canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2, which equals the J-cost of the golden ratio. Foundation and coupling-match arguments cite it as the RS-native value of α_s(M_Z). It is introduced by a one-line definitional equation, with no proof body.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio.
background
Recognition Science forces a unique nonnegative cost $J(x)=(x+x^{-1})/2-1$ (T5) and forces $\varphi$ as the self-similar fixed point of the composition law (T6). Because $1/\varphi=\varphi-1$, a short algebraic reduction yields $J(\varphi)=\varphi-3/2$.
The Foundation module (session 3) works in RS-native units imported from Constants and Cost. Its status line records the structural identification $\alpha_s(M_Z)=J(\varphi)\approx 0.11803$ against the PDG value 0.1179 (0.01$\sigma$). The present definition simply names that closed form so later certificates can refer to it by a single identifier.
proof idea
Definitional abbreviation only: the real is bound to the arithmetic expression $\varphi-3/2$. No tactics, no lemmas, and no proof obligations.
why it matters
Gives the Foundation layer a named yardstick for the strong-coupling match advertised in the module header. Sibling material (positivity of the threshold, AlphaStrRS4Cert and its inhabited certificate) can quote the constant without re-deriving $J(\varphi)=\varphi-3/2$. In the forcing chain it sits exactly at the T5–T6 junction: once $J$ is unique and $\varphi$ is forced, a concrete dimensionless number appears in the observed $\alpha_s$ band. It does not itself close the experimental comparison; it only supplies the RS-side expression.
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