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14 — Structural theorem index (no algorithms)
This section is an index of structural statements only.
It is a reference: each item is a theorem/lemma whose truth is independent of any particular certificate payload.
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For the clean separation between structure and certification, see:
13_LOGICAL_ARROWS_AND_CERTIFICATION_SEPARATION.md14A_ALGORITHMIC_CERTIFICATION_INDEX.md
14.1 Structural arrows (dependency map)
Reduction interface ⇒ finite presentation.
- Boundary descriptor bound and induced sofic/SFT presentation of the reduced dynamics.
- Files:
03_*,04_*,06_UNIFIED_REDUCTION_INTERFACE.md.
SCG + (PA) ⇒ periodic orbit realization + return density (structural consequence used by Paper 1).
- Files:
07_CERTIFICATION_PIPELINE.md,08_BREAKTHROUGH_PERIODIC_APPROXIMATION.md.
- Files:
Doeblin block + bounded-gap return ⇒ uniform projective contraction on the minimizing support.
- Files:
10A_PROJECTIVE_REGULARITY_CERTIFICATE_CHECKLIST.md,10C_CALIBRATED_PROJECTIVE_SECTION.md.
- Files:
Weighted inequality witness ⇒ cycle-average growth lower bound (no dilution).
- Files:
10D_EDGE_AUGMENTED_INEQUALITY_ENGINE.md.
- Files:
14.2 Theorem/lemma locator table
| ID | Statement | Where stated | What it feeds |
|---|---|---|---|
| T8.3 | (PA) from a positive bridge + bounded closing (BCB) | 08_BREAKTHROUGH_PERIODIC_APPROXIMATION.md | Paper 1 interface: (PA) for the reduced class |
| L8.1 | Quasi-multiplicativity inequality used in the PA proof | 08_BREAKTHROUGH_PERIODIC_APPROXIMATION.md | T8.3 closing estimate and certificate computation |
| L10D.1 | Path accumulation bound from weighted inequalities | 10D_EDGE_AUGMENTED_INEQUALITY_ENGINE.md | Cycle-average growth lower bounds on SCC subgraphs |
| T10D.2 | Spectral-radius lower bound for every directed cycle in H | 10D_EDGE_AUGMENTED_INEQUALITY_ENGINE.md | Safe pruning rule for edge selection |
| T10D.3 | Edge-augmented anti-dilution construction soundness | 10D_EDGE_AUGMENTED_INEQUALITY_ENGINE.md | Edge-scoped pruning without average dilution |
Notes.
- This table is intentionally short: it lists only the structural statements that are referenced as arrows in Section 13.
Anything that mentions a JSON payload, a procedure, an LP, or a verifier belongs in
14A_*instead.Prune-loop termination and safety; explicit quantitative gap.
- Files:
10E_PRUNE_LOOP_SOUNDNESS_AND_GMIN.md
- Files:
Main theorem assembly: quantified strict gap and rigidity consequences.
- Files:
15_MAIN_THEOREM_RIGIDITY_AND_CERTIFICATION.md
- Files:
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