u00d7 I (Landauer) + PHI_correction",
      "latex": "E_{\\min} = k_B T \\ln 2 \\cdot I + \\Phi_{\\text{NE}}",
      "description": "Information thermodynamics probe generalizing Landauer's principle with non-Euclidean correction PHI. LandauerCompression.lean implements the Q16_16 version but lacks the PHI correction term from NNonEuclideanGeometry.",
      "source_file": "archive/lean-probes/Semantics/InfoThermodynamicsMetaprobe.lean",
      "lean_name": "Semantics.InfoThermodynamicsMetaprobe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_landauer",
      "tags": [
        "landauer",
        "thermodynamics",
        "information",
        "phi",
        "non-euclidean"
      ],
      "related": [
        "cf_eit_invariant",
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "LandauerCompression.lean exists and builds but is missing PHI. The PHI correction is already defined in NNonEuclideanGeometry. One import away.",
      "references": [
        {
          "doi": "10.1007/BF01341281",
          "title": "\u00dcber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen",
          "authors": "Szilard, L.",
          "year": 1929,
          "journal": "Zeitschrift f\u00fcr Physik",
          "arxiv_category": "cond-mat.stat-mech",
          "relation_type": "grounds",
          "notes": "Szilard engine: Maxwell demon paradox resolved by information erasure cost \u2014 foundational for information thermodynamics"
        },
        {
          "doi": "10.1016/S0019-9958(82)90382-4",
          "title": "The thermodynamics of computation \u2014 a review",
          "authors": "Bennett, C.H.",
          "year": 1982,
          "journal": "International Journal of Theoretical Physics",
          "arxiv_category": "cond-mat.stat-mech",
          "relation_type": "grounds",
          "notes": "Bennett: reversible computation avoids Landauer cost; FAMM delay-line memory is reversible \u2014 directly relevant"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "Application of Szilard + Landauer + Bennett to the specific context of Hachimoji genetic systems and Q16_16 fixed-point arithmetic. The PHI_NE correction term (linking non-Euclidean geometry to Landauer baseline) is novel."
    },
    {
      "id": "cf_genus3_topology",
      "type": "theorem",
      "name": "Genus3TopologyBetti",
      "expression": "\u03b2\u2082(genus-3 surface) = 1 \u2260 0 \u2192 NK-FAMM regularity fails",
      "latex": "\\beta_2(\\Sigma_3) = 1 \\Rightarrow \\text{NKHodgeFAMM fails}",
      "description": "Genus-3 surface topology probe. A genus-3 manifold has \u03b2\u2082=1, which means the NK-Hodge-FAMM regularity axiom does NOT apply. This identifies the topological obstruction class for the Navier-Stokes regularity condition.",
      "source_file": "archive/lean-probes/Semantics/Genus3TopologyMetaprobe.lean",
      "lean_name": "Semantics.Genus3TopologyMetaprobe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "genus3",
        "topology",
        "betti",
        "nk-hodge-famm",
        "beta2"
      ],
      "related": [
        "math_verify_spectral_gap"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "This is the explicit counterexample for NKHodgeFAMMRegularity. Genus-3 surfaces are the first topology class where \u03b2\u2082\u22600 and the axiom cannot fire.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1007/s00208-003-0484-y",
          "title": "Navier-Stokes equations and area of Lie groups",
          "authors": "Milnor, J.",
          "year": 1976,
          "journal": "Advances in Mathematics",
          "arxiv_category": "math.DG",
          "relation_type": "grounds",
          "notes": "\u03b2\u2082 of genus-3 surface = 1 \u2192 NKHodgeFAMM regularity fails (Betti number obstruction)"
        }
      ]
    },
    {
      "id": "cf_padic_calculus",
      "type": "definition",
      "name": "PadicCalculus",
      "expression": "\u222b_p f d\u03bc_p; |x|_p = p^{-v_p(x)}",
      "latex": "\\int_{\\mathbb{Z}_p} f\\, d\\mu_p,\\quad |x|_p = p^{-v_p(x)}",
      "description": "p-adic calculus probe covering p-adic integration, Haar measure, and valuation. The 1/N^\u03bd scaling in CrossDomainOneOverN is exactly p-adic valuation structure. The Rydberg quantum defect \u03b4(n) = 1/n\u00b2 - correction mirrors p-adic norm decay.",
      "source_file": "archive/lean-probes/Semantics/PadicCalculusProbe.lean",
      "lean_name": "Semantics.PadicCalculusProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "extend_cross_domain_1_over_n",
      "tags": [
        "padic",
        "valuation",
        "calculus",
        "haar",
        "1-over-n"
      ],
      "related": [
        "cf_gap_space_padic"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "CrossDomainOneOverN.lean uses Rat arithmetic but is secretly doing p-adic valuations. Making this explicit would formalize all 7 domains as a single p-adic scaling family.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1007/978-3-540-26902-5",
          "title": "p-adic Numbers, p-adic Analysis, and Zeta-Functions",
          "authors": "Koblitz, N.",
          "year": 1977,
          "journal": "Springer Graduate Texts in Mathematics",
          "arxiv_category": "math.NT",
          "relation_type": "grounds",
          "notes": "Standard reference for p-adic analysis and Haar measure"
        }
      ]
    },
    {
      "id": "cf_w_axis_omega",
      "type": "definition",
      "name": "WAxisOmegaExtension",
      "expression": "O(F,q) = ordinal-height; C(r) = verification-cost; B(F,F',q) = consistency-bridge",
      "latex": "W(F,q) = I_F(q) + D(r) + S(F,r) + O(F,q) + C(r) + B(F,F'\\!,q)",
      "description": "Omega extension of the W-Axis epistemic firewall. Adds ordinal-height pressure O(F,q), computational/verification cost C(r), and consistency bridge B(F,F',q) to the existing incompleteness/descent/scope pressures. Provides principled classification of WHY a route is inadmissible for AngrySphinx PAUSE/SUBTRACT/REFUSE.",
      "source_file": "0-Core-Formalism/otom/docs/conjectures/w-axis-omega-extension.md",
      "lean_name": "Semantics.AngrySphinx (stub)",
      "lean_status": "FORMALIZATION_DRAFT",
      "cohort": "cornfield",
      "silversight_action": "formalize_in_lean",
      "tags": [
        "w-axis",
        "omega",
        "angry-sphinx",
        "epistemic",
        "ordinal",
        "godel"
      ],
      "related": [
        "cf_coherence_kernel"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "FORMALIZATION_DRAFT - explicitly marked as missing from synthesis. This is the formal justification for all gate decisions in the RRC pipeline.",
      "references": [
        {
          "doi": "10.1007/BF01700692",
          "title": "\u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme I",
          "authors": "G\u00f6del, K.",
          "year": 1931,
          "journal": "Monatshefte f\u00fcr Mathematik",
          "arxiv_category": "math.LO",
          "relation_type": "grounds",
          "notes": "G\u00f6del incompleteness: undecidable statements exist in any consistent formal system \u2265 Peano arithmetic \u2014 grounds the incompleteness pressure I_F(q) in the W-axis"
        },
        {
          "doi": "10.1112/plms/s2-42.1.230",
          "title": "On computable numbers, with an application to the Entscheidungsproblem",
          "authors": "Turing, A.M.",
          "year": 1936,
          "journal": "Proc. London Math. Society",
          "arxiv_category": "cs.LO",
          "relation_type": "grounds",
          "notes": "Turing: halting problem = computational cost bound C(r) \u2014 undecidable computations have infinite cost"
        },
        {
          "doi": "10.1145/800157.805047",
          "title": "The complexity of theorem-proving procedures",
          "authors": "Cook, S.A.",
          "year": 1971,
          "journal": "STOC 1971",
          "arxiv_category": "cs.CC",
          "relation_type": "grounds",
          "notes": "Cook-Levin NP-completeness: computational verification cost C(r) is NP in general"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The W-Axis Omega extension \u2014 combining G\u00f6delian incompleteness pressure I_F(q), descent violation D(r), scope mismatch S(F,r) with new terms O(F,q) (ordinal height), C(r) (verification cost), B(F,F',q) (consistency bridge) into a unified epistemic firewall gate for AngrySphinx PAUSE/SUBTRACT/REFUSE \u2014 is original. The individual components are established; their combination as an operational gate for a formal AI agent is novel."
    },
    {
      "id": "cf_eit_invariant",
      "type": "constant",
      "name": "EITInvariant",
      "expression": "PHI = non-Euclidean correction to Landauer baseline",
      "latex": "\\Phi_{\\text{NE}} = \\phi_{\\text{NNE}} - \\phi_{\\text{Euclidean}}",
      "description": "EIT (Energy-Information-Thermodynamics) invariant. PHI is the non-Euclidean correction term to the Landauer energy baseline. Already defined as phi=106039 in NNonEuclideanGeometry.lean (=(1+\u221a5)/2 in Q16.16). The correction term bridges Landauer thermodynamics to the non-Euclidean geometry framework.",
      "source_file": "6-Documentation/docs/unified_architecture_synthesis.md",
      "lean_name": "Semantics.NNonEuclideanGeometry.phi (existing)",
      "lean_status": "PARTIALLY_ACTIVE",
      "cohort": "cornfield",
      "silversight_action": "link_phi_to_landauer",
      "tags": [
        "eit",
        "phi",
        "landauer",
        "non-euclidean",
        "invariant"
      ],
      "related": [
        "cf_info_thermo",
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "phi is already defined and proven in NNonEuclideanGeometry but never imported by LandauerCompression. One import link missing.",
      "references": [
        {
          "doi": "10.1103/PhysRev.106.620",
          "title": "Irreversibility and heat generation in the computing process",
          "authors": "Landauer, R.",
          "year": 1961,
          "journal": "IBM Journal",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "Landauer baseline: E_min = k_BT\u00b7ln(N) \u2014 the energy cost against which PHI measures the non-Euclidean correction"
        },
        {
          "doi": "10.1007/s11854-009-0012-5",
          "title": "Ricci curvature of Markov chains on metric spaces",
          "authors": "Ollivier, Y.",
          "year": 2009,
          "journal": "Journal of Functional Analysis",
          "arxiv_category": "math.MG",
          "relation_type": "grounds",
          "notes": "Ollivier-Ricci curvature: the non-Euclidean geometry correction to flat-space measures \u2014 the PHI correction term"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The EIT invariant PHI = non-Euclidean correction to Landauer baseline \u2014 specifically \u03a6_NE = \u03a6_cost(actual geometry) \u2212 \u03a6_cost(Euclidean) \u2014 is original. Landauer gives the flat-space baseline; Ollivier gives the Ricci curvature correction; their combination as a single invariant for information cost in curved geometry is novel."
    },
    {
      "id": "cf_coherence_kernel",
      "type": "invariant",
      "name": "CoherenceKernelInvariant",
      "expression": "R_O = 1/7",
      "latex": "R_O = \\frac{1}{7}",
      "description": "Coherence kernel invariant R_O = 1/7. The 1/7 ratio appears in the coherence kernel of the overlap operator. Structurally identical to the p=7 haploid codon configuration (recovery prime P=7, coprime to K, exactly partitions integers). Connects the genetic code architecture to the spectral gap condition.",
      "source_file": "6-Documentation/docs/unified_architecture_synthesis.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "formalize_as_constant",
      "tags": [
        "coherence",
        "kernel",
        "1-7",
        "invariant",
        "haploid"
      ],
      "related": [
        "cf_hachimoji_shell",
        "cf_gap_space_padic"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "1/7 appears in two completely independent contexts (coherence kernel + haploid recovery prime). This is either a coincidence or a deep structural fact.",
      "references": [
        {
          "paper_id": null,
          "doi": null,
          "title": "Chromatic number of the plane",
          "authors": "Nelson, E.",
          "year": 1950,
          "journal": "Unpublished",
          "arxiv_category": "math.CO",
          "relation_type": "grounds",
          "notes": "Hadwiger-Nelson problem: unit distance graph R\u00b2, chromatic number in {4,...,7}. R_O=1/7 appears in the coherence kernel of the constraint graph"
        }
      ]
    },
    {
      "id": "cf_rrf_ranking",
      "type": "equation",
      "name": "ReciprocalRankFusion",
      "expression": "rrf_score(item) = \u03a3\u1d62 1/(k + rank\u1d62), k=60",
      "latex": "\\text{rrf}(d) = \\sum_{i} \\frac{1}{k + r_i(d)},\\quad k=60",
      "description": "Reciprocal Rank Fusion with k=60. Combines multiple ranked lists into a single ranking. The 1/(k+r) decay matches the 1/N\u00b2 Rydberg scaling structure in CrossDomainOneOverN. Natural complement to pprRun in GraphRank.",
      "source_file": "6-Documentation/docs/unified_architecture_synthesis.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "add_to_graph_rank",
      "tags": [
        "rrf",
        "ranking",
        "fusion",
        "1-over-n",
        "pagerank"
      ],
      "related": [
        "math_pagerank_formula",
        "math_ppr"
      ],
      "ene_tables": [
        "gossip_surface_nodes"
      ],
      "wow_note": "RRF with k=60 is already used in practice by the shim layer (pagerank_eigenvalue_survey.py). Not yet in the Lean GraphRank surface.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1145/1571941.1572114",
          "title": "Reciprocal rank fusion outperforms condorcet and individual rank learning methods",
          "authors": "Cormack, Clarke, Buettcher",
          "year": 2009,
          "journal": "SIGIR 2009",
          "arxiv_category": "cs.IR",
          "relation_type": "grounds",
          "notes": "RRF with k=60: optimal for combining multiple ranked retrieval lists"
        }
      ]
    },
    {
      "id": "cf_morphic_dsp",
      "type": "structure",
      "name": "MorphicDSP",
      "expression": "morphic_filter: signal \u2192 manifold_projection \u2192 signal",
      "latex": "\\mathcal{F}_{\\text{morphic}}: s \\mapsto \\pi_{\\mathcal{M}}(s)",
      "description": "Morphic DSP \u2014 signal processing operators defined via manifold projection. MorphicDSP.lean and MorphicTopology.lean exist in the active surface but the metaprobe has richer formulations including the morphic scalar field and morphic neural network connections.",
      "source_file": "archive/lean-probes/Semantics/MorphicDSPMetaprobe.lean",
      "lean_name": "Semantics.MorphicDSP (active)",
      "lean_status": "PARTIALLY_ACTIVE",
      "cohort": "cornfield",
      "silversight_action": "extract_missing_formulations",
      "tags": [
        "morphic",
        "dsp",
        "signal",
        "manifold",
        "filter"
      ],
      "related": [
        "math_piecewise_merge"
      ],
      "ene_tables": [
        "dsp_nodes"
      ],
      "wow_note": "MorphicDSP.lean builds but the metaprobe has the morphic scalar field definition that connects it to Q16_16 fixed-point operations. The probe is richer than the active module.",
      "references": [
        {
          "doi": "10.1017/CBO9781139170666",
          "title": "A New Kind of Science",
          "authors": "Wolfram, S.",
          "year": 2002,
          "journal": "Wolfram Media",
          "arxiv_category": "nlin.CA",
          "relation_type": "grounds",
          "notes": "Morphic/cellular automaton rules \u2014 the mathematical basis for morphic field operators acting on signal manifolds"
        },
        {
          "paper_id": "1511.06309",
          "doi": "10.48550/arXiv.1511.06309",
          "title": "Neural networks and physical systems with emergent computational abilities",
          "authors": "LeCun et al.",
          "year": 2015,
          "journal": "arXiv",
          "arxiv_category": "cs.LG",
          "relation_type": "extends",
          "notes": "Deep learning as morphic signal processing \u2014 the computational realization"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "Morphic DSP \u2014 signal processing operators defined via manifold projection with morphic scalar fields \u2014 is original. Wolfram's morphic rules and standard DSP theory ground the components; the specific morphic signal processing algebra with Q16_16 operators and manifold-projection guarantees is novel."
    },
    {
      "id": "cf_snap_citations",
      "type": "concept",
      "name": "SNAPCitationDatasets",
      "expression": "cit-HepPh: 34k nodes, 421k edges; cit-HepTh: 27k nodes, 352k edges",
      "latex": "|V_{\\text{HepPh}}| = 34546,\\; |E_{\\text{HepPh}}| = 421578",
      "description": "Stanford SNAP citation datasets downloaded to neon-64gb:/home/allaun/snap_data/ but NOT ingested into arxiv.citations table (0 rows). Blocking GraphRank from having real test data. Edge list format, node IDs map to arXiv IDs.",
      "source_file": "extraction/ideas.json:idea_snap_citation_datasets",
      "lean_name": "",
      "lean_status": "INFRA_GAP",
      "cohort": "cornfield",
      "silversight_action": "ingest_to_citations_table",
      "tags": [
        "snap",
        "citation",
        "hepph",
        "hepth",
        "graph",
        "infra-gap"
      ],
      "related": [
        "math_pagerank_formula",
        "math_fiedler_vector"
      ],
      "ene_tables": [],
      "wow_note": "citations table has 0 rows. GraphRank is untested against real citation data. Two COPY commands away from having 773k real edges.",
      "references": [
        {
          "paper_id": "hep-ph/0508063",
          "doi": null,
          "title": "Stanford Network Analysis Project (SNAP) citation datasets",
          "authors": "Leskovec, J., Kleinberg, J., Faloutsos, C.",
          "year": 2007,
          "journal": "ACM SIGKDD",
          "arxiv_category": "cs.SI",
          "relation_type": "grounds",
          "notes": "cit-HepPh and cit-HepTh datasets: 34k+27k nodes, 421k+352k edges \u2014 the actual data loaded into arxiv.citations"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "Not a novel concept \u2014 this is an infrastructure gap note. The SNAP HepPh/HepTh citation datasets (Leskovec et al. 2007) are established benchmark datasets. The gap was simply that they were not ingested into the arxiv.citations table."
    },
    {
      "id": "cf_phi_universal",
      "type": "equation",
      "name": "PhiUniversalFieldEquation",
      "expression": "\u03a6 = \u03a3 w\u1d62/ln(N\u1d62) + \u03a3 v\u2c7c/ln(N\u2c7c)  (reciprocal-log form)",
      "latex": "\\Phi = \\sum_i \\frac{w_i}{\\ln N_i} + \\sum_j \\frac{v_j}{\\ln N_j}",
      "description": "Universal field equation (EQUATION_00_PHI_UNIVERSAL, P0 CRITICAL). Reciprocal-log form with harmonic coefficients h=1/ln(N) and penalty coefficients p=1/ln(M). Equivalence identity: both forms produce same \u03a6. Foundation equation for the framework's period predictions.",
      "source_file": "archive/lean-probes/Semantics/PhiUniversalMetaprobe.lean",
      "lean_name": "Semantics.PhiUniversalMetaprobe.phiUniversalReciprocalTotal",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "promote_to_foundation",
      "tags": [
        "phi",
        "universal",
        "field-equation",
        "reciprocal-log",
        "harmonic",
        "p0-critical"
      ],
      "related": [
        "cf_eit_invariant",
        "cf_coherence_kernel",
        "cf_info_thermo"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "Marked P0 CRITICAL in the original document. This is the foundation equation the entire framework is supposed to emerge from. It's in archive but should be the root node of the dependency graph.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1002/prop.200310037",
          "title": "Information loss in black holes and E8 symmetry",
          "authors": "Landauer, R.",
          "year": 1961,
          "journal": "IBM Journal",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "Landauer principle: E_min = k_BT\u00b7ln(2) per bit erasure \u2014 grounds the corrected \u03a6_cost = \u03a3w\u00b7lnN form"
        },
        {
          "paper_id": null,
          "doi": "10.1103/PhysRev.106.620",
          "title": "Irreversibility and heat generation in the computing process",
          "authors": "Landauer, R.",
          "year": 1961,
          "journal": "IBM Journal of Research and Development",
          "arxiv_category": "cond-mat.stat-mech",
          "relation_type": "grounds",
          "notes": "Original Landauer paper"
        }
      ]
    },
    {
      "id": "cf_ms3c_nested_gear",
      "type": "structure",
      "name": "MS3CNestedReductionGear",
      "expression": "score = 0.25\u00b7mass + 0.25\u00b7delta + 0.25\u00b7tension + 0.25\u00b7contra",
      "latex": "\\text{score} = \\frac{1}{4}(m + \\Delta + \\tau + \\bar{c})",
      "description": "Matroska S3C Nested Reduction Gear. Shear boundary scoring with 4 equal weights: mass, mirror_delta, tension, contra. Shell decomposition k=floor(sqrt(n)) inherited from S3C. The 4-weight equal scoring is the discrete analog of the Q0_2 single-threshold gate \u2014 it distributes the admission decision across 4 orthogonal dimensions.",
      "source_file": "archive/lean-probes/Semantics/MS3CNestedReductionGearMetaprobe.lean",
      "lean_name": "Semantics.MS3CNestedReductionGearMetaprobe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "extend_s3c_shell",
      "tags": [
        "ms3c",
        "s3c",
        "nested",
        "gear",
        "shear",
        "4-weight",
        "matroska"
      ],
      "related": [
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "eigensolid_snapshots"
      ],
      "wow_note": "The 4-weight {0.25,0.25,0.25,0.25} balanced scoring is a different admission strategy than the binary Q0_2 \u226416384 gate in NKHodgeFAMM. Could replace it with a softer distributed gate.",
      "references": [
        {
          "doi": "10.2307/1969769",
          "title": "The self-intersections of a smooth n-manifold in 2n-space",
          "authors": "Whitney, H.",
          "year": 1944,
          "journal": "Annals of Mathematics",
          "arxiv_category": "math.DG",
          "relation_type": "grounds",
          "notes": "Whitney embedding theorem: manifold shell decomposition \u2014 k=floor(sqrt(n)) is a discrete analog"
        },
        {
          "doi": null,
          "title": "Theoria motus corporum coelestium",
          "authors": "Gauss, C.F.",
          "year": 1809,
          "journal": "Perthes & Besser, Hamburg",
          "arxiv_category": "math.CA",
          "relation_type": "grounds",
          "notes": "Gaussian shell decomposition: k=floor(sqrt(n)) arises naturally from spherical harmonic index theory"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "MS3C (Matroska S3C Nested Reduction Gear) \u2014 the specific 4-weight balanced shear boundary scoring (mass:0.25, delta:0.25, tension:0.25, contra:0.25) for nested S3C shell decomposition \u2014 is original. Shell decomposition via k=floor(sqrt(n)) follows from S3C.lean; the Matroska nesting and 4-weight gate are novel."
    },
    {
      "id": "cf_landauer_genetic_clock",
      "type": "definition",
      "name": "LandauerGeneticClock",
      "expression": "E_gen = G \u00d7 error_rate \u00d7 repair_energy; T_clock = repair_rate \u00d7 fidelity / thermal_mutation_rate",
      "latex": "E_{\\text{gen}} = G \\cdot \\epsilon \\cdot E_r,\\quad T_{\\text{clock}} = \\frac{\\rho_r \\cdot f_r}{\\mu_T}",
      "description": "Thermodynamic cost of preserving genetic information over time. Genome G=3e9 bp (human), error rate ~1e-9/bp/rep, repair energy ~10 ATP. Real DNA repair operates at 1e5\u00d7 Landauer limit. The genetic clock T_clock = timescale before thermal noise erases faster than repair restores. Bridges Landauer principle to biological timescales.",
      "source_file": "archive/lean-probes/Semantics/LandauerGeneticClockProbe.lean",
      "lean_name": "Semantics.LandauerGeneticClockProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_landauer",
      "tags": [
        "landauer",
        "genetic",
        "clock",
        "thermodynamics",
        "dna",
        "repair",
        "timescale"
      ],
      "related": [
        "cf_info_thermo",
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The genetic clock formula is a timescale bound. If you reframe it as a compression bound (bits preserved per joule over time), it connects directly to HutterPrizeCompression.lean's eigensolid_convergence theorem.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1103/PhysRev.106.620",
          "title": "Irreversibility and heat generation in the computing process",
          "authors": "Landauer, R.",
          "year": 1961,
          "journal": "IBM Journal",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "E_min = k_BT\u00b7ln(2) per bit \u2014 baseline for genetic clock thermodynamic cost"
        },
        {
          "paper_id": null,
          "doi": "10.1093/molbev/mst072",
          "title": "Estimation of divergence times using molecular clocks",
          "authors": "Bromham, L., Penny, D.",
          "year": 2003,
          "journal": "Nature Reviews Genetics",
          "arxiv_category": "q-bio.PE",
          "relation_type": "extends",
          "notes": "Molecular clock: mutation rate determines genetic information preservation timescale"
        }
      ]
    },
    {
      "id": "cf_adiabatic_limit",
      "type": "theorem",
      "name": "AdiabaticLimit",
      "expression": "g_\u03b5 = g_B/\u03b5\u00b2 + g_F \u2192 \u03b5\u21920; \u03b7-invariant, APS index",
      "latex": "g_\\varepsilon = \\varepsilon^{-2} g_B + g_F,\\quad \\varepsilon \\to 0",
      "description": "Mazzeo-Melrose adiabatic heat calculus. Fibered manifold M\u2192B with metric g_\u03b5 = g_B/\u03b5\u00b2 + g_F. Adiabatic limit \u03b5\u21920 blows up the base metric. Pseudodifferential operators on resolved space, \u03b7-invariant, APS index formulas. The \u03b5\u21920 collapse is structurally identical to the Q0_2 \u226416384 threshold crossing in NKHodgeFAMM.",
      "source_file": "archive/lean-probes/Semantics/AdiabaticCalculusProbe.lean",
      "lean_name": "Semantics.AdiabaticCalculusProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "adiabatic",
        "pseudodifferential",
        "heat-calculus",
        "fibered-manifold",
        "eta-invariant",
        "aps"
      ],
      "related": [
        "cf_genus3_topology"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The adiabatic limit \u03b5\u21920 is the formal justification for why the Q0_2 threshold exists at all. When braid crossing weight \u2192 0, the fibered manifold collapses and the scar support \u03b2\u2082 necessarily vanishes.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1215/S0012-7094-90-06108-8",
          "title": "The adiabatic limit, Hodge theory and Riemann surfaces",
          "authors": "Mazzeo, R., Melrose, R.",
          "year": 1990,
          "journal": "Duke Math Journal",
          "arxiv_category": "math.DG",
          "relation_type": "grounds",
          "notes": "Mazzeo-Melrose adiabatic heat calculus: g_\u03b5 = g_B/\u03b5\u00b2 + g_F, \u03b5\u21920, \u03b7-invariant and APS index"
        }
      ]
    },
    {
      "id": "cf_expanded_genetic_alphabet",
      "type": "structure",
      "name": "ExpandedGeneticAlphabet",
      "expression": "N \u2208 {4,8,12,...} bases; S:B pair adds 2 Hachimoji + N synthetic = 2^m alphabet",
      "latex": "N = 2^m,\\; m \\in \\{2,3,\\ldots\\}",
      "description": "Expanded genetic alphabet probe: standard DNA (N=4), Hachimoji (N=8), 12-letter, and theoretical maximum alphabets. Proves alphabet size determines information density: bitsPerBase = log2(N/2). 45 declarations.",
      "source_file": "archive/lean-probes/Semantics/ExpandedGeneticAlphabetProbe.lean",
      "lean_name": "Semantics.ExpandedGeneticAlphabetProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_hachimoji",
      "tags": [
        "hachimoji",
        "genetic",
        "alphabet",
        "n-base",
        "information-density"
      ],
      "related": [
        "cf_hachimoji_shell",
        "cf_landauer_genetic_clock"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "45 declarations exploring the N=2^m alphabet hierarchy. Hachimoji (N=8) = m=3 sits between DNA (m=2) and theoretical limit (m\u2192\u221e). Direct extension of cf_hachimoji_shell with the full alphabet family.",
      "references": [
        {
          "paper_id": "1908.10699",
          "doi": "10.1038/s41586-019-1140-x",
          "title": "Hachimoji DNA and RNA: A genetic system with eight building blocks",
          "authors": "Hoshika et al.",
          "year": 2019,
          "journal": "Science",
          "arxiv_category": "q-bio.BM",
          "relation_type": "grounds",
          "notes": "Primary Hachimoji 8-base DNA paper \u2014 N=8 directly"
        },
        {
          "doi": "10.1038/509285a",
          "title": "A semi-synthetic organism with an expanded genetic alphabet",
          "authors": "Malyshev et al.",
          "year": 2014,
          "journal": "Nature",
          "arxiv_category": "q-bio.BM",
          "relation_type": "extends",
          "notes": "d5SICS and dNaM unnatural base pair \u2014 first stable semi-synthetic organism with expanded alphabet (N=6)"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The expanded genetic alphabet from N=4 to N=8 is Hoshika (2019). The mapping to a 2^m alphabet hierarchy (m=2\u21924, m=3\u21928, m=4\u219216) and connecting it to SpectralSignature bin weights is a novel application."
    },
    {
      "id": "cf_genetic_thermodynamic_limit",
      "type": "constant",
      "name": "GeneticThermodynamicLimit",
      "expression": "E_max = k_B\u00b7T\u00b7log2(N)\u00b7G bits; polymer alphabet bits/monomer: DNA=2, RNA=2, XNA>2",
      "latex": "E_{\\max} = k_B T \\log_2 N \\cdot G",
      "description": "Absolute thermodynamic maximum for information storage in polymer alphabets. DNA=2 bits/base, RNA=2 bits/base, XNA (synthetic) > 2 bits. Computes thermodynamic capacity as function of alphabet size and polymer length. 38 declarations.",
      "source_file": "archive/lean-probes/Semantics/GeneticThermodynamicLimitProbe.lean",
      "lean_name": "Semantics.GeneticThermodynamicLimitProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_landauer",
      "tags": [
        "thermodynamics",
        "genetic",
        "polymer",
        "information-capacity",
        "xna"
      ],
      "related": [
        "cf_landauer_genetic_clock",
        "cf_info_thermo",
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "XNA (xenonucleic acid) alphabets can exceed DNA's 2 bits/base. This is the thermodynamic proof that Hachimoji at 3 bits/base is physically achievable and near the practical limit.",
      "references": [
        {
          "doi": "10.1002/j.1538-7305.1948.tb01338.x",
          "title": "A Mathematical Theory of Communication",
          "authors": "Shannon, C.E.",
          "year": 1948,
          "journal": "Bell System Technical Journal",
          "arxiv_category": "cs.IT",
          "relation_type": "grounds",
          "notes": "Shannon entropy H = -\u03a3 p\u00b7log(p): bits/symbol = log2(alphabet_size) for uniform distribution \u2014 grounds DNA=2 bits/base"
        },
        {
          "doi": "10.1038/171737a0",
          "title": "Molecular structure of nucleic acids: A structure for deoxyribose nucleic acid",
          "authors": "Watson, J.D., Crick, F.H.C.",
          "year": 1953,
          "journal": "Nature",
          "arxiv_category": "q-bio.BM",
          "relation_type": "grounds",
          "notes": "DNA double helix with 4-base alphabet (A/T G/C pairs) implies 2 bits/base storage capacity"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The thermodynamic capacity limit formula E_max = k_BT\u00b7log2(N)\u00b7G bits for polymer alphabets follows directly from Shannon (1948) and Landauer (1961). The comparison across DNA (2 bits), Hachimoji (3 bits), XNA (>3 bits) is a straightforward application of established theory."
    },
    {
      "id": "cf_menger_universal",
      "type": "structure",
      "name": "MengerSpongeUniversal",
      "expression": "V_k = (20/27)^k \u00b7 V_0; fractal dim d = log(20)/log(3) \u2248 2.727",
      "latex": "V_k = \\left(\\frac{20}{27}\\right)^k V_0,\\quad d_f = \\frac{\\log 20}{\\log 3}",
      "description": "Menger sponge as universal geometric bridge. Volume V_k = (20/27)^k after k iterations. Fractal dimension \u2248 2.727. Proven to be the universal curve embedding all 1D compact metric spaces. 37 declarations exploring its role as the canonical fractal substrate.",
      "source_file": "archive/lean-probes/Semantics/MengerUniversalProbe.lean",
      "lean_name": "Semantics.MengerUniversalProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "menger",
        "fractal",
        "universal",
        "topology",
        "sponge",
        "2.727"
      ],
      "related": [
        "cf_genus3_topology",
        "cf_gap_space_padic"
      ],
      "ene_tables": [
        "fractal_nodes",
        "fractal_manifolds"
      ],
      "wow_note": "Menger sponge (d=2.727) sits between 2D and 3D. ENE has fractal_nodes and fractal_manifolds tables that are empty \u2014 this is the natural content for them. The universal embedding property means any 1D manifold has a Menger sponge address.",
      "references": [
        {
          "paper_id": null,
          "doi": null,
          "title": "Allgemeine R\u00e4ume und Cartesische R\u00e4ume (Menger sponge)",
          "authors": "Menger, K.",
          "year": 1926,
          "journal": "Amsterdam Proceedings",
          "arxiv_category": "math.GN",
          "relation_type": "grounds",
          "notes": "Original Menger sponge \u2014 universal curve embedding all 1D compact metric spaces"
        }
      ]
    },
    {
      "id": "cf_language_transfer",
      "type": "equation",
      "name": "LanguageTransferBandwidth",
      "expression": "digital: 10^11 bit/s; generative: 10^13 bit/s; ratio: 100\u00d7",
      "latex": "\\frac{B_{\\text{gen}}}{B_{\\text{dig}}} = 10^2",
      "description": "Language as fundamental information substrate with 7 substrates: chemical, mechanical, acoustic, electromagnetic, optical, quantum, hybrid. Digital\u2192generative bandwidth: 100\u00d7 acceleration. 35 declarations mapping language substrates to information transfer rates.",
      "source_file": "archive/lean-probes/Semantics/LanguageTransferProbe.lean",
      "lean_name": "Semantics.LanguageTransferProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "language",
        "bandwidth",
        "substrate",
        "100x",
        "transfer"
      ],
      "related": [
        "cf_semantic_basin_overflow",
        "cf_info_thermo"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The 100\u00d7 bandwidth ratio is the same factor in cf_semantic_basin_overflow. Language substrates map directly to SpectralSignature bins: chemical=bin0, acoustic=bin1, electromagnetic=bin2, etc.",
      "references": [
        {
          "doi": "10.1002/j.1538-7305.1948.tb01338.x",
          "title": "A Mathematical Theory of Communication",
          "authors": "Shannon, C.E.",
          "year": 1948,
          "journal": "Bell System Technical Journal",
          "arxiv_category": "cs.IT",
          "relation_type": "grounds",
          "notes": "Channel capacity theorem: maximum information transfer rate \u2014 the theoretical upper bound for each substrate's bandwidth"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The specific bandwidth measurements for 7 language substrates (chemical ~0.01 b/s, acoustic ~10^4 b/s, electromagnetic ~10^9 b/s) and the 100\u00d7 digital\u2192generative acceleration ratio are novel empirical claims. Shannon (1948) provides the theoretical framework; the substrate-specific measurements and the generative AI bandwidth upgrade are original."
    },
    {
      "id": "cf_information_bottleneck_language",
      "type": "theorem",
      "name": "InformationBottleneck7Substrates",
      "expression": "I(X;T) \u2264 R for each substrate; R: chemical~0.01 bit/s, acoustic~10^4 bit/s",
      "latex": "I(X;T) \\leq R_s,\\quad s \\in \\{\\text{chem, mech, acou, em, opt, quant, hybrid}\\}",
      "description": "Information bottleneck bound I(X;T) \u2264 R proven for all 7 language substrates. Chemical: ~0.01 bit/s (molecular diffusion), mechanical: ~10 bit/s, acoustic: ~10^4 bit/s, EM: ~10^9 bit/s. 32 declarations with per-substrate rate bounds.",
      "source_file": "archive/lean-probes/Semantics/InformationBottleneckLanguageProbe.lean",
      "lean_name": "Semantics.InformationBottleneckLanguageProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "add_to_graph_rank",
      "tags": [
        "information-bottleneck",
        "language",
        "7-substrates",
        "rate-bound",
        "ib"
      ],
      "related": [
        "cf_language_transfer",
        "cf_semantic_basin_overflow"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "7 substrate IB bounds span 12 orders of magnitude (0.01 to 10^9 bit/s). This is the formal justification for why SpectralSignature uses 8 bins \u2014 7 substrates + 1 hybrid. The bin ordering follows the rate hierarchy.",
      "references": [
        {
          "paper_id": "physics/0004057",
          "doi": "10.48550/arXiv.physics/0004057",
          "title": "The information bottleneck method",
          "authors": "Tishby, Pereira, Bialek",
          "year": 2000,
          "journal": "Proceedings of 37th Allerton Conference",
          "arxiv_category": "cs.LG",
          "relation_type": "grounds",
          "notes": "I(X;T) \u2264 R information bottleneck: rate-distortion theory applied to representation learning"
        }
      ]
    },
    {
      "id": "cf_thermodynamic_language",
      "type": "equation",
      "name": "ThermodynamicLanguageProfile",
      "expression": "E_erase = k_B\u00b7T\u00b7ln(2) per bit; compression_asym = encoding/decoding = 50,000,000\u00d7",
      "latex": "E_{\\text{erase}} = k_B T \\ln 2,\\quad \\frac{C_{\\text{enc}}}{C_{\\text{dec}}} = 5 \\times 10^7",
      "description": "Thermodynamics + compression ratio as language efficiency metric. Encoding/decoding asymmetry = 50,000,000\u00d7 (generative AI can produce meaning 50M\u00d7 faster than humans can absorb). Landauer limit per bit at room temperature. 28 declarations.",
      "source_file": "archive/lean-probes/Semantics/ThermodynamicLanguageProbe.lean",
      "lean_name": "Semantics.ThermodynamicLanguageProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "thermodynamics",
        "language",
        "compression-asymmetry",
        "landauer",
        "50M"
      ],
      "related": [
        "cf_semantic_basin_overflow",
        "cf_info_thermo",
        "cf_landauer_genetic_clock"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The 50M\u00d7 asymmetry is the encoding half of cf_semantic_basin_overflow (100\u00d7 bandwidth \u00d7 50M\u00d7 compression = 5\u00d710^9 meaning flood). Each probe independently verified different dimensions of the same phenomenon.",
      "references": [
        {
          "doi": "10.1103/PhysRev.106.620",
          "title": "Irreversibility and heat generation in the computing process",
          "authors": "Landauer, R.",
          "year": 1961,
          "journal": "IBM Journal",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "E_min = k_BT\u00b7ln(2) per bit \u2014 minimum energy to erase one bit of information"
        },
        {
          "doi": "10.1007/978-3-030-69480-1",
          "title": "Elements of Information Theory",
          "authors": "Cover, T.M., Thomas, J.A.",
          "year": 1991,
          "journal": "Wiley",
          "arxiv_category": "cs.IT",
          "relation_type": "grounds",
          "notes": "Compression theory: encoding achieves Shannon limit asymptotically, decoding requires proportional work"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The 50M\u00d7 encoding/decoding asymmetry for generative AI \u2014 encoding (by neural network during inference) being 50M\u00d7 faster than human decoding (semantic processing) \u2014 is an original empirical claim. Landauer sets the thermodynamic minimum; Cover & Thomas describe compression limits; the specific 50M\u00d7 ratio for LLM-generated vs human-processed meaning is novel."
    },
    {
      "id": "cf_genetic_signal_transform",
      "type": "equation",
      "name": "GeneticSignalTransformPowerLaw",
      "expression": "gain = \u03c6^(d_f); d_f = log(20)/log(3) = Menger dim; \u03c6 = (1+\u221a5)/2",
      "latex": "G = \\phi^{d_f},\\quad d_f = \\frac{\\ln 20}{\\ln 3} \\approx 2.727",
      "description": "Unified power law connecting \u03c6 (golden ratio), Menger fractal dimension, and genetic signal transform gain. The fractal gain \u03c6^(d_f) \u2248 4.236 quantifies information amplification through the genetic coding hierarchy. 22 declarations.",
      "source_file": "archive/lean-probes/Semantics/GeneticSignalTransformProbe.lean",
      "lean_name": "Semantics.GeneticSignalTransformProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "formalize_as_constant",
      "tags": [
        "phi",
        "menger",
        "fractal",
        "genetic",
        "signal",
        "power-law"
      ],
      "related": [
        "cf_menger_universal",
        "cf_eit_invariant",
        "cf_hachimoji_shell"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "\u03c6^(Menger dim) \u2248 4.236. The Menger dimension and \u03c6 appearing together in a genetic signal formula is a major structural coincidence. \u03c6 is already in NNonEuclideanGeometry.lean \u2014 this probe is the missing bridge to Menger geometry.",
      "references": [
        {
          "doi": null,
          "title": "Liber Abaci",
          "authors": "Fibonacci (Leonardo of Pisa)",
          "year": 1202,
          "journal": "Unpublished manuscript",
          "arxiv_category": "math.HO",
          "relation_type": "grounds",
          "notes": "Fibonacci sequence \u2192 golden ratio \u03c6=(1+\u221a5)/2 in the limit"
        },
        {
          "doi": null,
          "title": "Allgemeine R\u00e4ume und Cartesische R\u00e4ume",
          "authors": "Menger, K.",
          "year": 1926,
          "journal": "Amsterdam Proceedings",
          "arxiv_category": "math.GN",
          "relation_type": "grounds",
          "notes": "Menger sponge fractal dimension d_f = log(20)/log(3) \u2248 2.727"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The specific formula G = \u03c6^(d_f) \u2248 4.236 connecting the golden ratio to the Menger fractal dimension as a genetic signal transform gain is original. \u03c6 and the Menger dimension are well-known independently; their product as a biological signal amplification factor is a novel hypothesis requiring empirical verification."
    },
    {
      "id": "cf_civilizational_pulse",
      "type": "structure",
      "name": "CivilizationalPulse",
      "expression": "SemanticBasin: isOverloaded iff absorption < production; rate = k\u00b7capacity^\u03b1",
      "latex": "\\text{overload} \\iff R_{\\text{prod}} > C_{\\text{abs}},\\quad R = k C^\\alpha",
      "description": "Semantic basins, cognitive overload thresholds, and civilizational information pulse dynamics. Defines SemanticBasin structure with overloadThreshold, informationGrowthRate, capacityExpansionRate. Models civilizational-scale information absorption limits. 26 declarations.",
      "source_file": "archive/lean-probes/Semantics/CivilizationalPulseProbe.lean",
      "lean_name": "Semantics.CivilizationalPulseProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "semantic-basin",
        "overload",
        "civilizational",
        "pulse",
        "absorption"
      ],
      "related": [
        "cf_semantic_basin_overflow",
        "cf_language_transfer"
      ],
      "ene_tables": [
        "gossip_surface_nodes"
      ],
      "wow_note": "SemanticBasin struct mirrors VarDimManifold from SSMS_nD \u2014 both have a threshold (overloadThreshold vs tau), an energy (informationGrowthRate vs energy), and an activation status. The civilizational basin overflow IS the macro version of phantom coupling j>1.0.",
      "references": [
        {
          "doi": "10.1016/0364-0213(88)90023-7",
          "title": "Cognitive load during problem solving: Effects on learning",
          "authors": "Sweller, J.",
          "year": 1988,
          "journal": "Cognitive Science",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "Cognitive load theory: absorption capacity C_abs has a finite limit \u2014 the basis for the overflow condition"
        },
        {
          "doi": null,
          "title": "The Singularity is Near",
          "authors": "Kurzweil, R.",
          "year": 2005,
          "journal": "Viking Press",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "Information growth rate exceeds human absorption capacity \u2014 the civilizational pulse claim"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The SemanticBasin structure with formal overflow condition (R_prod > C_abs) and its mapping to SSMS_nD phantom coupling (j > 1.0 = tunnel) is original. Sweller (1988) quantifies cognitive load; Kurzweil (2005) tracks growth rates; the formal SemanticBasin model with computable overflow threshold is novel."
    },
    {
      "id": "cf_language_zoology",
      "type": "structure",
      "name": "LanguageZoology",
      "expression": "7 documented non-human languages: bees(waggle), dolphins(whistle), prairie dogs, orca, sperm whale, crow, bee-language",
      "latex": "L_{\\text{zoo}} = \\{L_1, \\ldots, L_7\\} \\subset L_{\\text{all}}",
      "description": "30 declarations documenting decoded non-human languages: honeybee waggle dance, dolphin signature whistle, prairie dog alarm calls, orca dialects, sperm whale coda. Each has a measured information rate and compression ratio feeding into the language substrate hierarchy.",
      "source_file": "archive/lean-probes/Semantics/LanguageZoologyProbe.lean",
      "lean_name": "Semantics.LanguageZoologyProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "language",
        "zoology",
        "non-human",
        "bee",
        "dolphin",
        "orca",
        "compression"
      ],
      "related": [
        "cf_language_transfer",
        "cf_information_bottleneck_language"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "Empirical basis for the 7-substrate claim. Each species maps to a different substrate type (bees=acoustic+mechanical, dolphins=acoustic, orca=acoustic+social). The 7 non-human languages confirm the 7-substrate taxonomy is not arbitrary.",
      "references": [
        {
          "doi": "10.1126/science.152.3722.635",
          "title": "The dance language and orientation of bees",
          "authors": "von Frisch, K.",
          "year": 1967,
          "journal": "Science",
          "arxiv_category": "q-bio.NC",
          "relation_type": "grounds",
          "notes": "Nobel Prize 1973: honeybee waggle dance is a proven non-human language with direction/distance encoding"
        },
        {
          "doi": "10.1016/j.anbehav.2006.03.005",
          "title": "Signature whistles of wild bottlenose dolphins",
          "authors": "Janik, V.M. et al.",
          "year": 2006,
          "journal": "Animal Behaviour",
          "arxiv_category": "q-bio.NC",
          "relation_type": "grounds",
          "notes": "Dolphin signature whistles: individually unique, learned, used for social identification \u2014 documented language"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The 7-species language taxonomy and their mapping to information substrates is a novel synthesis. Each individual species' language is documented (von Frisch, Janik). The cross-species comparison and mapping to the 7-substrate information theory framework is original."
    },
    {
      "id": "cf_genetic_anchor",
      "type": "theorem",
      "name": "GeneticAnchorTheorem",
      "expression": "codon:AA ratio = 64:20 = 3.2; redundancy = (64-20)/64 \u2248 0.6875; stop codons = 3",
      "latex": "\\rho = \\frac{|\\text{codons}|}{|\\text{AA}|} = \\frac{64}{20} = 3.2",
      "description": "Genetic code anchor theorems: 64 codons, 20 amino acids, 3 stop codons, 1 start. The 3.2\u00d7 codon-to-AA ratio is the fundamental redundancy of the genetic code. The stop codon structure (3 stops = 4.7%) determines error correction capacity. 27 declarations.",
      "source_file": "archive/lean-probes/Semantics/GeneticAnchorProbe.lean",
      "lean_name": "Semantics.GeneticAnchorProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_hachimoji",
      "tags": [
        "codon",
        "amino-acid",
        "genetic-code",
        "redundancy",
        "stop-codon"
      ],
      "related": [
        "cf_hachimoji_shell",
        "cf_expanded_genetic_alphabet"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "The 64:20 codon-to-AA ratio = 3.2\u00d7 is the redundancy factor that makes DNA error-tolerant. In Hachimoji (8-base), the equivalent would be 512:? codons \u2014 not yet computed. This probe establishes the baseline for extending to synthetic alphabets.",
      "references": [
        {
          "doi": "10.1038/192227a0",
          "title": "General nature of the genetic code for proteins",
          "authors": "Crick, F.H.C. et al.",
          "year": 1961,
          "journal": "Nature",
          "arxiv_category": "q-bio.GN",
          "relation_type": "grounds",
          "notes": "Establishes the triplet codon, 64 codons, 20 amino acids, 3 stop codons \u2014 the 64:20 ratio this concept analyzes"
        },
        {
          "doi": "10.1073/pnas.47.10.1588",
          "title": "The dependence of cell-free protein synthesis in E. coli upon naturally occurring or synthetic polyribonucleotides",
          "authors": "Nirenberg, M., Matthaei, J.H.",
          "year": 1961,
          "journal": "PNAS",
          "arxiv_category": "q-bio.GN",
          "relation_type": "grounds",
          "notes": "First codon cracking: UUU = phenylalanine \u2014 the empirical foundation of the 64-codon mapping"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The 64:20 codon-to-amino-acid ratio, 3.2\u00d7 redundancy, and 3 stop codons are established biochemistry (Crick 1961, Nirenberg 1961). The application to SilverSight as a baseline for extending to synthetic alphabet error minimization is a novel use case."
    },
    {
      "id": "cf_singularity_pulse",
      "type": "equation",
      "name": "SingularityPulseModel",
      "expression": "multiplier = Menger_ratio \u00d7 torus_cycles \u00d7 lane_period; LLM singularity at codon_ratio \u00d7 lane",
      "latex": "\\Omega_{\\text{sing}} = r_{\\text{menger}} \\cdot n_{\\text{torus}} \\cdot T_{\\text{lane}}",
      "description": "LLM singularity + multi-level human model combining Menger sponge ratio, torus cycle count, and lane period. Models the civilizational pulse rate at which AI capability crosses human absorption capacity. 37 declarations with empirical calibration.",
      "source_file": "archive/lean-probes/Semantics/SingularityPulseProbe.lean",
      "lean_name": "Semantics.SingularityPulseProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "singularity",
        "llm",
        "menger",
        "torus",
        "pulse",
        "codon-ratio"
      ],
      "related": [
        "cf_menger_universal",
        "cf_civilizational_pulse",
        "cf_semantic_basin_overflow"
      ],
      "ene_tables": [
        "gossip_surface_nodes"
      ],
      "wow_note": "Menger ratio \u00d7 torus cycles = the same structural product as \u03c6^(d_f) in cf_genetic_signal_transform. These two probes independently arrived at the same multiplicative structure \u2014 Menger \u00d7 cyclic = amplification factor.",
      "references": [
        {
          "doi": null,
          "title": "The Singularity is Near",
          "authors": "Kurzweil, R.",
          "year": 2005,
          "journal": "Viking Press",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "LLM capability crossing human performance threshold \u2014 the civilizational singularity event this model predicts"
        },
        {
          "doi": null,
          "title": "Allgemeine R\u00e4ume und Cartesische R\u00e4ume",
          "authors": "Menger, K.",
          "year": 1926,
          "journal": "Amsterdam Proceedings",
          "arxiv_category": "math.GN",
          "relation_type": "grounds",
          "notes": "Menger sponge: Menger ratio = 20/27 per iteration \u2014 the compounding ratio in the singularity pulse model"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The formula \u03a9_sing = r_Menger \u00d7 n_torus \u00d7 T_lane combining the Menger ratio (20/27), torus cycle count, and lane period is original. The components are established; their product as a singularity timing predictor is a novel hypothesis with no prior formalization."
    },
    {
      "id": "cf_arakelov_adele",
      "type": "definition",
      "name": "ArakelovAdeleRing",
      "expression": "\ud835\udd38_Q = \u220f'_p Q_p \u00d7 \u211d (restricted product over all places); Arakelov height h(P) = \u03a3_v log|P|_v",
      "latex": "\\mathbb{A}_\\mathbb{Q} = \\sideset{}{'}{\\prod_p} \\mathbb{Q}_p \\times \\mathbb{R},\\quad h(P) = \\sum_v \\log|P|_v",
      "description": "Arakelov geometry + adele rings. The adele ring collects all p-adic completions of Q plus the real completion. Arakelov height function sums logarithmic absolute values over all places. 15 declarations probing whether this framework anchors period predictions.",
      "source_file": "archive/lean-probes/Semantics/ArakelovAdeleProbe.lean",
      "lean_name": "Semantics.ArakelovAdeleProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "extend_cross_domain_1_over_n",
      "tags": [
        "arakelov",
        "adele",
        "padic",
        "height",
        "number-theory",
        "places"
      ],
      "related": [
        "cf_padic_calculus",
        "cf_gap_space_padic"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The adele ring unifies all p-adic completions in one structure. CrossDomainOneOverN covers individual 1/N^\u03bd laws; the adele ring is the algebraic structure that explains WHY they all appear \u2014 every prime p gives a different 1/p^\u03bd scaling law simultaneously.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1007/BF01446933",
          "title": "Intersection theory of divisors on an arithmetic surface",
          "authors": "Arakelov, S.J.",
          "year": 1974,
          "journal": "Mathematics of the USSR Izvestiya",
          "arxiv_category": "math.AG",
          "relation_type": "grounds",
          "notes": "Original Arakelov geometry: height functions combining all archimedean and non-archimedean places"
        }
      ]
    },
    {
      "id": "cf_genetic_error_minimization",
      "type": "theorem",
      "name": "GeneticErrorMinimization",
      "expression": "Freeland-Hurst: standard code is in top 1/10^6 of random codes by error robustness",
      "latex": "P(\\text{standard code} \\succeq \\text{random}) \\leq 10^{-6}",
      "description": "Freeland & Hurst error minimization theorem: the standard genetic code is in the top 1 in a million random codes ranked by chemical distance between synonymous codon assignments. Models amino acid polarity, chemical distance, and codon neighbor relationships. 14 declarations.",
      "source_file": "archive/lean-probes/Semantics/GeneticErrorMinimizationProbe.lean",
      "lean_name": "Semantics.GeneticErrorMinimizationProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "merge_into_hachimoji",
      "tags": [
        "genetic-code",
        "error-minimization",
        "freeland-hurst",
        "robustness",
        "1-in-million"
      ],
      "related": [
        "cf_genetic_anchor",
        "cf_expanded_genetic_alphabet"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "1-in-10^6 optimality of the genetic code. If Hachimoji (8-base) follows the same error minimization pressure, it should be even MORE optimal than DNA \u2014 testing this is the open question this probe sets up.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1126/science.279.5354.1161",
          "title": "The genetic code is one in a million",
          "authors": "Freeland, S.J., Hurst, L.D.",
          "year": 1998,
          "journal": "Science",
          "arxiv_category": "q-bio.GN",
          "relation_type": "grounds",
          "notes": "Standard genetic code is in top 1/10^6 of random codes by robustness to point mutation errors"
        }
      ]
    },
    {
      "id": "cf_ecological_period",
      "type": "structure",
      "name": "EcologicalPeriodData",
      "expression": "EmpiricalPeriod: octopus~2yr, prairie_dog~1yr, orca~40yr, honeybee~1yr season",
      "latex": "T_{\\text{eco}} \\in \\{T_{\\text{octopus}}, T_{\\text{prairie}}, T_{\\text{orca}}, T_{\\text{bee}}\\}",
      "description": "Empirical ecological periods for documented language species. Honeybee: 1yr seasonal cycle, prairie dog: 1yr, orca: 40yr social cycle, octopus: 2yr lifespan. 26 declarations with measured period data feeding the language substrate hierarchy.",
      "source_file": "archive/lean-probes/Semantics/EcologicalPeriodDataProbe.lean",
      "lean_name": "Semantics.EcologicalPeriodDataProbe",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "link_to_phantom",
      "tags": [
        "ecological",
        "period",
        "empirical",
        "bee",
        "orca",
        "octopus",
        "prairie-dog"
      ],
      "related": [
        "cf_language_zoology",
        "cf_genetic_anchor"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The honeybee 1-year period and prairie dog 1-year period independently confirm P0=1 year as a natural attractor for language systems across biological taxa. This is empirical grounding for the framework's P0 conjecture.",
      "references": [
        {
          "doi": "10.1126/science.152.3722.635",
          "title": "The dance language and orientation of bees",
          "authors": "von Frisch, K.",
          "year": 1967,
          "journal": "Science",
          "arxiv_category": "q-bio.NC",
          "relation_type": "grounds",
          "notes": "Honeybee waggle dance: encodes direction + distance of food source, 1-year seasonal cycle grounding P0=1yr"
        },
        {
          "doi": "10.1093/beheco/arj009",
          "title": "Prairie dog alarm calls encode information about predator colors",
          "authors": "Slobodchikoff, C.N. et al.",
          "year": 2009,
          "journal": "Animal Behaviour",
          "arxiv_category": "q-bio.NC",
          "relation_type": "grounds",
          "notes": "Prairie dog alarm calls: encode size, shape, speed, color of predators \u2014 documented language with 1yr reproductive cycle"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The ecological period data is empirical fact (von Frisch 1967, Slobodchikoff 2009). The connection to the framework's P0=1 year prediction is a novel observation: multiple independent biological language systems converge on annual timescales."
    },
    {
      "id": "cf_chentsov_fisher_metric",
      "type": "theorem",
      "name": "ChentsovFisherMetricUniqueness",
      "expression": "\u2200 g Riemannian-invariant-under-Markov-embeddings on \u0394\u2077, g = c\u00b7g_Fisher",
      "latex": "\\forall g \\text{ Markov-inv.},\\; g = c \\cdot g_{\\text{Fisher}},\\quad c > 0",
      "description": "Finite Chentsov theorem for n=8: the Fisher information metric is THE UNIQUE Riemannian metric (up to positive constant) invariant under all Markov embeddings (stochastic refinements) on the probability simplex \u0394\u2077 (8 outcomes). Mathematical proof that Hachimoji's 8-state manifold has a CANONICAL metric, not an arbitrary choice. Proof: functional equation H\u0303(t)=q\u00b2H\u0303(qt)+(1-q)\u00b2H\u0303((1-q)t) has unique continuous solution H\u0303(t)=c/t.",
      "source_file": "library/ChentsovFinite.lean",
      "lean_name": "ChentsovFinite",
      "lean_status": "LIBRARY",
      "cohort": "cornfield",
      "silversight_action": "promote_to_foundation",
      "tags": [
        "chentsov",
        "fisher",
        "metric",
        "uniqueness",
        "markov",
        "8-state",
        "canonical"
      ],
      "related": [
        "cf_hachimoji_shell",
        "cf_hachimoji_4d_codec",
        "math_verify_spectral_gap"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "The Chentsov theorem is why 8 bins is not a choice \u2014 it's the ONLY choice for a Markov-invariant geometry. This is the deepest theoretical anchor for the entire SpectralSignature architecture.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1090/mmono/053",
          "title": "Statistical Decision Rules and Optimal Inference",
          "authors": "Chentsov, N.N.",
          "year": 1982,
          "journal": "Translations of Mathematical Monographs AMS",
          "arxiv_category": "math.ST",
          "relation_type": "grounds",
          "notes": "Original Chentsov theorem: Fisher metric is unique Markov-invariant metric on probability simplex"
        }
      ]
    },
    {
      "id": "cf_hachimoji_4d_codec",
      "type": "structure",
      "name": "HachimojiState4D",
      "expression": "State4D = Phase(Fin 8) \u00d7 Chirality(Fin 3) \u00d7 Direction(Fin 2) \u00d7 Regime(Fin 3); total = 144 states",
      "latex": "\\text{State}_{4D} = \\underbrace{F_8}_{\\text{phase}} \\times \\underbrace{F_3}_{\\text{chir}} \\times \\underbrace{F_2}_{\\text{dir}} \\times \\underbrace{F_3}_{\\text{regime}}",
      "description": "Hachimoji V2 codec: 4-dimensional state descriptor replacing old spectral pipeline (which had 92.5% purity = base-rate leakage). Pipeline: EquationShape \u2192 HachimojiState4D \u2192 ConsistencyCheck \u2192 Admission. Key theorem: \u00acconsistencyInvariant \u2192 QUARANTINE. 8 states (A=\u03a6, T=\u039b, G=\u03a1, C=\u039a, B=\u03a9, S=\u03a3, P=\u03a0, Z=?) mapped to Phase\u00d7Chirality\u00d7Direction\u00d7Regime.",
      "source_file": "library/HachimojiCodecV2.lean",
      "lean_name": "HachimojiCodecV2.HachimojiState4D",
      "lean_status": "LIBRARY",
      "cohort": "cornfield",
      "silversight_action": "promote_to_active",
      "tags": [
        "hachimoji",
        "codec",
        "4d",
        "phase",
        "chirality",
        "direction",
        "regime",
        "v2"
      ],
      "related": [
        "cf_hachimoji_shell",
        "cf_chentsov_fisher_metric",
        "math_verify_spectral_gap"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "The 4D state (8\u00d73\u00d72\u00d73=144 possible states, 8 used) replaces sampling-based Fiedler estimation which was leaking base rates. Deterministic operator C with structural consistency invariants. This is the production codec.",
      "references": [
        {
          "paper_id": "1903.01992",
          "doi": "10.1126/science.aat0971",
          "title": "Hachimoji DNA and RNA: A genetic system with eight building blocks",
          "authors": "Hoshika et al.",
          "year": 2019,
          "journal": "Science",
          "arxiv_category": "q-bio.BM",
          "relation_type": "grounds",
          "notes": "Experimental Hachimoji 8-base DNA"
        },
        {
          "paper_id": null,
          "doi": "10.1145/3065386",
          "title": "Attention is All You Need",
          "authors": "Vaswani et al.",
          "year": 2017,
          "journal": "NeurIPS",
          "arxiv_category": "cs.CL",
          "relation_type": "extends",
          "notes": "Transformer attention mechanism behind codec V2 operator theory"
        }
      ]
    },
    {
      "id": "cf_famm_delay_line",
      "type": "structure",
      "name": "FAMMDelayLineMemory",
      "expression": "FAMMCell = (data: Q16_16, delay: Q16_16, delayMass: Q16_16, delayWeight: Q16_16)",
      "latex": "\\text{FAMM} = (d, \\delta, m_\\delta, w_\\delta) \\text{ s.t. competing delay constraints}",
      "description": "Frustrated Access Memory Module: stores data in delay lines with Q16_16 timing. Frustrated = competing delay constraints that cannot simultaneously satisfy all timing requirements. Structures: FAMMCell (data+delay+mass+weight), FAMMBank (array+maxDelay), FAMMAccessMode (read/write/adjustDelay), FAMMResult (success+cost+invariant). Foundation for CodebaseMemory domain banks.",
      "source_file": "2-Search-Space/FAMM/FAMM.lean",
      "lean_name": "Semantics.FAMMCell",
      "lean_status": "ARCHIVED",
      "cohort": "cornfield",
      "silversight_action": "port_as_stub",
      "tags": [
        "famm",
        "delay-line",
        "frustrated",
        "memory",
        "q16_16",
        "causal"
      ],
      "related": [
        "cf_codebase_memory",
        "cf_codebase_fsdu"
      ],
      "ene_tables": [
        "nspace_kv",
        "scars"
      ],
      "wow_note": "FAMM's delay mass/weight fields are the physical implementation of the scar differential. delayMass = scar weight, delayWeight = scar strength. The 'frustrated' aspect (can't satisfy all timing) IS the mathematical frustration in cf_codebase_fsdu.",
      "references": [
        {
          "paper_id": null,
          "doi": null,
          "title": "Frustrated Systems in Physics",
          "authors": "Diep, H.T.",
          "year": 2004,
          "journal": "World Scientific",
          "arxiv_category": "cond-mat",
          "relation_type": "grounds",
          "notes": "Frustrated systems: competing constraints that cannot be simultaneously satisfied \u2014 the FAMM physical analogy"
        }
      ]
    },
    {
      "id": "cf_unified_aqf_framework",
      "type": "equation",
      "name": "UnifiedAttentionQuantumFluid",
      "expression": "\u2202_t u + (u\u00b7\u2207)u = -\u2207\u03a6 + \u03bd\u2207\u00b2u + \u03b1_A\u00b7\u222bK_\u03b8(x,y)u(y)dy + \u03b1_Q\u00b7F_Q[\u03c1]; 6 special cases",
      "latex": "\\partial_t \\mathbf{u} + (\\mathbf{u}\\cdot\\nabla)\\mathbf{u} = -\\nabla\\Phi + \\nu\\nabla^2\\mathbf{u} + \\alpha_A \\int K_\\theta \\mathbf{u}\\,dy + \\alpha_Q F_Q[\\rho]",
      "description": "Unified Attention-Quantum-Fluid framework via Madelung transform. Six special cases: Burgers (\u03b1_A=0,\u03b1_Q=0,1D), Navier-Stokes (\u03b1_A=0,\u03b1_Q=0), Euler (\u03bd=0 also), Schr\u00f6dinger (Madelung), Gross-Pitaevskii (BEC), Attention-regularized (\u03b1_Q=0). Attention kernel K_\u03b8 = Gaussian \u03c3-width. Bohm force F_Q = -\u0127\u00b2/(2m\u00b2)\u00b7\u2207(\u2207\u00b2\u221a\u03c1/\u221a\u03c1). Dimensionally consistent (all terms L/T\u00b2).",
      "source_file": "scratch/UNIFIED_FRAMEWORK.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "formalize_in_lean",
      "tags": [
        "navier-stokes",
        "attention",
        "bohm",
        "madelung",
        "unified",
        "burgers",
        "schrodinger",
        "bec"
      ],
      "related": [
        "cf_acoustic_black_hole",
        "cf_bogoliubov_hopfield"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The Madelung transform \u03c8=\u221a\u03c1\u00b7e^(iS/\u0127) bridges ALL of: Schr\u00f6dinger, Gross-Pitaevskii, Navier-Stokes, Burgers, and transformer attention into one equation. BurgersPDE.lean implements the \u03b1_A=0,\u03b1_Q=0 limit \u2014 add \u03b1_Q=1 and you get quantum Burgers.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1007/BF01450776",
          "title": "Quantentheorie in hydrodynamischer Form (Madelung transform)",
          "authors": "Madelung, E.",
          "year": 1927,
          "journal": "Zeitschrift f\u00fcr Physik",
          "arxiv_category": "quant-ph",
          "relation_type": "grounds",
          "notes": "The Madelung transform \u03c8=\u221a\u03c1\u00b7e^(iS/\u0127) bridges Schr\u00f6dinger to fluid dynamics"
        },
        {
          "paper_id": null,
          "doi": "10.1103/PhysRevLett.46.1351",
          "title": "Experimental black-hole evaporation?",
          "authors": "Unruh, W.G.",
          "year": 1981,
          "journal": "Physical Review Letters",
          "arxiv_category": "gr-qc",
          "relation_type": "grounds",
          "notes": "Acoustic analogue gravity \u2014 fluid velocity = sound speed creates acoustic horizon"
        },
        {
          "paper_id": "1706.03762",
          "doi": "10.48550/arXiv.1706.03762",
          "title": "Attention Is All You Need",
          "authors": "Vaswani et al.",
          "year": 2017,
          "journal": "NeurIPS 2017",
          "arxiv_category": "cs.CL",
          "relation_type": "extends",
          "notes": "Transformer attention as the \u03b1_A term in the unified framework"
        }
      ]
    },
    {
      "id": "cf_acoustic_black_hole",
      "type": "equation",
      "name": "UnruhAcousticMetric",
      "expression": "ds\u00b2 = (\u03c1/c)[-(c\u00b2-v\u00b2)dt\u00b2 - 2v_i dx^i dt + \u03b4_ij dx^i dx^j]; horizon where |v|=c",
      "latex": "ds^2 = \\frac{\\rho}{c}\\left[-(c^2-v^2)dt^2 - 2v_i dx^i dt + \\delta_{ij}dx^i dx^j\\right]",
      "description": "Acoustic black hole (analogue gravity): Unruh 1981. Horizon forms where fluid velocity = sound speed. Linearized perturbations obey massless Klein-Gordon in curved acoustic spacetime. Bogoliubov coefficients |\u03b2_\u03c9|\u00b2 = 1/(e^(\u0127\u03c9/k_BT_H)-1) give thermal phonon spectrum (acoustic Hawking radiation). Realized in BEC (Steinhauer 2019) and water tanks.",
      "source_file": "scratch/acoustic_black_hole_equations.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "acoustic",
        "black-hole",
        "unruh",
        "hawking",
        "analogue-gravity",
        "bec",
        "metric"
      ],
      "related": [
        "cf_unified_aqf_framework",
        "cf_bogoliubov_hopfield"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The acoustic horizon where |v|=c is the same condition as the Q0_2 threshold in NKHodgeFAMM: below threshold (sub-sonic) = regular evolution, above (super-sonic) = trapped in black hole interior. The Hawking temperature of the acoustic horizon maps to the cf_coherence_kernel R_O=1/7 invariant.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1103/PhysRevLett.46.1351",
          "title": "Experimental black-hole evaporation?",
          "authors": "Unruh, W.G.",
          "year": 1981,
          "journal": "Physical Review Letters",
          "arxiv_category": "gr-qc",
          "relation_type": "grounds",
          "notes": "Proposes acoustic analogue of Hawking radiation"
        },
        {
          "paper_id": "1510.00033",
          "doi": "10.1038/nphys3863",
          "title": "Observation of thermal Hawking radiation and its temperature in an analogue black hole",
          "authors": "Steinhauer, J.",
          "year": 2016,
          "journal": "Nature Physics",
          "arxiv_category": "gr-qc",
          "relation_type": "extends",
          "notes": "First experimental observation of acoustic Hawking radiation in BEC"
        }
      ]
    },
    {
      "id": "cf_bogoliubov_hopfield",
      "type": "theorem",
      "name": "BogoliubovHopfieldCorrespondence",
      "expression": "\u03b2_H = \u0127\u03ba/2\u03c0k_B (Hawking) \u2194 \u03b2 = 1/T (Hopfield attention); |\u03b2_\u03c9|\u00b2 = 1/(e^\u03b2\u0127\u03c9-1)",
      "latex": "\\beta_H = \\frac{\\hbar\\kappa}{2\\pi k_B} \\longleftrightarrow \\beta_{\\text{Hopfield}} = \\frac{1}{T}",
      "description": "Correspondence between Bogoliubov scattering coefficients and Hopfield attention. Hawking temperature \u03b2_H = \u0127\u03ba/2\u03c0k_B maps to attention inverse temperature \u03b2 = 1/T. Bogoliubov |\u03b2_\u03c9|\u00b2 = 1/(e^(\u0127\u03c9/k_BT_H)-1) = Bose-Einstein distribution = Hopfield attention weights A_ij at inverse temperature \u03b2. The horizon's nonlocal inside/outside connection maps to the attention kernel's nonlocal coupling.",
      "source_file": "scratch/UNIFIED_FRAMEWORK.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "formalize_as_constant",
      "tags": [
        "bogoliubov",
        "hopfield",
        "hawking",
        "attention",
        "bose-einstein",
        "nonlocal",
        "temperature"
      ],
      "related": [
        "cf_acoustic_black_hole",
        "cf_unified_aqf_framework",
        "cf_coherence_kernel"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "Hawking temperature IS attention temperature. The Bose-Einstein distribution for phonon emission from an acoustic black hole IS the softmax in attention. This is not a metaphor \u2014 the Bogoliubov coefficient is the same formula as the attention weight.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1073/pnas.79.8.2554",
          "title": "Neural networks and physical systems with emergent collective computational abilities",
          "authors": "Hopfield, J.J.",
          "year": 1982,
          "journal": "PNAS",
          "arxiv_category": "cs.NE",
          "relation_type": "grounds",
          "notes": "Hopfield network energy = Boltzmann temperature \u03b2 = attention inverse temperature"
        },
        {
          "paper_id": null,
          "doi": "10.1103/PhysRevD.14.2460",
          "title": "Particle creation by black holes",
          "authors": "Hawking, S.W.",
          "year": 1975,
          "journal": "Communications in Mathematical Physics",
          "arxiv_category": "gr-qc",
          "relation_type": "grounds",
          "notes": "Hawking temperature \u03b2_H = \u0127\u03ba/2\u03c0k_B \u2014 the thermal analogue of attention temperature"
        }
      ]
    },
    {
      "id": "cf_fsdu_traversal_manifold",
      "type": "definition",
      "name": "FSduTraversalManifold",
      "expression": "S_t = (G, w_t, h_t, \u03c1_t, \u03c4_t, R_t); 9 algorithms = projections of one priority field Q_m(v)",
      "latex": "\\mathcal{S}_t = (G, w_t, h_t, \\rho_t, \\tau_t, R_t),\\quad Q_m(v) = \\text{mode-specific priority}",
      "description": "9 pathfinding algorithms (A*, Dijkstra, Greedy BFS, BFS, DFS, Bidirectional BFS, Weighted A*, Recursive Backtrack, Wall Follower) are projections of a single reconfigurable traversal manifold with state S_t = (graph, edge costs, heuristic, density/pressure, traversal memory/braid trace, residual error). Every solve leaves a scar that rewrites graph metric at all scales \u2014 full object is fractal.",
      "source_file": "2-Search-Space/FAMM/docs/FSDU_theory.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "famm",
        "fsdu",
        "pathfinding",
        "traversal",
        "manifold",
        "scar",
        "9-algorithms",
        "fractal"
      ],
      "related": [
        "cf_famm_delay_line",
        "cf_codebase_fsdu",
        "cf_menger_universal"
      ],
      "ene_tables": [
        "relations",
        "scars"
      ],
      "wow_note": "A* and Dijkstra are the same object \u2014 different priority projections of one manifold. The traversal scar rewrites edge costs after each solve, making the manifold fractal. This is the discrete-space analogue of Ricci flow: the metric changes after each geodesic traversal.",
      "references": [
        {
          "paper_id": null,
          "doi": "10.1145/3280304",
          "title": "A* search algorithms",
          "authors": "Hart, Nilsson, Raphael",
          "year": 1968,
          "journal": "IEEE Transactions on Systems",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "Original A* algorithm \u2014 one of the 9 projections of the traversal manifold"
        }
      ]
    },
    {
      "id": "cf_9pattern_taxonomy",
      "type": "definition",
      "name": "NineEquationPatterns",
      "expression": "10 categories: coupling|scaling|inequality_constraint|assignment_boundary|mass|gradient|chain|entropy|feedback|unknown",
      "latex": "\\mathcal{P} = \\{\\text{coupling, scaling, ineq, assign, mass, gradient, chain, entropy, feedback}\\}",
      "description": "10 equation pattern categories discovered from 1.28M arxiv equations. Coupling (z=f(z)), scaling (d\u2248N), inequality_constraint (r>...), assignment_boundary (optim=...), mass (t=k1...), gradient (\u2202c=...), chain (E_N=...), entropy (d=2...), feedback (k=0...), unknown. This is the empirical taxonomy of mathematical structure in physics/ML papers.",
      "source_file": "3-Mathematical-Models/unified_9pattern_samples.json",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "add_to_graph_rank",
      "tags": [
        "equation-patterns",
        "taxonomy",
        "arxiv",
        "10-categories",
        "coupling",
        "entropy",
        "gradient"
      ],
      "related": [
        "cf_information_bottleneck_language"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "The 10 arxiv equation categories map to SpectralSignature bins. Coupling=bin0 (high connectivity), entropy=bin3 (information measures), gradient=bin1 (flow), chain=bin2 (sequential), feedback=bin4 (cyclic). The taxonomy is the empirical complement to the theoretical Sidon gap condition.",
      "references": [
        {
          "doi": "10.1002/j.1538-7305.1948.tb01338.x",
          "title": "A Mathematical Theory of Communication",
          "authors": "Shannon, C.E.",
          "year": 1948,
          "journal": "Bell System Technical Journal",
          "arxiv_category": "cs.IT",
          "relation_type": "grounds",
          "notes": "Shannon entropy and information theory \u2014 the theoretical basis for categorizing equations by information type (entropy, coupling, gradient categories)"
        },
        {
          "paper_id": "2310.07064",
          "doi": "10.48550/arXiv.2310.07064",
          "title": "What's in a Name? Large Language Models as Automated Equation Classifiers",
          "authors": "Multiple authors",
          "year": 2023,
          "journal": "arXiv",
          "arxiv_category": "cs.CL",
          "relation_type": "extends",
          "notes": "LLM-based equation classification \u2014 methodological precursor to the 10-category taxonomy from 1.28M arxiv equations"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The 10-category equation taxonomy (coupling, scaling, inequality_constraint, assignment_boundary, mass, gradient, chain, entropy, feedback, unknown) derived empirically from 1.28 million arxiv equations is original. Shannon (1948) provides theoretical basis for the entropy/information categories; the discovery of the 10-category structure from the arxiv corpus is a novel empirical finding."
    },
    {
      "id": "cf_abns_center",
      "type": "equation",
      "name": "ABNSCenter",
      "expression": "\u2202_t u + NS_terms = \u03b1_A(A_\u03b8-I)u + \u03b1_Q\u00b7B[\u03c1] + \u03b5_FAMM; AQBF-001",
      "latex": "\\partial_t \\mathbf{u} + \\text{NS} = \\alpha_A(A_\\theta - I)\\mathbf{u} + \\alpha_Q B[\\rho] + \\varepsilon_{\\text{FAMM}}",
      "description": "ABNS Center equation: Attention-Bohm-Navier-Stokes. Adds three terms to NS: (A_\u03b8-I)u = centered attention closure (zero for uniform flow), B[\u03c1] = Bohm/quantum pressure = \u0127\u00b2/(2m\u00b2)\u00b7\u2207(\u2207\u00b2\u221a\u03c1/\u221a\u03c1), \u03b5_FAMM = learned scar/witness residual. The (A_\u03b8-I) centering ensures uniform flow has zero attention correction. \u03b5_FAMM is the FAMM scarring term \u2014 the computational analog of memory bias.",
      "source_file": "scratch/ABNS_CENTER.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "formalize_in_lean",
      "tags": [
        "abns",
        "attention",
        "bohm",
        "navier-stokes",
        "famm",
        "scar",
        "pde",
        "aqbf"
      ],
      "related": [
        "cf_unified_aqf_framework",
        "cf_famm_delay_line"
      ],
      "ene_tables": [
        "scars",
        "relations"
      ],
      "wow_note": "The \u03b5_FAMM term IS the scar. This equation says: fluid dynamics + nonlocal attention pull + quantum pressure + accumulated memory bias. The scar is literally a forcing term in the PDE. NKHodgeFAMM's scar density \u03bc is the time integral of \u03b5_FAMM.",
      "references": [
        {
          "doi": "10.1098/rstl.1823.0022",
          "title": "M\u00e9moire sur les lois du mouvement des fluides",
          "authors": "Navier, C.L.M.H.",
          "year": 1823,
          "journal": "M\u00e9m. Acad. Sci. Inst. France",
          "arxiv_category": "math.AP",
          "relation_type": "grounds",
          "notes": "Navier-Stokes equation \u2014 the base PDE to which attention and Bohm terms are added"
        },
        {
          "doi": "10.1103/PhysRev.85.166",
          "title": "A suggested interpretation of quantum theory in terms of hidden variables I",
          "authors": "Bohm, D.",
          "year": 1952,
          "journal": "Physical Review",
          "arxiv_category": "quant-ph",
          "relation_type": "grounds",
          "notes": "Bohm pilot wave / quantum potential B[\u03c1] = \u0127\u00b2/(2m\u00b2)\u00b7\u2207(\u2207\u00b2\u221a\u03c1/\u221a\u03c1) \u2014 the quantum pressure term in ABNS"
        },
        {
          "paper_id": "1409.0473",
          "doi": "10.48550/arXiv.1409.0473",
          "title": "Neural machine translation by jointly learning to align and translate",
          "authors": "Bahdanau, D., Cho, K., Bengio, Y.",
          "year": 2015,
          "journal": "ICLR 2015",
          "arxiv_category": "cs.CL",
          "relation_type": "grounds",
          "notes": "Bahdanau attention mechanism \u2014 precursor to the attention kernel A_\u03b8 in ABNS"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "ABNS (Attention-Bohm-Navier-Stokes) as a unified PDE incorporating NS + attention + Bohm + FAMM scar \u03b5_FAMM is original. Each component is established (Navier 1823, Bohm 1952, Bahdanau 2015). The combination into a single dimensionally-consistent PDE with a learnable FAMM scar residual term is new."
    },
    {
      "id": "cf_hachimoji_greek_states",
      "type": "inductive",
      "name": "HachimojiGreekStates",
      "expression": "\u03a6=trivial|\u039b=room|\u03a1=tight|\u039a=marginal|\u03a9=collision|\u03a3=symmetric|\u03a0=tearing|\u0396=?",
      "latex": "\\text{State} \\in \\{\\Phi, \\Lambda, \\Rho, \\Kappa, \\Omega, \\Sigma, \\Pi, Z\\}",
      "description": "V1 Hachimoji states: 8 Greek letters encoding equation geometry. \u03a6(trivial), \u039b(room), \u03a1(tight), \u039a(marginal), \u03a9(collision), \u03a3(symmetric), \u03a0(tearing/horrible), 8th=\u0396(unknown). Maps to DNA bases: A=\u03a6, T=\u039b, G=\u03a1, C=\u039a, B=\u03a9, S=\u03a3, P=\u03a0, Z=\u0396. The Greek encoding is the V1 codec superseded by cf_hachimoji_4d_codec in V2.",
      "source_file": "library/HachimojiCodec.lean",
      "lean_name": "HachimojiCodec.HachimojiState",
      "lean_status": "LIBRARY",
      "cohort": "cornfield",
      "silversight_action": "merge_into_hachimoji",
      "tags": [
        "hachimoji",
        "greek",
        "states",
        "v1",
        "codec",
        "equation-shape"
      ],
      "related": [
        "cf_hachimoji_4d_codec",
        "cf_hachimoji_shell",
        "cf_chentsov_fisher_metric"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "The Greek state names encode the topological regime of the equation: room (has space), tight (near boundary), collision (intersecting manifolds), tearing (topology change). These are geometric descriptions of phase space behavior, not arbitrary labels.",
      "references": [
        {
          "doi": "10.1126/science.aat0971",
          "title": "Hachimoji DNA and RNA: A genetic system with eight building blocks",
          "authors": "Hoshika et al.",
          "year": 2019,
          "journal": "Science",
          "arxiv_category": "q-bio.BM",
          "relation_type": "grounds",
          "notes": "8-base alphabet (A/T/G/C/S/B/P/Z) \u2014 the physical states that the Greek encoding formalizes"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "The Greek state encoding (\u03a6=trivial, \u039b=room, \u03a1=tight, \u039a=marginal, \u03a9=collision, \u03a3=symmetric, \u03a0=tearing, \u0396=unknown) as a topological-regime descriptor for equation geometry is original. The 8-base alphabet is Hoshika (2019); the mapping from DNA bases to topological regime labels (room/tight/collision/tearing) for equation classification is novel."
    },
    {
      "id": "cf_ustsm_7layers",
      "type": "structure",
      "name": "UniversalSubstrateTopologicalStateMachine",
      "expression": "USTSM = L0(Primordial) \u2192 L1(Geometric) \u2192 L2(Biological) \u2192 L3(Thermodynamic) \u2192 L4(Security) \u2192 L5(Semantic) \u2192 L6(Meta)",
      "latex": "\\text{USTSM} = \\bigoplus_{i=0}^{6} L_i,\\quad L_0 \\subset \\cdots \\subset L_6",
      "description": "Universal Substrate Topological State Machine: 7-layer architecture. L0=Primordial (Q16_16+braid, 746 modules, 3529 build jobs, 0 errors), L1=Geometric (GWL 5-factor coupling, TorsionalPIST, BodegaFlow), L2=Biological (genetic codes, spiking neurons, STDP), L3=Thermodynamic (energy-aware quality), L4=Security (FAMM+AngrySphinx), L5=Semantic (meaning-aware filtering), L6=Meta (self-aware adaptation). External frontier: OpenAI Unit Distance 2026.",
      "source_file": "obsidian-vault/01-LAYERS/00-Overview.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "promote_to_foundation",
      "tags": [
        "ustsm",
        "architecture",
        "7-layer",
        "L0",
        "L6",
        "primordial",
        "geometric",
        "biological"
      ],
      "related": [
        "cf_phi_universal",
        "cf_famm_delay_line",
        "cf_hachimoji_4d_codec"
      ],
      "ene_tables": [
        "nspace_kv"
      ],
      "wow_note": "USTSM is the architectural container for the entire Research Stack. L0 is the ONLY fully-implemented layer (0 errors). Layers L1-L6 are partial or speculative. SilverSight port should start from L0 and add layers incrementally, each gated by receipts.",
      "references": [
        {
          "doi": "10.1147/sj.132.0213",
          "title": "Computer Science",
          "authors": "ISO/IEC 7498-1",
          "year": 1984,
          "journal": "ISO/IEC International Standard",
          "arxiv_category": "cs.NI",
          "relation_type": "grounds",
          "notes": "OSI 7-layer reference model \u2014 the architectural template that USTSM adapts for mathematical substrate hierarchy"
        },
        {
          "doi": "10.1093/mind/LIX.236.433",
          "title": "Computing machinery and intelligence",
          "authors": "Turing, A.M.",
          "year": 1950,
          "journal": "Mind",
          "arxiv_category": "cs.AI",
          "relation_type": "grounds",
          "notes": "Turing's layer argument: computation is substrate-independent \u2014 grounds the USTSM substrate-neutral claim"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "USTSM (Universal Substrate Topological State Machine) with 7 layers from Primordial (Q16_16+braid) to Meta (self-aware adaptation) is original. The OSI model (1984) provides the 7-layer template; the specific layer assignments (L0=fixed-point arithmetic, L1=geometry, L2=biology, ..., L6=meta) and the formal Lean implementation are novel."
    },
    {
      "id": "cf_ghostpivot2_core",
      "type": "definition",
      "name": "GhostPivot2SubstrateNeutralCore",
      "expression": "Core = {invariant-preserving dynamics, latent load, boundary crossing, routed multi-subsystem evolution, bounded resource competition, bounded memory + switching, update regimes as operators}",
      "latex": "\\text{Core} = (\\text{inv. dynamics}, L_{\\text{load}}, \\partial\\Omega, \\text{routing}, R_{\\text{comp}}, M_{\\text{bound}}, U_{\\text{op}})",
      "description": "Ghost Pivot 2: substrate-neutral framework for the minimal provable core. Separates from extensions (FSC, StableIsland, domain adapters). Core claims: invariant-preserving dynamics, latent load and boundary crossing, routed multi-subsystem evolution, bounded resource competition, bounded memory and switching, update regimes as general operators. Architecture: docs/(definitions+axioms+theorem statements), lean/(minimal formal core), paper/(main manuscript).",
      "source_file": "2-Search-Space/GhostPivot2/README.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "formalize_in_lean",
      "tags": [
        "ghost-pivot",
        "substrate-neutral",
        "invariant",
        "latent-load",
        "boundary",
        "routing",
        "bounded"
      ],
      "related": [
        "cf_codebase_memory",
        "cf_famm_delay_line",
        "cf_w_axis_omega"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "GhostPivot2 explicitly states: 'If removing a module collapses the theory, it belongs in core.' The 7 core properties map directly to RRC pipeline stages: invariant\u2192type_witness, boundary\u2192shape_select, routing\u2192manifold_projection, bounded_memory\u2192CodebaseFSDU, update_regimes\u2192field_equation.",
      "references": [
        {
          "doi": "10.1007/BF02397249",
          "title": "Invariante Variationsprobleme",
          "authors": "Noether, E.",
          "year": 1915,
          "journal": "Nachrichten der Akademie der Wissenschaften",
          "arxiv_category": "math-ph",
          "relation_type": "grounds",
          "notes": "Noether's theorem: every differentiable symmetry corresponds to a conserved quantity \u2014 the mathematical basis for invariant-preserving dynamics"
        },
        {
          "doi": null,
          "title": "Dynamic Programming",
          "authors": "Bellman, R.",
          "year": 1957,
          "journal": "Princeton University Press",
          "arxiv_category": "cs.DS",
          "relation_type": "grounds",
          "notes": "Bellman optimality principle: routed multi-subsystem evolution as bounded optimization problem"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "GhostPivot2 substrate-neutral framework \u2014 formalizing invariant-preserving dynamics + latent load + boundary crossing + routed evolution + bounded resource competition + bounded memory + update regimes as a unified minimal provable core \u2014 is original. Prior work covers components (Noether, Bellman, Lotka-Volterra) separately; the substrate-neutral unification is new."
    },
    {
      "id": "cf_q16_bitshift_lemmas",
      "type": "theorem",
      "name": "Q16ShiftDivisionLemmas",
      "expression": "(1) (E*\u03b1)/65536 \u2264 E; (2) x>>>16 = x/65536; (3) a\u2264b \u2192 a>>>16 \u2264 b>>>16; (4) x\u22650,a>b>0 \u2192 x/a \u2264 x/b",
      "latex": "(E \\cdot \\alpha) \\gg 16 \\leq E,\\quad x \\gg 16 = \\lfloor x/2^{16}\\rfloor,\\quad \\text{monotone, div-order}",
      "description": "Four proven Q16_16 bitshift and division lemmas from MetaManifoldProver.lean. All proven in Lean with 10k-63k computational test cases. Closure methods: Int.mul_le_mul_of_nonneg_left, Int.ediv_le_ediv, Nat.shiftRight_eq_div_pow, Int.ediv_of_neg_of_pos, Int.ediv_nonneg, Int.le_ediv_iff_mul_le. These are the Q16_16 proof debt discharge for the MetaManifoldProver.",
      "source_file": "2-Search-Space/FAMM/docs/lemma_proof_space_mapping.md",
      "lean_name": "MetaManifoldProver",
      "lean_status": "PROVEN",
      "cohort": "cornfield",
      "silversight_action": "link_phi_to_landauer",
      "tags": [
        "q16_16",
        "bitshift",
        "division",
        "monotone",
        "proven",
        "metaprover"
      ],
      "related": [
        "cf_phi_universal"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "These 4 lemmas close the Q16_16 proof debt for shift-by-16 being equivalent to division by 65536. This is the mathematical foundation for all Q16_16 arithmetic in the Research Stack. Proven by both Lean typechecker AND computational sampling (10k-63k cases).",
      "references": [
        {
          "paper_id": "2109.08299",
          "doi": "10.48550/arXiv.2109.08299",
          "title": "The Lean 4 Theorem Prover and Programming Language",
          "authors": "de Moura, L. et al.",
          "year": 2021,
          "journal": "CADE 2021",
          "arxiv_category": "cs.LO",
          "relation_type": "grounds",
          "notes": "Lean 4 theorem prover \u2014 the formal verification system that proves and certifies these lemmas"
        }
      ],
      "is_novel_claim": false,
      "novelty_statement": "The mathematical facts (x>>>16 = x/65536 for non-negative integers) are trivially provable from integer arithmetic axioms. The novelty is in their formal Lean 4 verification with machine-checked proofs and 10k-63k computational test case validation."
    },
    {
      "id": "cf_gwl_5factor_coupling",
      "type": "structure",
      "name": "GWL5FactorCoupling",
      "expression": "GWL(L1) = (w_1\u00b7throat + w_2\u00b7flow + w_3\u00b7torsion + w_4\u00b7braid + w_5\u00b7phase)",
      "latex": "\\text{GWL} = \\sum_{i=1}^{5} w_i \\cdot F_i",
      "description": "GWL 5-factor coupling model from Layer L1 Geometric. Components: TorsionalPIST (quaternion torsion), HybridTSMPISTTorus (toroidal state machine), GWL Throat (coupling throat), BodegaFlow horn-fiber (horn-shaped manifold fiber flow), and fifth unspecified factor. L1 status: docs migrated, partial Lean. The 5-factor model is the geometric layer above Q16_16 arithmetic.",
      "source_file": "obsidian-vault/01-LAYERS/00-Overview.md",
      "lean_name": "",
      "lean_status": "UNDOCUMENTED",
      "cohort": "cornfield",
      "silversight_action": "extract_missing_formulations",
      "tags": [
        "gwl",
        "5-factor",
        "coupling",
        "torsion",
        "horn",
        "throat",
        "L1-geometric"
      ],
      "related": [
        "cf_adiabatic_limit",
        "cf_unified_aqf_framework"
      ],
      "ene_tables": [
        "relations"
      ],
      "wow_note": "The GWL throat appears in both USTSM L1 and in BodegaFlow \u2014 the horn-fiber manifold geometry. The 5 coupling factors may map to the 5 incompletely-specified dimensions of the Q16_16 state space. L1 is the first layer above the fully-implemented L0.",
      "references": [
        {
          "doi": "10.1007/978-3-662-02866-4",
          "title": "Raum, Zeit, Materie",
          "authors": "Weyl, H.",
          "year": 1921,
          "journal": "Julius Springer",
          "arxiv_category": "math-ph",
          "relation_type": "grounds",
          "notes": "Weyl gauge theory: the mathematical framework for coupling constants \u2014 GWL coupling factors generalize this"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "GWL 5-factor coupling (throat + flow + torsion + braid + phase) for Layer L1 geometric operations in USTSM is original. Weyl's gauge coupling theory (1921) provides the mathematical framework; the specific 5-factor decomposition for the Research Stack's geometric layer is novel."
    },
    {
      "id": "cf_anti_braid_storm",
      "type": "theorem",
      "name": "AntiBraidStormAdversarial",
      "expression": "adversarial dual: \u2200 BraidState s, test Yang-Baxter invariance AND receipt aliasing under Anti-BraidStorm",
      "latex": "\\text{Anti-BraidStorm}(s) \\Rightarrow \\text{Yang-Baxter violated} \\vee \\text{receipt alias}",
      "description": "Anti-BraidStorm: adversarial dual of BraidStorm that tests Yang-Baxter invariance and receipt aliasing as a validation layer for the eigensolid compressor. If Anti-BraidStorm finds a Yang-Baxter violation, the braid crossing is invalid. If it finds receipt aliasing (two states map to the same receipt), the codec is non-injective. Part of the BraidEigensolid 10-section structure.",
      "source_file": "obsidian-vault/00-MAP/Glossary.md",
      "lean_name": "Semantics.AntiBraidStorm",
      "lean_status": "DEFINED",
      "cohort": "cornfield",
      "silversight_action": "link_to_nk_hodge",
      "tags": [
        "anti-braidsterm",
        "yang-baxter",
        "adversarial",
        "receipt-aliasing",
        "validation"
      ],
      "related": [
        "cf_chentsov_fisher_metric",
        "math_verify_spectral_gap"
      ],
      "ene_tables": [
        "eigensolid_snapshots"
      ],
      "wow_note": "The Anti-BraidStorm is the security layer for the eigensolid codec. Yang-Baxter violation = the braid is not a valid knot invariant. Receipt aliasing = two different equations hash to the same codec state. Both are catastrophic failures. AntiBraidStorm.lean exists in the active Semantics surface.",
      "references": [
        {
          "doi": "10.1103/PhysRevLett.19.1312",
          "title": "Some exact results for the many-body problem in one dimension with repulsive delta-function interaction",
          "authors": "Yang, C.N.",
          "year": 1967,
          "journal": "Physical Review Letters",
          "arxiv_category": "math-ph",
          "relation_type": "grounds",
          "notes": "Yang-Baxter equation origin: R12\u00b7R13\u00b7R23 = R23\u00b7R13\u00b7R12 \u2014 the braid invariance condition that Anti-BraidStorm tests"
        },
        {
          "doi": "10.2307/1971440",
          "title": "A polynomial invariant for knots via von Neumann algebras",
          "authors": "Jones, V.F.R.",
          "year": 1985,
          "journal": "Bulletin of the AMS",
          "arxiv_category": "math.QA",
          "relation_type": "grounds",
          "notes": "Jones polynomial: braid closure invariant \u2014 the basis for receipt aliasing detection in Anti-BraidStorm"
        }
      ],
      "is_novel_claim": true,
      "novelty_statement": "Anti-BraidStorm \u2014 an adversarial testing procedure that checks Yang-Baxter invariance and receipt non-aliasing for eigensolid compression \u2014 is original. Yang-Baxter equation (1967) and Jones polynomial (1985) provide the mathematical invariants; their use as adversarial validation gates for a formal codec is new."
    }
  ]
}