canonicalThreshold
plain-language theorem explainer
Names the real constant φ − 3/2, which equals the J-cost of the golden ratio and is the RS prediction for the QCD coupling α_s(M_Z) ≈ 0.11803. Anyone citing the Module 1 structural match to PDG uses this yardstick. It is a bare definition, not a proved identity.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of Recognition Science.
background
Recognition Science Module 1 treats the strong coupling at the Z pole as a pure cost evaluation. The cost functional is $J(x) = (x + x^{-1})/2 - 1$, forced unique by the T5 step of the unified forcing chain; equivalently $J(x) = \cosh(\log x) - 1$.
The golden ratio $\varphi$ is the self-similar fixed point forced at T6. Because $\varphi$ satisfies $\varphi^2 = \varphi + 1$, one has $1/\varphi = \varphi - 1$, and a short algebra yields $J(\varphi) = \varphi - 3/2$. Numerically this is $\approx 0.11803$, matching the PDG value $\alpha_s(M_Z) = 0.1180$ quoted in the module header.
The module imports only Constants (for $\varphi$) and Cost (for $J$). No external QCD input enters the definition itself.
proof idea
There is no proof body: the declaration is a one-line definition equating canonicalThreshold to the real expression $\varphi - 3/2$. Downstream positivity or equality lemmas (e.g. that the threshold is positive, or that it equals $J(\varphi)$) are separate declarations.
why it matters
This constant is the numerical anchor of Physics RS Module 1. The module claims a structural theorem (zero sorry, zero axiom) that the RS cost of $\varphi$ reproduces $\alpha_s(M_Z)$. Naming $\varphi - 3/2$ once keeps every later certificate and comparison free of magic numbers.
It sits on the T5–T6 segment of the forcing chain: J-uniqueness plus the forced self-similar fixed point already determine the value; the eight-tick and $D=3$ steps are not required here. The PDG match is reported as RS_PASS in the module doc. No open scaffold is attached to the definition itself.
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