canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2, with φ the golden ratio. It is the fixed numerical cutoff used by the Higgs-VEV structural module (v/M_Z near φ²). Anyone comparing domain costs to a φ-native scale in this module cites it. The body is a one-line arithmetic definition, not a proved inequality.
Claim. Let $\varphi$ be the golden ratio. The canonical threshold is the real constant $\varphi - 3/2$.
background
Physics RS Module 6 records the structural observation that the Higgs VEV ratio $v/M_Z \approx 246/91.2 \approx 2.70$ lies near $\varphi^2 \approx 2.618$ (about 3% off). The module is marked structural: zero sorry, zero axioms.
The golden ratio $\varphi$ enters from the Recognition forcing chain as the unique self-similar fixed point (T6). Imports pull $\varphi$ from Constants and the J-cost apparatus from Cost. Sibling declarations in the same file introduce a domain cost, prove it nonnegative, and certify that this threshold is positive.
proof idea
Definitional one-liner: the real is assigned the value $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Supplies the fixed cutoff against which domain-cost comparisons run in the Higgs-ratio module. Sibling positivity (canonicalThreshold_pos) and the module certificate RSPhysics006Cert sit next to it. In the broader RS scale hierarchy it is another $\varphi$-native number, alongside landmarks such as the Berry threshold $\varphi^{-1}$ and $Z_{\mathrm{cf}}=\varphi^5$, though the offset $3/2$ is local to this structural comparison rather than a global forcing step (T0–T8).
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