IndisputableMonolith.Verification.FibSubstCert
Verification certificate module for the two-letter Fibonacci substitution system. It packages the necessity result that letter-count recurrences are Fibonacci into a checkable cert object used by the verification layer. The module is thin: it imports the FibSubst necessity development and exposes a named certificate wrapper rather than new mathematics.
claimA verification certificate for the two-letter substitution system whose letter-count sequences obey the Fibonacci recurrence $F_{n}=F_{n-1}+F_{n-2}$ (with the standard substitution-induced growth).
background
Recognition Science uses discrete substitution dynamics on short alphabets to force integer recurrences that later pin periods and dimensions in the forcing chain. The upstream module FibSubst develops a two-letter substitution system and proves that the induced letter-count sequences satisfy Fibonacci recurrences.
This module sits in the Verification domain. Its role is not to reprove those recurrences, but to expose them as a certificate-shaped object that downstream verification and audit tooling can name, import, and discharge against. The only substantive import besides Mathlib is the necessity development for the Fibonacci substitution.
proof idea
Definition and packaging module rather than a new proof development. It imports the FibSubst necessity results and wraps them as a FibSubstCert certificate object for the verification layer. No independent tactic proof burden is introduced here; the mathematics lives upstream.
why it matters in Recognition Science
Fibonacci count recurrences appear whenever RS needs a minimal integer growth law from a two-symbol rewrite system (octave bookkeeping, discrete ladder steps, and related necessity arguments). By certifying the FibSubst necessity package, this module gives the verification layer a single named handle instead of ad-hoc imports of the raw necessity file.
No downstream used_by edges are recorded yet, so the cert is presently a leaf in the graph: available for audit and for later wiring into broader verification aggregates. It does not itself advance T0–T8; it only makes the Fibonacci-substitution necessity claim machine-checkable in the Verification hierarchy.
scope and limits
- Does not reprove the Fibonacci recurrence; that lives in the FibSubst necessity module.
- Does not claim uniqueness of the two-letter substitution among all rewrite systems.
- Does not derive physical constants, mass rungs, or forcing-chain steps T5–T8.
- Does not record downstream consumers yet; used_by is empty.