docs/theorem-runtime-manifest.json

{
  "schemaVersion": 2,
  "generatedBy": "anchor-gates-instill-subagent",
  "observedAt": "2026-05-30",
  "canonicalRule": "A theorem claim is active only when its runtime hook and validation command are present in GitHub. Lean proof status is scoped separately from runtime test status.",
  "wiredGateCount": 35,
  "claimedGateCount": 35,
  "gapCount": 0,
  "gapNote": "All 35 anchor formula gates now have TypeScript runtime files in packages/policy/src/gates/. 30 gates added in feat/policy-gates-instill-anchor-g1-g35. 4 gates are STAGED-ADVISORY where Lean proof has open sorries.",
  "stagedAdvisoryGates": [
    "A7-BekensteinBound",
    "TH4-LambdaCategoryComposability",
    "TH_L3-BekensteinSoundness",
    "LiuHuiPi-axiom"
  ],
  "testValidationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts && npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
  "entries": [
    {
      "id": "RUNTIME-FALSE-POSITION",
      "theorem": "Lutar.Calibration.FalsePosition.false_position_correct",
      "formula": "FalsePosition",
      "lineage": "Rhind Mathematical Papyrus problems 24-29 / false position",
      "leanFile": "Lutar/Calibration/FalsePosition.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/falsePosition_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Runtime gate is tested; cite Lean proof status separately when making formal claims."
    },
    {
      "id": "RUNTIME-MADHAVA-BOUND",
      "theorem": "Lutar.PACBayes.MadhavaBound.madhavaRemainderBound_nonneg",
      "formula": "MadhavaBound",
      "lineage": "Madhava / Kerala school arctangent series",
      "leanFile": "Lutar/PACBayes/MadhavaBound.lean",
      "leanStatus": "theorem-with-tracked-sorries",
      "runtimeFile": "packages/policy/src/gates/madhavaBound_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Full arctangent specialization still has tracked Lean sorries; runtime enforces numeric remainder threshold."
    },
    {
      "id": "RUNTIME-LIU-HUI-PI",
      "theorem": "Lutar.Banach.LiuHuiPi.sideSquared_bounds",
      "formula": "LiuHuiPi",
      "lineage": "Liu Hui polygon-doubling \u03c0 approximation",
      "leanFile": "Lutar/Banach/LiuHuiPi.lean",
      "leanStatus": "axiom-advisory",
      "runtimeFile": "packages/policy/src/gates/liuHuiPi_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": true,
      "caveat": "Convergence is axiom/tracked in Lean; runtime enforces approximation threshold. STAGED-ADVISORY by design."
    },
    {
      "id": "RUNTIME-ADVERSARIAL-ROBUSTNESS",
      "theorem": "Lutar.Composition.Robustness.robustness_preserved_by_composition",
      "formula": "AdversarialRobustness",
      "lineage": "Banach/Lipschitz robustness specialization",
      "leanFile": "Lutar/Composition/AdversarialRobustness.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/adversarialRobustness_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Numeric gate is the Lipschitz special case, not the full abstract metric theorem."
    },
    {
      "id": "RUNTIME-SUMMATION-INVARIANT",
      "theorem": "Lutar.Khipu.SummationInvariant.khipuReceipt_checksum_invariant",
      "formula": "SummationInvariant",
      "lineage": "Inka khipu summation-cord accounting",
      "leanFile": "Lutar/Khipu/SummationInvariant.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/summationInvariant_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Runtime checks additive receipt invariants."
    },
    {
      "id": "RUNTIME-PARETO-STABILIZATION",
      "theorem": "Lutar.Thesis.ParetoStabilization.th_v18_11_pareto_stabilization",
      "formula": "ParetoStabilization",
      "lineage": "Lynch 1996 Distributed Algorithms Ch.8; finite discrete Pareto frontier",
      "leanFile": "Lutar/Thesis/TH_V18_11_ParetoFiniteStabilization.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/pareto_stabilization.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Pareto stabilization enforced in finite rounds; runtime iterates up to maxRounds."
    },
    {
      "id": "RUNTIME-A1-SOUNDNESS-AXIOM",
      "theorem": "soundnessAxiom",
      "formula": "SoundnessAxiom",
      "lineage": "SZL Doctrine v6 A1: conjunctive Lambda floor >=0.90",
      "leanFile": "Lutar/Gate/SoundnessAxiom.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/soundnessAxiom_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Enforces conjunctive 9-axis Lambda floor; no open sorries in gate Lean file."
    },
    {
      "id": "RUNTIME-A2-MORAL-GROUNDING-FLOOR",
      "theorem": "moralGroundingFloor",
      "formula": "MoralGroundingFloor",
      "lineage": "SZL Doctrine v6 A2: moral grounding >= 0.95 with ORCID requirement",
      "leanFile": "Lutar/Gate/MoralGrounding.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/moralGroundingFloor_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "ORCID absence collapses moral grounding score to 0."
    },
    {
      "id": "RUNTIME-A3-MEASURABILITY-HONESTY-FLOOR",
      "theorem": "measurabilityHonestyFloor",
      "formula": "MeasurabilityHonestyFloor",
      "lineage": "SZL Doctrine v6 A3: honesty floor with unsupported-claim penalty",
      "leanFile": "Lutar/Gate/MeasurabilityHonesty.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/measurabilityHonestyFloor_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Each unsupported claim subtracts 0.05 from effective score."
    },
    {
      "id": "RUNTIME-A4-DUAL-WITNESS-DISJOINTNESS",
      "theorem": "dualWitnessDisjointness",
      "formula": "DualWitnessDisjointness",
      "lineage": "SZL Doctrine v6 A4: two witnesses must be distinct identities",
      "leanFile": "Lutar/Gate/DualWitness.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/dualWitnessDisjointness_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Identity disjointness checked by string comparison of witness IDs."
    },
    {
      "id": "RUNTIME-A5-DETERMINISTIC-REPLAY",
      "theorem": "deterministicReplay",
      "formula": "DeterministicReplay",
      "lineage": "SZL Doctrine v6 A5: N replay runs must produce identical root hashes",
      "leanFile": "Lutar/Gate/DeterministicReplay.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/deterministicReplay_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Replay determinism enforced over configurable number of runs."
    },
    {
      "id": "RUNTIME-A6-HASH-CHAIN-INTEGRITY",
      "theorem": "hashChainIntegrity",
      "formula": "HashChainIntegrity",
      "lineage": "SZL Doctrine v6 A6: SHA-256 hash chain over receipt sequence",
      "leanFile": "Lutar/Gate/HashChainIntegrity.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/hashChainIntegrity_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "SHA-256 collision resistance is assumed (axiom), not Lean-proven."
    },
    {
      "id": "STAGED-A7-BEKENSTEIN-BOUND",
      "theorem": "bekensteinBound",
      "formula": "BekensteinBound",
      "lineage": "Bekenstein 1981 PRL47 information bound; TH6 DPI formally discharges",
      "leanFile": "Lutar/Gate/BekensteinBound.lean",
      "leanStatus": "conjectured",
      "runtimeFile": "packages/policy/src/gates/bekensteinBound_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "staged-advisory",
      "stagedAdvisory": true,
      "caveat": "STAGED-ADVISORY. Lean proof pending; gate defaults to enforced:false, severity:warning."
    },
    {
      "id": "RUNTIME-A8-INGEST-DISCIPLINE",
      "theorem": "ingestDiscipline",
      "formula": "IngestDiscipline",
      "lineage": "SZL Doctrine v6 A8: bounded ingest queue with epoch timestamps",
      "leanFile": "Lutar/Gate/IngestDiscipline.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/ingestDiscipline_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Ingest queue depth and epoch freshness enforced at gate boundary."
    },
    {
      "id": "RUNTIME-A9-DOCTRINE-COMPLETENESS",
      "theorem": "doctrineCompleteness",
      "formula": "DoctrineCompleteness",
      "lineage": "SZL Doctrine v6 A9: all required doctrine clauses present in receipt",
      "leanFile": "Lutar/Gate/DoctrineCompleteness.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/doctrineCompleteness_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Checks presence of all required doctrine clause fields; no content validation."
    },
    {
      "id": "RUNTIME-A10-TEMPORAL-CONSISTENCY",
      "theorem": "temporalConsistency",
      "formula": "TemporalConsistency",
      "lineage": "SZL Doctrine v6 A10: receipt timestamps must be causally ordered",
      "leanFile": "Lutar/Gate/TemporalConsistency.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/temporalConsistency_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Causal ordering enforced over receipt timestamp sequence."
    },
    {
      "id": "RUNTIME-A11-CAUSAL-SEPARABILITY",
      "theorem": "causalSeparability",
      "formula": "CausalSeparability",
      "lineage": "SZL Doctrine v6 A11: decisions may not carry unexplained causal loops",
      "leanFile": "Lutar/Gate/CausalSeparability.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/causalSeparability_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Causal loop detection is structural (DAG check), not semantic."
    },
    {
      "id": "RUNTIME-A12-CONSTRUCTIVE-TRANSPARENCY",
      "theorem": "constructiveTransparency",
      "formula": "ConstructiveTransparency",
      "lineage": "SZL Doctrine v6 A12: every decision must cite a constructive evidence chain",
      "leanFile": "Lutar/Gate/ConstructiveTransparency.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/constructiveTransparency_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Evidence chain field presence checked; content provenance is a separate concern."
    },
    {
      "id": "RUNTIME-A14-ECONOMIC-GROUNDING",
      "theorem": "economicGrounding",
      "formula": "EconomicGrounding",
      "lineage": "SZL Doctrine v6 A14: decision must have an economic cost receipt above floor",
      "leanFile": "Lutar/Gate/EconomicGrounding.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/economicGrounding_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Economic cost floor enforced; currency normalization is caller responsibility."
    },
    {
      "id": "RUNTIME-T1-RHO-CLOSURE-COMPOSITION",
      "theorem": "rhoClosureComposition",
      "formula": "RhoClosureComposition",
      "lineage": "Category-theoretic rho-closure: composed organs inherit closure property",
      "leanFile": "Lutar/Gate/RhoClosureComposition.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/rhoClosureComposition_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Closure composition checked over finite organ list."
    },
    {
      "id": "RUNTIME-T2-LAMBDA-MONOTONICITY",
      "theorem": "lambda_monotonicity",
      "formula": "LambdaMonotonicity",
      "lineage": "Lutar/Thesis/TH_V18_01_LambdaMonotonicity.lean; Lambda monotone in each argument",
      "leanFile": "Lutar/Gate/LambdaMonotonicity.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/lambdaMonotonicity_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Pointwise vector comparison; geometric mean used as Lambda proxy."
    },
    {
      "id": "RUNTIME-T3-MERKLE-DAG-BATCH",
      "theorem": "merkleDagBatch",
      "formula": "MerkleDagBatch",
      "lineage": "Merkle/SCITT receipt DAG: acyclic batch hash chain",
      "leanFile": "Lutar/Gate/MerkleDagBatch.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/merkleDagBatch_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "DAG acyclicity checked; full Merkle proof path verification is separate."
    },
    {
      "id": "RUNTIME-T4-BEKENSTEIN-ENTROPY-MEASURE",
      "theorem": "Lutar.DPI.dpi_bound_monotone",
      "formula": "BekensteinEntropyMeasure",
      "lineage": "Elementary DPI byte-count bound (Cover-Thomas, Elements of Information Theory 2006, sec 2.8.1): chain entropy <= 8*sizeBytes; the bound's positivity and monotonicity are the proven theorem TH6 (Lutar/DPI/DPIBound.lean). NOT the physical Bekenstein entropy-area proportionality, which has no SZL counterpart (F1-4 errata).",
      "leanFile": "Lutar/DPI/DPIBound.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/bekensteinEntropyMeasure_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Runtime numeric predicate is independently testable; the byte bound dpiEntropyBound r = sizeBytes * 8 is kernel-checked (zero sorry) as theorem TH6 in Lutar/DPI/DPIBound.lean (dpi_bound_positive, dpi_bound_monotone). The prior phantom citation Lutar/Gate/BekensteinEntropyMeasure.lean never existed in lutar-lean and has been removed."
    },
    {
      "id": "RUNTIME-T5-REPLAY-DETERMINISM",
      "theorem": "replayDeterminism",
      "formula": "ReplayDeterminism",
      "lineage": "K10v2 PRNG replay: deterministic root produces identical receipt stream",
      "leanFile": "Lutar/Gate/ReplayDeterminism.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/replayDeterminism_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Replay hash comparison; PRNG seed handling is caller responsibility."
    },
    {
      "id": "RUNTIME-T6-CONJUNCTIVE-GATE-COUNTEREXAMPLE",
      "theorem": "conjunctiveGateCounterexample",
      "formula": "ConjunctiveGateCounterexample",
      "lineage": "Logical gate composition: counterexample witness for non-trivial conjunctive failure",
      "leanFile": "Lutar/Gate/ConjunctiveGate.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/conjunctiveGateCounterexample_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Counterexample witnesses are logged to receipt for audit."
    },
    {
      "id": "RUNTIME-T7-PRIVACY-MASK",
      "theorem": "privacyMask",
      "formula": "PrivacyMask",
      "lineage": "Lutar/DPI/SCITTMaskEntropy.lean: DPI H(mask(X)) <= H(X)",
      "leanFile": "Lutar/Gate/PrivacyMask.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/privacyMask_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Redaction field masking enforced; entropy monotonicity is the formal backing."
    },
    {
      "id": "RUNTIME-T8-SINGLE-WITNESS-EXCLUSION",
      "theorem": "singleWitnessExclusion",
      "formula": "SingleWitnessExclusion",
      "lineage": "SZL Doctrine v6 T8: single witness insufficient for high-stakes decisions",
      "leanFile": "Lutar/Gate/SingleWitnessExclusion.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/singleWitnessExclusion_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Minimum witness count enforced at gate boundary."
    },
    {
      "id": "RUNTIME-T9-CROSS-REGION-POLICY",
      "theorem": "crossRegionPolicy",
      "formula": "CrossRegionPolicy",
      "lineage": "SZL Doctrine v6 T9: decisions spanning regions require multi-region receipts",
      "leanFile": "Lutar/Gate/CrossRegionPolicy.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/crossRegionPolicy_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Region tags checked for coverage; actual data residency is a separate enforcement."
    },
    {
      "id": "RUNTIME-T10-DOCTRINE-ENFORCEMENT",
      "theorem": "doctrineEnforcement",
      "formula": "DoctrineEnforcement",
      "lineage": "SZL Doctrine v6 T10: enforcement clauses must be flagged and receipt-anchored",
      "leanFile": "Lutar/Gate/DoctrineEnforcement.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/doctrineEnforcement_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Enforcement clause flags checked; content of flags is caller responsibility."
    },
    {
      "id": "RUNTIME-TH1-COMPOSABILITY",
      "theorem": "composability",
      "formula": "Composability",
      "lineage": "Lutar/Composition/CompositionOverhead.lean: linear overhead bound for N composed systems",
      "leanFile": "Lutar/Gate/Composability.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/composability_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Linear overhead bound enforced; asymptotic claim is the formal backing."
    },
    {
      "id": "RUNTIME-TH2-REPLAY-DOI-DUALITY",
      "theorem": "replayDoiDuality",
      "formula": "ReplayDoiDuality",
      "lineage": "SZL Doctrine v6 TH2: DOI citation and replay root must be paired",
      "leanFile": "Lutar/Gate/ReplayDoiDuality.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/replayDoiDuality_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "DOI format and replay root presence checked; DOI resolution is not performed at gate time."
    },
    {
      "id": "RUNTIME-TH3-ANATOMY-REDUCTION",
      "theorem": "anatomyReduction",
      "formula": "AnatomyReduction",
      "lineage": "SZL Doctrine v6 TH3: 7-layer anatomy reduces to verifiable receipt chain",
      "leanFile": "Lutar/Gate/AnatomyReduction.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/anatomyReduction_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Layer coverage checked; layer content validation is a separate concern."
    },
    {
      "id": "STAGED-TH4-LAMBDA-CATEGORY-COMPOSABILITY",
      "theorem": "lambdaCategoryComposability",
      "formula": "LambdaCategoryComposability",
      "lineage": "Pending Lutar/LaxFunctor.lean; lax functor property for Lambda over organ category",
      "leanFile": "Lutar/Gate/LambdaCategoryComposability.lean",
      "leanStatus": "conjectured",
      "runtimeFile": "packages/policy/src/gates/lambdaCategoryComposability_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "staged-advisory",
      "stagedAdvisory": true,
      "caveat": "STAGED-ADVISORY. Pending LaxFunctor.lean formalization. Gate defaults to enforced:false."
    },
    {
      "id": "RUNTIME-TH5-RECEIPT-CHAIN-CONFLUENCE",
      "theorem": "receiptChainConfluence",
      "formula": "ReceiptChainConfluence",
      "lineage": "Church-Rosser confluence: concurrent receipt chains reduce to same root",
      "leanFile": "Lutar/Gate/ReceiptChainConfluence.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/receiptChainConfluence_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Confluence enforced by deterministic hash ordering; formal confluence proof is the backing."
    },
    {
      "id": "RUNTIME-TH6-BEKENSTEIN-ENTROPY-DPI",
      "theorem": "bekensteinEntropyDpi",
      "formula": "BekensteinEntropyDpi",
      "lineage": "Cover-Thomas DPI: I(X;Z) <= I(X;Y); entropy non-increasing through masking",
      "leanFile": "Lutar/DPI/DPIBound.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/bekensteinEntropyDpi_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Numeric DPI monotonicity enforced over discrete label distributions."
    },
    {
      "id": "RUNTIME-TH7-CURRY-HOWARD-RECEIPT-CALCULUS",
      "theorem": "curryHowardReceiptCalculus",
      "formula": "CurryHowardReceiptCalculus",
      "lineage": "Curry-Howard: receipt terms are proofs; proof terms are programs",
      "leanFile": "Lutar/Gate/CurryHowardReceiptCalculus.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/policy/src/gates/curryHowardReceiptCalculus_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Receipt term structure checked; full type-theoretic correspondence is lineage."
    },
    {
      "id": "CONJECTURE-THL1-LAMBDA-UNIQUENESS",
      "theorem": "lambdaUniquenessConjecture",
      "formula": "LambdaUniquenessConjecture",
      "lineage": "Lutar/Thesis/TH_V18_12 Lambda uniqueness: only one Lambda satisfies A1-A4",
      "leanFile": "Lutar/Uniqueness.lean",
      "leanStatus": "conjecture-open",
      "runtimeFile": "packages/policy/src/gates/lambdaUniquenessConjecture_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": true,
      "caveat": "CONJECTURE \u2014 NOT a theorem. \u039b uniqueness is Conjecture 1 per Doctrine v11. Gate validates scoring consistency; formal uniqueness is unproven. Gate file renamed to lambdaUniquenessConjecture_gate.ts.",
      "status": "CONJECTURE",
      "proven": false,
      "lambda_statement": "Conjecture 1 (NOT a theorem \u2014 LOCKED by Doctrine v11)"
    },
    {
      "id": "RUNTIME-THL2-LAMBDA-MINMAX-BOUNDS",
      "theorem": "lambdaMinMaxBounds",
      "formula": "LambdaMinMaxBounds",
      "lineage": "Lambda min/max bounds: floor <= Lambda(v) <= ceil for all valid v",
      "leanFile": "Lutar/Gate/LambdaMinMaxBounds.lean",
      "leanStatus": "theorem-with-2-tracked-sorries-in-wider-repo",
      "runtimeFile": "packages/policy/src/gates/lambdaMinMaxBounds_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Gate Lean file has 0 sorries; 2 sorries exist elsewhere in lutar-lean (not in this gate's proof)."
    },
    {
      "id": "STAGED-THL3-BEKENSTEIN-SOUNDNESS",
      "theorem": "bekensteinSoundness",
      "formula": "BekensteinSoundness",
      "lineage": "Measured: 49.5% fire rate under uniform seed (ouroboros v6.3.0, n=8000); formal proof pending lutar-lean PR #12",
      "leanFile": "Lutar/BekensteinSoundness.lean",
      "leanStatus": "measured-conjectured-pending-PR12",
      "runtimeFile": "packages/policy/src/gates/bekensteinSoundness_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "staged-advisory",
      "stagedAdvisory": true,
      "caveat": "STAGED-ADVISORY. Lean formal proof pending lutar-lean PR #12. Gate defaults to enforced:false."
    },
    {
      "id": "RUNTIME-THL4-RHO-CLOSURE-PRODUCTION",
      "theorem": "rhoClosureProduction",
      "formula": "RhoClosureProduction",
      "lineage": "Measured: 100% rho-closure rate over 8000 ouroboros v6.3.0 production calls",
      "leanFile": "Lutar/Gate/RhoClosureProduction.lean",
      "leanStatus": "measured-empirical",
      "runtimeFile": "packages/policy/src/gates/rhoClosureProduction_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "validationCommand": "npx tsx packages/policy/src/gates/__tests__/policy_gates_extended.test.ts",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Empirically measured 100% closure; gate enforces minimum closure rate."
    },
    {
      "id": "RUNTIME-THRESHOLD-POLICY-SEVERITY",
      "theorem": "IQ-01 severity-indexed witness threshold gate",
      "formula": "ThresholdPolicySeverity",
      "lineage": "2-of-N / 3-of-N witness threshold invariant from cross-corpus doctrine synthesis",
      "leanFile": null,
      "runtimeFile": "packages/policy/src/gates/thresholdPolicySeverity_gate.ts",
      "exportFile": "packages/policy/src/gates/index.ts",
      "testFile": "packages/policy/src/gates/__tests__/policy_gates.test.ts",
      "validationCommand": "npm run test:policy-gates",
      "claimStatus": "verified-runtime",
      "caveat": "TypeScript runtime gate is tested and emits a DSSE-shaped HMAC receipt on allow; Lean formalization is not claimed."
    },
    {
      "id": "RUNTIME-QEC-LINEAGE",
      "theorem": "Lutar.QEC.HammingFoundations / Shor / CSS / Kitaev runtime parity",
      "formula": "QECLineage",
      "lineage": "Hamming, Shor, CSS, Kitaev, Preskill QEC lineage",
      "leanFile": "Lutar/QEC/*",
      "leanStatus": "mixed-green-red",
      "runtimeFile": "packages/qec-integrity/src/qec_lineage.ts",
      "exportFile": "packages/qec-integrity/src/index.ts",
      "testFile": "packages/qec-integrity/src/qec_lineage.test.ts",
      "validationCommand": "npm run test:qec",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Runtime parity tests are real; do not claim full quantum threshold theorem. Kitaev/CSS Lean files fail lake build."
    },
    {
      "id": "RUNTIME-RECEIPT-SUBSTRATE",
      "theorem": "Operational receipt hash-chain integrity",
      "formula": "ReceiptSubstrate",
      "lineage": "Merkle/SCITT/DSSE-style receipt discipline",
      "leanFile": "Lutar/DPI/* and Lutar/SBOMProvenance.lean",
      "leanStatus": "theorem",
      "runtimeFile": "packages/receipt-substrate/src/index.ts",
      "exportFile": "packages/receipt-substrate/src/index.ts",
      "testFile": "packages/receipt-substrate/src/receipt_substrate.test.ts",
      "validationCommand": "npm test --prefix packages/receipt-substrate",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Local quorum labels are not external cryptographic signer verification."
    },
    {
      "id": "RUNTIME-KNOWLEDGE-THEOREMS",
      "theorem": "TH1-TH7 theorem lookup",
      "formula": "KnowledgeGraph",
      "lineage": "Ouroboros thesis theorem catalog",
      "leanFile": "packages/a11oy-knowledge/src/theorems.ts",
      "leanStatus": "theorem",
      "runtimeFile": "packages/a11oy-knowledge/src/theorems.ts",
      "exportFile": "packages/a11oy-knowledge/src/index.ts",
      "testFile": "packages/a11oy-knowledge/src/theorems_lookup.test.ts",
      "validationCommand": "npm run test:knowledge:lookup",
      "claimStatus": "verified-runtime",
      "stagedAdvisory": false,
      "caveat": "Lookup reachability is runtime-verified; proof status remains per theorem."
    },
    {
      "id": "STAGED-WHEELER-WINDOW",
      "theorem": "Lutar.Wheeler.DelayedChoiceClosure",
      "formula": "DelayedChoiceClosure",
      "lineage": "Wheeler delayed-choice receipt closure",
      "leanFile": "Lutar/Wheeler/DelayedChoiceClosure.lean",
      "leanStatus": "lean-backed",
      "runtimeFile": null,
      "exportFile": null,
      "testFile": null,
      "validationCommand": null,
      "claimStatus": "lean-backed-needs-runtime",
      "stagedAdvisory": true,
      "caveat": "Proof substrate exists; no A11oy TypeScript runtime gate wired yet. Not counted in the 35 anchor gates."
    },
    {
      "id": "STAGED-FEYNMAN-KNOT",
      "theorem": "Lutar.Feynman.PathIntegralAuditSum / Lutar.Feynman.FeynmanLineage",
      "formula": "AuditReidemeister",
      "lineage": "Feynman, Witten, Bar-Natan, Reidemeister, audit-knot calculus",
      "leanFile": "Lutar/Feynman/* and Lutar/Knot/*",
      "leanStatus": "conjectured",
      "runtimeFile": null,
      "exportFile": null,
      "testFile": null,
      "validationCommand": null,
      "claimStatus": "historical-roadmap",
      "stagedAdvisory": true,
      "caveat": "Citation lineage is real; audit-Reidemeister invariance remains conjectural/tracked. Not counted in the 35 anchor gates."
    }
  ]
}