# Theorem and claim index

Proof labels are those of the consolidated manuscript. An index entry is not an independent proof check. Read each assumption before applying a result.

| ID | Result | Proof location | Novelty status |
|---|---|---|---|
| R1 | Passive response nonaccumulation | [3.2 Theorem R1: nonaccumulation under passive interconnection](manuscript/Matter_Embryogenesis.md#32-theorem-r1-nonaccumulation-under-passive-interconnection) | Established variational corollary reconstructed |
| R2 | Measured response plus final-seal certificate | [3.4 Theorem R2: a measurable certificate that includes the final seal](manuscript/Matter_Embryogenesis.md#34-theorem-r2-a-measurable-certificate-that-includes-the-final-seal) | Restricted derived bound |
| R3 | Bounded positive reserve reachability | [4.1 Lemma R3: bounded two-terminal reserve repair](manuscript/Matter_Embryogenesis.md#41-lemma-r3-bounded-two-terminal-reserve-repair) | Constructive restricted fabrication lemma; priority unverified |
| R4 | Finite-horizon adaptive inspection confidence | [4.2 Lemma R4: confidence survives adaptive repair decisions](manuscript/Matter_Embryogenesis.md#42-lemma-r4-confidence-survives-adaptive-repair-decisions) | Standard concentration plus union bound reconstructed |
| R5 | Postorder access preservation | [4.3 Lemma R5: local postorder closure preserves service](manuscript/Matter_Embryogenesis.md#43-lemma-r5-local-postorder-closure-preserves-service) | Standard dependency/termination corollary |
| R6 | Response-certified developmental maturation | [4.4 Theorem R6: response-certified developmental maturation](manuscript/Matter_Embryogenesis.md#44-theorem-r6-response-certified-developmental-maturation) | Candidate integrated contribution; independent priority unverified |
| R7 | Recoverability liability of closure | [5.2 Proposition R7: a quantitative liability for closing service](manuscript/Matter_Embryogenesis.md#52-proposition-r7-a-quantitative-liability-for-closing-service) | Imported user quadratic theory applied to fabrication |
| R8 | Power-weighted deterministic response envelope | [6.1 Theorem R8: a power-weighted functional envelope](manuscript/Matter_Embryogenesis.md#61-theorem-r8-a-power-weighted-functional-envelope) | Dirichlet/Thomson corollary reconstructed |
| R9 | Power-participation fault concentration | [6.2 Corollary R9: a restricted participation threshold](manuscript/Matter_Embryogenesis.md#62-corollary-r9-a-restricted-participation-threshold) | Restricted derived concentration law; not universal phase transition |
| A | Developmental family compression and counting obstruction | [7.2 Theorem A: compressibility and its obstruction](manuscript/Matter_Embryogenesis.md#72-theorem-a-compressibility-and-its-obstruction) | Established program/counting arguments restated |
| E | Positional-information lower bound | [7.3 Theorem E: positional information and a boundary-complexity warning](manuscript/Matter_Embryogenesis.md#73-theorem-e-positional-information-and-a-boundary-complexity-warning) | Fano inequality application |
| B/F | Finite basis for rational passive networks | [8.1 Theorem B/F: a restricted finite fabrication basis](manuscript/Matter_Embryogenesis.md#81-theorem-bf-a-restricted-finite-fabrication-basis) | Elementary construction conditional on unbuilt active primitives |
| D | Causal-volume and flux growth bounds | [10.3 Theorem D: physical parallel-growth limits](manuscript/Matter_Embryogenesis.md#103-theorem-d-physical-parallel-growth-limits) | Basic locality/conservation derivation |
| H1/H2 | Reliability-access window and redundancy-access reversal | [10.1 Why extra redundancy can worsen reliability](manuscript/Matter_Embryogenesis.md#101-why-extra-redundancy-can-worsen-reliability) | Retained v1 derived model; priority unverified |
| G1 | Projective response composition and absolute-calibration no-go | [6A.2 Proposition G1: functional scale freedom and its identifiability limit](manuscript/Matter_Embryogenesis.md#6a2-proposition-g1-functional-scale-freedom-and-its-identifiability-limit) | Established ingredients reconstructed; not a new projective metric |
| G2 | Exact reachable-scale interval and minimum material | [6A.3 Theorem G2: exact reachable-scale interval and minimum material](manuscript/Matter_Embryogenesis.md#6a3-theorem-g2-exact-reachable-scale-interval-and-minimum-material) | Candidate fabrication-specific combination of elementary interval and monotonicity reasoning; priority unverified |
| G3 | Finite-noise and finite-increment projective repair | [6A.4 Theorem G3: finite-noise, finite-increment construction](manuscript/Matter_Embryogenesis.md#6a4-theorem-g3-finite-noise-finite-increment-construction) | Restricted constructive derivation; independent priority unverified |
| G4 | Exact reserve-controlled finite-size yield law | [6A.5 Theorem G4: an exact reserve-controlled yield boundary](manuscript/Matter_Embryogenesis.md#6a5-theorem-g4-an-exact-reserve-controlled-yield-boundary) | Classical order-statistics derivation applied to the new reserve condition; not a universal physical transition |
| G5 | Relative-metrology confidence and differential-bias no-go | [6A.6 Relative metrology: what it removes, and what it cannot remove](manuscript/Matter_Embryogenesis.md#6a6-relative-metrology-what-it-removes-and-what-it-cannot-remove) | Established relative calibration/effective-resistance mathematics explicitly credited |
| G6 | Gauge-aware developmental maturation with one uncalibrated witness | [6A.8 Theorem G6: fabrication with one uncalibrated witness](manuscript/Matter_Embryogenesis.md#6a8-theorem-g6-fabrication-with-one-uncalibrated-witness) | Candidate integrated fabrication theorem; independent novelty and molecular realization unverified |