IndisputableMonolith.Verification.PhiNonDegenerateCert
Verification certificate that the RS self-similar scale φ is non-degenerate (strictly greater than 1, cost and ladder do not collapse). Downstream verification and constant-export code cite it to justify φ-powers and J-evaluations. The module is a thin packaging layer over Constants, not a deep existence proof.
claimA verification certificate that the Recognition Science scale $\varphi$ (self-similar fixed point of the forcing chain) is non-degenerate: $\varphi \neq 1$, the $J$-cost stays strictly positive away from $1$, and $\varphi$-ladder steps remain invertible.
background
Recognition Science forces a unique dimensionless scale $\varphi$ as the self-similar fixed point of the Recognition Composition Law and the $J$-cost $J(x)=(x+x^{-1})/2-1$ (forcing step T6). Non-degeneracy means that fixed point is not the trivial root $x=1$ where $J$ vanishes, so geometric powers $\varphi^r$ and eight-tick octave structure stay well-defined.
This module lives in the Verification domain. It imports Mathlib and IndisputableMonolith.Constants, whose module doc records the RS time quantum $\tau_0=1$ tick and the native constant suite. The certificate is the named object PhiNonDegenerateCert exposed by the module.
proof idea
Certificate/definition module rather than a long tactic development. It packages non-degeneracy facts already available from Constants (and Mathlib inequalities on the golden-ratio fixed point) into a single verification-facing certificate. No independent forcing argument is re-derived here; the structure is export and naming for downstream checks.
why it matters in Recognition Science
Non-degenerate $\varphi$ is a prerequisite for the $\varphi$-ladder mass formula, the eight-tick octave (T7), and any claim that uses $\varphi^{\pm n}$ or $J(\varphi^k)$. The module sits in Verification so audit and export layers can point at one certificate instead of ad-hoc inequalities. The dependency graph currently lists no used_by edges, so it is an available cert rather than a node already wired into a parent theorem on this page. It supports the T5–T6 uniqueness story without reopening the full UnifiedForcingChain.
scope and limits
- Does not re-prove uniqueness of φ from the Recognition Composition Law.
- Does not derive spatial dimension D=3 or the eight-tick period.
- Does not bound α or export numerical mass values.
- Does not claim non-degeneracy for arbitrary real bases, only the RS φ.
- Graph shows no downstream used_by edges on this page.