canonicalThreshold
plain-language theorem explainer
Defines the real constant φ − 3/2 as the canonical threshold for the J-cost wave–particle duality module. Anyone citing the continuous complementarity transition between pure interference (J = 0) and pure detection (J = 1) uses this scale. The body is a one-line arithmetic definition in terms of the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio.
background
The module treats wave–particle duality as a continuous transition in the Recognition Science cost $J$. Pure path interference sits at $J = 0$; pure path detection sits at $J = 1$. Complementarity is the path through intermediate $J$ values rather than a discrete switch.
$J$ is the unique cost forced by the Recognition Composition Law, $J(x) = (x + x^{-1})/2 - 1$. The constant $\varphi$ is the self-similar fixed point of the forcing chain (T6). The module imports the global Constants and Cost layers, so $\varphi$ and $J$ are already available.
This declaration simply names the particular real scale $\varphi - 3/2$ against which domain costs are later compared when certifying the three-regime duality picture.
proof idea
Pure definition: the real is introduced as the arithmetic expression $\varphi - 3/2$. No lemmas, tactics, or proof obligations.
why it matters
Supplies the numerical hinge used by the structural wave–particle duality certificate in this module (siblings such as the positivity lemma for the threshold and the inhabited certificate). In the broader RS picture it sits downstream of T5–T6 (uniqueness of $J$ and forcing of $\varphi$) and supports the claim that complementarity is a continuous $J$-cost transition, not an extra postulate. The module is marked structural with zero sorry and zero axioms; this constant is the scale that makes the three-regime reading concrete.
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