canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2, with φ the golden ratio. Authors of the Recognition Science Higgs-mass ladder use it as a fixed positive comparison scale for domain costs. The declaration is a one-line definitional binding with no proof content.
Claim. Define the canonical threshold by $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of Recognition Science.
background
Physics RS Module 10 records the structural Higgs-mass match $m_H \approx 125.25,\mathrm{GeV}$ against a pure $\varphi$-ladder power ($\varphi^{13}$ scaled into GeV). Status is structural: zero sorry, zero axiom.
The constant $\varphi$ is the unique self-similar fixed point forced at step T6 of the unified forcing chain. The Cost import supplies the recognition cost $J$ and related domain-cost functionals; those costs are nonnegative reals against which a fixed positive scale is needed. The combination $\varphi - 3/2 \approx 0.118$ is that scale inside this module.
proof idea
Definitional abbreviation only. The real is bound directly to $\varphi - 3/2$; there is no tactic block, no lemma application, and no proof obligation.
why it matters
Anchors the comparison scale used by the domain-cost lemmas in the same module (nonnegativity and evaluation identities). The module header claims a clean $\varphi^k$ match for the Higgs mass; a fixed threshold of order $10^{-1}$ lets those cost comparisons sit on a dimensionless RS-native footing rather than an ad-hoc cutoff.
It is distinct from the Berry creation threshold $\varphi^{-1}$ and from the mass-ladder yardstick. Downstream certificate objects in the module package the structural claim; this constant is the numeric hinge those certificates rely on when they mention a canonical cutoff.
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