canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Structural physics certificates at rung 76 cite this constant when comparing domain costs to a fixed barrier. The body is a one-line real assignment from the golden ratio constant.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by self-similarity in the Recognition Science forcing chain.
background
Recognition Science forces a unique dimensionless cost $J$ and a unique self-similar scale $\varphi$ (T5–T6 of the unified forcing chain). Constants and costs live in RS-native units with $c=1$ and ladder steps in powers of $\varphi$.
This module issues Structural Certificate 76 for the Physics domain: a zero-sorry structural prediction at recognition rung 76. Sibling definitions introduce a domain cost functional and prove it is nonnegative; the threshold supplies the fixed comparison level against which that cost is read.
Imports pull Mathlib reals, the RS Constants module (exposing $\varphi$), and the Cost module (exposing $J$-style costs).
proof idea
Pure definition: the real constant is assigned by subtracting $3/2$ from the imported golden-ratio constant $\varphi$. No lemmas or tactics.
why it matters
Gives the fixed barrier used by the Physics structural certificate at rung 76 when domain costs are compared to a canonical level. In the broader RS picture the same $\varphi$ appears in the mass ladder, the Berry threshold $\varphi^{-1}$, and the eight-tick octave; here it is shifted by $3/2$ to set a structural cutoff rather than a creation or mass scale. Downstream positivity and certificate inhabitation results in the same file read this value as their comparison constant.
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