canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, with φ the RS self-similar fixed point. Domain-coverage and milestone certificates in this physics module treat it as the cut separating admissible from inadmissible cost values. The body is a one-line constant definition, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
This module is a structural milestone certificate (FinalModule_1395): zero sorry, zero axioms, aimed at domain-coverage bookkeeping in Recognition Science physics. It imports the global constants (including φ) and the cost layer.
In RS, φ is forced as the unique self-similar scale (forcing step T6). Cost is measured by the J-functional $J(x)=(x+x^{-1})/2-1$ and related defect distances. Sibling names in the file (domainCost, canonicalThreshold_pos, MilestoneCert) indicate that domain costs are compared against a fixed real cut; this definition supplies that cut as φ minus three-halves.
Numerically φ ≈ 1.618 so the threshold is a small positive number near 0.118, sitting well below the Berry creation scale φ^{-1} and far from the eight-tick and D=3 landmarks.
proof idea
No proof. The declaration is a bare def that binds the name to the real expression φ − 3/2 drawn from the Constants import. Downstream positivity or comparison lemmas (e.g. the sibling canonicalThreshold_pos) must discharge any inequalities separately.
why it matters
Gives a single named real cut for the domain-coverage milestone certificate in FinalModule_1395. Parent consumers are the local milestone certificate and any domainCost comparisons that ask whether a cost clears the cut; the module doc frames the whole file as a structural theorem for that coverage claim.
Within the broader RS chain it is bookkeeping, not a forcing step: it does not re-derive φ (T6), the J-uniqueness law (T5/RCL), the eight-tick octave (T7), or D=3 (T8). It only freezes the numerical threshold those later certificates quote. Open work, if any, lives in proving positivity and inhabitation of the milestone certificate, not in this constant itself.
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