canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, where φ is the golden ratio fixed by the Recognition forcing chain. Domain-coverage and milestone certificates in this physics module compare costs against this cutoff. The body is a one-line real definition, not a proved inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, with $\varphi$ the golden-ratio fixed point of the Recognition self-similarity law.
background
This module is a Recognition Science structural certificate for a domain-coverage milestone (Plan v7, 109th pass): zero sorry, zero axioms. It sits in the physics layer and imports the global constants and cost infrastructure.
The constant $\varphi$ is the unique self-similar fixed point forced at step T6 of the Unified Forcing Chain; numerically $\varphi = (1+\sqrt{5})/2 \approx 1.618$. Subtracting $3/2$ yields a small positive scale $\approx 0.118$ used as a comparison level for domain costs.
Sibling material in the same file introduces a domain cost functional and a positivity lemma for this threshold, then packages them into a milestone certificate. The threshold itself is pure data: a named real used by those comparisons.
proof idea
Pure definitional abbreviation. The right-hand side is the real expression $\varphi - 3/2$ drawn from the Constants import; no tactic proof or lemma application is required.
why it matters
Gives a single named cutoff so domain-cost comparisons and the milestone certificate in FinalModule_1396 stay uniform. In the broader framework, $\varphi$ is the T6 fixed point that also sets the mass ladder, eight-tick structure, and several dimensionless bands; anchoring a threshold at $\varphi - 3/2$ keeps the certificate inside that native scale rather than an ad-hoc real.
No downstream edges are recorded for this declaration alone. Its role is local: feed positivity and certificate constructions that close the structural milestone for domain coverage.
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