canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, the cut used when scoring domain-cost coverage in this milestone module. Anyone checking the FinalModule_1398 structural certificate or positivity of the threshold cites it. The body is a one-line definitional abbreviation of the golden ratio minus three halves.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the self-similar fixed point of Recognition Science.
background
This module is a structural certificate for a domain-coverage milestone in Recognition Science (Plan v7, 109th pass): zero sorry, zero axioms. It sits in the physics layer and imports the global constants and the J-cost infrastructure.
The constant $\varphi$ is the unique self-similar fixed point forced by the T6 step of the unified forcing chain; numerically $\varphi = (1+\sqrt{5})/2$. Domain costs in the sibling definitions measure how far a configuration sits from admissible recognition structure; a fixed real cut is needed to decide coverage.
The value $\varphi - 3/2$ is slightly positive ($\approx 0.118$) and is the module's chosen comparison level for those cost checks.
proof idea
Pure definition: the identifier is bound to the real expression $\varphi - 3/2$. No proof obligations, no lemmas applied.
why it matters
Supplies the numeric cut that the milestone certificate and its positivity lemma (canonicalThreshold_pos) rely on when asserting domain coverage. In the broader framework it is a local bookkeeping constant, not a new physical law: $\varphi$ itself is already forced by T6, and the offset $3/2$ is the module's chosen margin relative to that scale. Downstream certificate inhabitants use the threshold to turn cost comparisons into a single structural yes/no for the 1398 milestone.
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