canonicalThreshold
plain-language theorem explainer
The real constant φ − 3/2 is fixed as the canonical cost threshold for RS string-landscape comparisons. Domain-cost and certification arguments cite it as the cutoff separating admissible from excluded configurations. The declaration is a pure definitional abbreviation of that number; no proof obligations arise.
Claim. Let $\varphi$ be the golden-ratio fixed point forced by Recognition self-similarity. The canonical threshold is the real number $\varphi - \tfrac{3}{2}$.
background
Recognition Science forces a unique self-similar scale $\varphi$ (T6 in the forcing chain). Costs and mass rungs are measured on the $\varphi$-ladder; numerical cutoffs that gate admissible configurations are therefore naturally written as simple shifts of $\varphi$.
This module compares the string-theory vacuum count (~$10^{500}$) with RS-native counts built from powers of $\varphi$ (including $\varphi^{\varphi^D}$ and gap-scaled ladders). Domain costs are scored against a fixed real cutoff. The present definition supplies that cutoff as $\varphi - 3/2 \approx 0.118$.
The module is marked structural: zero sorry, zero axioms. It does not derive string compactifications; it only records the RS-side numerical gate used by the comparison.
proof idea
Pure definition. The body is the difference of the imported constant $\varphi$ (from Constants) and the rational $3/2$. No lemmas, tactics, or rewriting are involved.
why it matters
Anchors the numerical gate used by sibling positivity and certification results (canonicalThreshold_pos, cert, cert_inhabited) inside the RS string-landscape module. Those results treat configurations whose domain cost lies below this threshold as the RS-admissible set when contrasting landscape cardinalities.
The constant is native to the $\varphi$-ladder forced at T6; it does not itself invoke the Recognition Composition Law, the eight-tick octave, or $D=3$, but inherits the same scale those landmarks fix. It closes no open forcing step; it only standardizes the cutoff the structural landscape comparison needs.
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