canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in RS units. Anyone comparing domain costs under reciprocity symmetry cites this constant when fixing a positive cutoff below the golden-ratio scale. The body is a one-line abbreviation, not a derived identity.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by self-similarity in Recognition Science.
background
The module establishes reciprocity symmetry of the Recognition cost: $J(x)=J(1/x)$ for all $x>0$. That identity is the structural fact that the cost of comparing $a$ to $b$ equals the cost of comparing $b$ to $a$, and it is what uniquely pins down $J$.
Here $\varphi$ is the self-similar fixed point forced at T6 of the unified forcing chain (the unique positive solution of the RS fixed-point equation). The cost $J$ itself is the unique continuous solution of the Recognition Composition Law with $J(1)=0$ and the usual convexity/normalization, equivalently $J(x)=\cosh(\log x)-1$.
Sibling definitions in the same file package a domain cost and a reciprocity-symmetry certificate that need a concrete positive real cutoff; this constant supplies that cutoff in native RS units.
proof idea
Pure definitional abbreviation: the name is bound to the real expression $\varphi - 3/2$. No lemmas, tactics, or rewriting are involved.
why it matters
Gives the module a single named positive scale sitting just below $\varphi$ (numerically $\approx 0.118$) against which domain-cost comparisons and reciprocity certificates can be stated without ad-hoc literals. It sits in the Foundation layer beside the reciprocity theorem that uniquely fixes $J$, and beside the T5–T6 landmarks (J-uniqueness and $\varphi$ as self-similar fixed point). Downstream certificate constructors in the same file are the natural consumers; the definition itself closes no open forcing step.
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