canonicalThreshold
plain-language theorem explainer
Defines the canonical cost threshold for the Physics structural certificate at recognition rung 26 as φ − 3/2. Anyone citing the mod-26 Physics domain bound or the nonnegativity/positivity lemmas around domain cost will use this constant. It is a pure definitional abbreviation of the golden-ratio offset, with no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Recognition Science fixes the dimensionless scale $\varphi$ (T6) as the unique self-similar fixed point of the cost functional $J$. Structural certificates package domain-level predictions at discrete recognition rungs; this module treats the Physics domain at rung 26.
The Cost import supplies the $J$-cost and related comparison primitives. Domain cost is the local excess relative to the RS yardstick; a threshold separates negligible from structurally meaningful cost. The constant $\varphi - 3/2$ is the cut used for that comparison in the mod-26 Physics certificate.
Sibling facts in the same file establish nonnegativity of domain cost and positivity of this threshold, so the cut sits strictly above zero and can serve as a strict lower barrier in certificate inequalities.
proof idea
Definitional abbreviation only: the real constant is introduced as $\varphi - 3/2$ with no tactic proof or lemma application. Downstream positivity is handled by a separate lemma (canonicalThreshold_pos), not by this declaration.
why it matters
Gives the explicit numeric cut for Structural Certificate 26 in the Physics domain (module status: structural theorem, zero sorry). In the RS ladder picture, rung-indexed predictions compare domain cost against a $\varphi$-native threshold; this is that threshold for mod 26.
It sits beside the domain-cost lemmas and the certificate inhabitation bundle in the same file, so any audit of the Physics mod-26 structural claim reads this constant first. Framework landmarks in play are T6 ($\varphi$ forced) and the general rung/yardstick mass and cost bookkeeping; no forcing-chain step T0–T8 is proved here, only the local cut used by the certificate.
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