canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Anyone bounding superposition or domain costs against a fixed cutoff cites this constant. It is a pure definitional abbreviation of the golden-ratio offset, not a derived inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the self-similarity relation of Recognition Science.
background
The module treats the J-cost of a two-level superposition $\psi = \alpha|0\rangle + \beta|1\rangle$ as $J(|\alpha|/|\beta|)$, with $J(x) = (x + x^{-1})/2 - 1$. Equal amplitudes give $J(1) = 0$, so a maximally coherent state carries zero recognition cost.
Constants live in RS-native units with $\varphi$ the unique positive fixed point of the self-similarity map (forcing step T6). The present definition simply names the offset $\varphi - 3/2$ for later comparison with domain costs.
proof idea
Pure definition: the identifier is bound to the real expression $\varphi - 3/2$. No lemmas or tactics are involved.
why it matters
Supplies the fixed numeric cutoff used by the superposition-cost certificate infrastructure in the same module (positivity of the threshold, non-negativity of domain cost, and the inhabited certificate). It sits inside the Foundation layer that packages J-cost comparisons before they feed higher forcing or measurement arguments. The value is not itself a forcing theorem; it is the conventional yardstick against which those comparisons are stated.
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