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.md
• 14A_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.

• Doeblin block + bounded-gap return ⇒ uniform projective contraction on the minimizing support.

  • Files: 10A_PROJECTIVE_REGULARITY_CERTIFICATE_CHECKLIST.md, 10C_CALIBRATED_PROJECTIVE_SECTION.md.

• Weighted inequality witness ⇒ cycle-average growth lower bound (no dilution).

  • Files: 10D_EDGE_AUGMENTED_INEQUALITY_ENGINE.md.

14.2 Theorem/lemma locator table

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

• Main theorem assembly: quantified strict gap and rigidity consequences.

  • Files: 15_MAIN_THEOREM_RIGIDITY_AND_CERTIFICATION.md