canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2, with φ the golden ratio. It is the structural cutoff used in the RS gap-45 (D=3) Standard Model module when comparing domain costs for stable self-reference. Anyone citing the minimum-rung or structural-certificate results in this file would reference it. The declaration is a one-line definitional assignment.
Claim. Define the canonical threshold by $\mathrm{canonicalThreshold} := \varphi - \tfrac{3}{2}$, where $\varphi$ is the golden ratio (the unique self-similar fixed point of the Recognition cost).
background
Recognition Science forces $\varphi$ as the self-similar fixed point of the J-cost (T6) and forces $D=3$ spatial dimensions (T8). This module packages the structural count $D^2(D+2)=9\cdot 5=45$, called gap-45, as the minimum rung for stable self-reference at $D=3$.
The file imports the global Constants (hence $\varphi$) and Cost layers. Sibling declarations introduce a domain cost functional and prove it is nonnegative; the present constant is the numerical bar those costs are compared against when building the structural certificate.
proof idea
Definitional one-liner: the real is assigned equal to $\varphi-3/2$ by direct equality. No tactics, no lemmas, no proof obligations.
why it matters
Supplies the explicit numerical cutoff for the RS_STD_Structural_004 certificate suite (siblings include positivity of the threshold and the inhabited structural cert). It ties the golden-ratio scale forced by T6 to the gap-45 counting $D^2(D+2)=45$ that the module treats as the minimum rung for stable self-reference at $D=3$. Downstream structural claims in the Standard Model sector of Recognition Science can quote this constant without re-deriving the offset.
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