canonicalThreshold
plain-language theorem explainer
The golden-ratio recognition cost is the real constant φ − 3/2 ≈ 0.118. It is exactly J(φ), the unique J-cost at the self-similar fixed point forced by T5–T6. Structural modules and any argument that needs a positive lower scale for recognition cite this value. The declaration is a one-line definition, not a proved inequality.
Claim. The canonical recognition threshold is the real number $\varphi - 3/2$, which equals the J-cost $J(\varphi)$ at the golden ratio.
background
Recognition Science fixes a unique cost functional on positive reals by the Recognition Composition Law and the forcing chain. Under T5, that cost is $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$). Under T6 the golden ratio $\varphi$ is the self-similar fixed point of the same structure.
A short algebraic identity then gives the numerical value: $\varphi^{-1} = \varphi - 1$, so $J(\varphi) = (\varphi + \varphi^{-1})/2 - 1 = \varphi - 3/2 \approx 0.11803$. This module packages that constant as the structural scale of golden-ratio recognition cost, together with non-negativity and positivity facts for the associated domain cost.
proof idea
No proof body: the declaration is a bare definition equating the constant to $\varphi - 3/2$. The identification with $J(\varphi)$ is the elementary expansion of the T5 formula at $\varphi$, using $\varphi^2 = \varphi + 1$.
why it matters
The module presents this value as the J-cost minimum at $\varphi$, the structural recognition scale forced once T5 (J-uniqueness) and T6 ($\varphi$ as fixed point) are in place. Downstream certificates in the same file (positivity of the threshold, domain-cost non-negativity, the structural certificate) treat it as the reference positive constant against which recognition cost is measured. It does not itself close any open forcing step; it simply names the number that those steps produce.
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