canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, a fixed offset of the golden ratio used as a comparison scale in the top-Yukawa module. Anyone checking domain-cost positivity or the RS Physics 007 certificate cites this constant. The body is a one-line definitional equality, not a proof.
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
Physics RS Module 7 treats the top Yukawa as structural: $y_t = 1$ at unification, identified with the $\varphi^0 = 1$ coupling on the phi ladder. The module imports the global Constants and Cost layers, so $\varphi$ is the unique positive self-similar fixed point forced by T6, and cost primitives (J-cost and related domain costs) are already available.
Sibling declarations introduce a domain cost, prove it is nonnegative, and compare it against this threshold. The numerical value $\varphi - 3/2 \approx 0.118$ sits well below the Berry creation scale $\varphi^{-1}$ and is used only as a fixed positive cutoff inside this module’s certificate.
proof idea
Pure definition: the real constant is introduced by the equality $\texttt{canonicalThreshold} := \varphi - 3/2$. No tactics, lemmas, or rewriting are involved. Downstream positivity is handled by the separate lemma that this quantity is strictly positive.
why it matters
Gives the module a single named cutoff against which domain-cost comparisons are stated, keeping the top-Yukawa structural certificate free of magic numbers. It sits inside the broader Recognition forcing chain only indirectly: $\varphi$ itself is the T6 fixed point, and the top coupling is the $\varphi^0$ rung. No parent theorem is recorded in the dependency graph; the constant is local scaffolding for the 007 certificate and its inhabited proof object.
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