canonicalThreshold
plain-language theorem explainer
Defines the canonical cost threshold as φ − 3/2 for the Recognition Science structural physics certificate at rung 36. Physicists citing the mod-36 structural prediction use this constant as the comparison level for domain cost. The body is a one-line real definition from the golden ratio.
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
Recognition Science forces the golden ratio $\varphi$ as the unique self-similar fixed point (forcing chain T6). Constants and cost live in the imported Constants and Cost modules; the J-cost $J(x)=(x+x^{-1})/2-1$ and related defect measures sit upstream of structural certificates.
This module is the structural physics certificate at recognition rung 36 (Plan v7, 120th pass). It is marked a structural theorem with zero sorry and zero axioms. Sibling material includes a domain cost functional, its nonnegativity, and a positivity lemma for the same threshold.
The numerical value $\varphi-3/2\approx 0.118$ sits well below the Berry creation scale $\varphi^{-1}$ and is used as a fixed comparison level when checking that domain cost stays controlled on the certificate.
proof idea
Pure definition: the real constant is introduced by the single equation $\varphi - 3/2$. No proof obligations, tactics, or lemmas are involved. Downstream positivity is handled by a separate lemma on the same constant.
why it matters
Structural Certificate 36 packages an RS physics prediction at a fixed recognition rung. The threshold supplies the numerical bar against which domain cost is judged inside that certificate and its inhabitation proof. It ties the local physics claim to the global forcing of $\varphi$ (T6) and to the cost layer imported from the monolith. No parent used-by edges are recorded on the page; the constant is local scaffolding for the mod-36 cert bundle rather than a chain step T0–T8 itself.
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