canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2. Structural Module 7 (J-cost ratio symmetry) uses it as a fixed comparison level against domain costs. Pure abbreviation of a Constants expression; no proof obligation.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ is the Recognition Science self-similar fixed point (golden ratio).
background
Module RS_MTH_Structural_007 treats Recognition J-cost symmetry: $J(x)=J(1/x)$. The cost $J$ is the unique nonnegative functional forced by the Recognition Composition Law, with closed form $J(x)=(x+x^{-1})/2-1$.
The constant $\varphi$ is imported from Constants (T6 fixed point of self-similarity). Domain cost in this module is the J-cost evaluated on a positive real ratio; nonnegativity and evaluation lemmas sit beside this definition.
The numerical level $\varphi-3/2\approx 0.118$ is a fixed real cut used for threshold comparisons inside the structural certificate, not a dynamical Berry threshold ($\varphi^{-1}$).
proof idea
Definitional abbreviation only: the name is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no sorry.
why it matters
Gives Module 7 a single named cut for comparing domain costs under J-symmetry. Sibling positivity (canonicalThreshold_pos) and the module certificate (RSMTHStructural007Cert) are the natural consumers. It is scaffolding for structural bookkeeping, not a forcing-chain step (T0–T8) and not the mass-ladder or alpha-band machinery. Keeps the threshold explicit so later inequalities do not hard-code $\varphi-3/2$.
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