THEOREM_INDEX.md

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	Established variational corollary reconstructed
R2	Measured response plus final-seal certificate	3.4 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	Constructive restricted fabrication lemma; priority unverified
R4	Finite-horizon adaptive inspection confidence	4.2 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	Standard dependency/termination corollary
R6	Response-certified developmental maturation	4.4 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	Imported user quadratic theory applied to fabrication
R8	Power-weighted deterministic response envelope	6.1 Theorem R8: a power-weighted functional envelope	Dirichlet/Thomson corollary reconstructed
R9	Power-participation fault concentration	6.2 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	Established program/counting arguments restated
E	Positional-information lower bound	7.3 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	Elementary construction conditional on unbuilt active primitives
D	Causal-volume and flux growth bounds	10.3 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	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	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	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	Restricted constructive derivation; independent priority unverified
G4	Exact reserve-controlled finite-size yield law	6A.5 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	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	Candidate integrated fabrication theorem; independent novelty and molecular realization unverified