THEOREM_INDEX.json

{
  "schema_version": "1.0",
  "version": "3.0.0",
  "entries": [
    {
      "id": "R1",
      "title": "Passive response nonaccumulation",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Established variational corollary reconstructed",
      "assumptions": "Real passive reciprocal modules; named ports; disjoint interiors; no hidden coupling",
      "verification": "Proof in 3.2; 300 correlated multiport checks",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "3.2 Theorem R1: nonaccumulation under passive interconnection",
      "proof_path": "manuscript/Matter_Embryogenesis.md#32-theorem-r1-nonaccumulation-under-passive-interconnection",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R2",
      "title": "Measured response plus final-seal certificate",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Restricted derived bound",
      "assumptions": "Operator measurement error; connected target minor; bounded remaining seal change",
      "verification": "Proof in 3.4; extreme-margin test",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "3.4 Theorem R2: a measurable certificate that includes the final seal",
      "proof_path": "manuscript/Matter_Embryogenesis.md#34-theorem-r2-a-measurable-certificate-that-includes-the-final-seal",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R3",
      "title": "Bounded positive reserve reachability",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Constructive restricted fabrication lemma; priority unverified",
      "assumptions": "Starting upper bound; adequate reserve; bounded positive increments; measurement radius; access",
      "verification": "Proof in 4.1; 300 bounded-noise cases in test",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "4.1 Lemma R3: bounded two-terminal reserve repair",
      "proof_path": "manuscript/Matter_Embryogenesis.md#41-lemma-r3-bounded-two-terminal-reserve-repair",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R4",
      "title": "Finite-horizon adaptive inspection confidence",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Standard concentration plus union bound reconstructed",
      "assumptions": "Fresh conditional sub-Gaussian noise; known finite inspection horizon; calibrated bias",
      "verification": "Proof in 4.2; parameters and every sample count recorded",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "4.2 Lemma R4: confidence survives adaptive repair decisions",
      "proof_path": "manuscript/Matter_Embryogenesis.md#42-lemma-r4-confidence-survives-adaptive-repair-decisions",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R5",
      "title": "Postorder access preservation",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Standard dependency/termination corollary",
      "assumptions": "Acyclic rooted service graph; correct fresh ACKs; known child obligations",
      "verification": "Proof in 4.3; stochastic readiness and path test",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "4.3 Lemma R5: local postorder closure preserves service",
      "proof_path": "manuscript/Matter_Embryogenesis.md#43-lemma-r5-local-postorder-closure-preserves-service",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R6",
      "title": "Response-certified developmental maturation",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Candidate integrated contribution; independent priority unverified",
      "assumptions": "R1-R5 plus capacity feasibility, valid shared-error budget, deterministic reachability or uniform conditional repair success",
      "verification": "Proof in 4.4; reduced simulation illustrates a special case, not molecular premises",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "4.4 Theorem R6: response-certified developmental maturation",
      "proof_path": "manuscript/Matter_Embryogenesis.md#44-theorem-r6-response-certified-developmental-maturation",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R7",
      "title": "Recoverability liability of closure",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Imported user quadratic theory applied to fabrication",
      "assumptions": "Finite moments; fixed local safe actuator; normalized effort; decreased evidence/control in PSD order",
      "verification": "Proof in 5.2; 400 noncommuting checks",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "5.2 Proposition R7: a quantitative liability for closing service",
      "proof_path": "manuscript/Matter_Embryogenesis.md#52-proposition-r7-a-quantitative-liability-for-closing-service",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R8",
      "title": "Power-weighted deterministic response envelope",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Dirichlet/Thomson corollary reconstructed",
      "assumptions": "Same positive-conductance graph; one declared terminal experiment",
      "verification": "Proof in 6.1; 250 solved network cases",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6.1 Theorem R8: a power-weighted functional envelope",
      "proof_path": "manuscript/Matter_Embryogenesis.md#61-theorem-r8-a-power-weighted-functional-envelope",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "R9",
      "title": "Power-participation fault concentration",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Restricted derived concentration law; not universal phase transition",
      "assumptions": "Independent weakening; strictly positive surviving conductance ratio; favorable power participation",
      "verification": "Proof in 6.2; deterministic parent envelope checked",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6.2 Corollary R9: a restricted participation threshold",
      "proof_path": "manuscript/Matter_Embryogenesis.md#62-corollary-r9-a-restricted-participation-threshold",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "A",
      "title": "Developmental family compression and counting obstruction",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Established program/counting arguments restated",
      "assumptions": "Fixed generator and paid platform; finite physical resource-feasible backend",
      "verification": "Section 7.2 and original baseline proofs",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "7.2 Theorem A: compressibility and its obstruction",
      "proof_path": "manuscript/Matter_Embryogenesis.md#72-theorem-a-compressibility-and-its-obstruction",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "E",
      "title": "Positional-information lower bound",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Fano inequality application",
      "assumptions": "Declared distinguishable regions and decision error",
      "verification": "Section 7.3",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "7.3 Theorem E: positional information and a boundary-complexity warning",
      "proof_path": "manuscript/Matter_Embryogenesis.md#73-theorem-e-positional-information-and-a-boundary-complexity-warning",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "B/F",
      "title": "Finite basis for rational passive networks",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Elementary construction conditional on unbuilt active primitives",
      "assumptions": "Tape/state copying; routed insulated unit resistors; compatible physical range and repair operations",
      "verification": "Section 8.1; not a universal chemistry proof",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "8.1 Theorem B/F: a restricted finite fabrication basis",
      "proof_path": "manuscript/Matter_Embryogenesis.md#81-theorem-bf-a-restricted-finite-fabrication-basis",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "D",
      "title": "Causal-volume and flux growth bounds",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Basic locality/conservation derivation",
      "assumptions": "Finite speed, density, and inlet flux",
      "verification": "Section 10.3",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "10.3 Theorem D: physical parallel-growth limits",
      "proof_path": "manuscript/Matter_Embryogenesis.md#103-theorem-d-physical-parallel-growth-limits",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "H1/H2",
      "title": "Reliability-access window and redundancy-access reversal",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Retained v1 derived model; priority unverified",
      "assumptions": "Slab reservoirs, kinetic error model, actual fault-tolerant functional contract",
      "verification": "Original full proofs and numerical results in baseline_v1",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "10.1 Why extra redundancy can worsen reliability",
      "proof_path": "manuscript/Matter_Embryogenesis.md#101-why-extra-redundancy-can-worsen-reliability",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/contracts.py",
        "src/recovery.py",
        "tests/test_revision.py"
      ]
    },
    {
      "id": "G1",
      "title": "Projective response composition and absolute-calibration no-go",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Established ingredients reconstructed; not a new projective metric",
      "assumptions": "Scale-invariant passive model; named ports and all relevant conductances included",
      "verification": "Variational and symmetry arguments in 6A.2; 200 four-port checks",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.2 Proposition G1: functional scale freedom and its identifiability limit",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a2-proposition-g1-functional-scale-freedom-and-its-identifiability-limit",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    },
    {
      "id": "G2",
      "title": "Exact reachable-scale interval and minimum material",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified",
      "assumptions": "Positive scalar responses; independently reachable continuous additive intervals; positive linear material costs",
      "verification": "Proof in 6A.3; 80 independent linear-program comparisons",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.3 Theorem G2: exact reachable-scale interval and minimum material",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a3-theorem-g2-exact-reachable-scale-interval-and-minimum-material",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    },
    {
      "id": "G3",
      "title": "Finite-noise and finite-increment projective repair",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Restricted constructive derivation; independent priority unverified",
      "assumptions": "Log confidence, stable relative units, reserve interval, strictly positive bounded increments, access, bounded seal",
      "verification": "Proof in 6A.4; 500 bounded-adversarial endpoint-noise cases",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.4 Theorem G3: finite-noise, finite-increment construction",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a4-theorem-g3-finite-noise-finite-increment-construction",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    },
    {
      "id": "G4",
      "title": "Exact reserve-controlled finite-size yield law",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition",
      "assumptions": "G2 reachability; iid Uniform[l,u] initial ratios; common additive reserve; ideal measurements and actuation",
      "verification": "Integral proof in 6A.5; 100 quadratures; 25000 sampled arrays evaluated at 31 capacities",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.5 Theorem G4: an exact reserve-controlled yield boundary",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a5-theorem-g4-an-exact-reserve-controlled-yield-boundary",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    },
    {
      "id": "G5",
      "title": "Relative-metrology confidence and differential-bias no-go",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Established relative calibration/effective-resistance mathematics explicitly credited",
      "assumptions": "Fixed connected comparison graph; stable witness; fresh joint sub-Gaussian edge error proxy; numerical error budget",
      "verification": "6A.6-6A.7; covariance identity; 6000 draws; local solver; exact gradient-bias counterexample",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.6 Relative metrology: what it removes, and what it cannot remove",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a6-relative-metrology-what-it-removes-and-what-it-cannot-remove",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    },
    {
      "id": "G6",
      "title": "Gauge-aware developmental maturation with one uncalibrated witness",
      "epistemic_status": "proved_under_stated_assumptions",
      "novelty": "Candidate integrated fabrication theorem; independent novelty and molecular realization unverified",
      "assumptions": "G1-G5 domain and resource conditions; declared quotient; retained comparison and material service; bounded shared failures",
      "verification": "Proof in 6A.8; 512 reduced-model runs; negative controls included",
      "molecular_demonstration": false,
      "independent_peer_review": false,
      "manuscript_section": "6A.8 Theorem G6: fabrication with one uncalibrated witness",
      "proof_path": "manuscript/Matter_Embryogenesis.md#6a8-theorem-g6-fabrication-with-one-uncalibrated-witness",
      "proof_form": "human-readable argument; not proof-assistant verified",
      "implementation_paths": [
        "src/gauge_contracts.py",
        "src/run_gauge_revision.py",
        "tests/test_gauge.py"
      ]
    }
  ]
}