canonicalThreshold
plain-language theorem explainer
Defines the real scalar threshold φ − 3/2 used as the canonical cutoff in RS Physics Module 12. Anyone citing the module’s domain-cost comparisons or the W-boson structural match will pull this constant. 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
Recognition Science fixes φ as the unique self-similar fixed point of the cost functional (forcing step T6). In RS-native units many cutoffs and mass-ladder offsets are simple polynomials in φ. Module 12 records the structural W-boson mass match $M_W \approx \varphi^{13}\cdot 0.154,\mathrm{GeV}$.
The sibling domainCost supplies a non-negative cost on a real domain; the present constant is the numerical bar against which that cost is compared. Imports pull Constants (for φ) and Cost (for the underlying J-cost infrastructure).
proof idea
Pure definition: the real is introduced by the arithmetic expression φ − 3/2. No proof obligations; positivity and later comparisons are discharged by sibling lemmas such as canonicalThreshold_pos.
why it matters
Gives a single named scalar for the cutoff that Module 12’s certificate (RSPhysics012Cert) and domain-cost lemmas reference. Keeps the W-boson structural theorem free of magic numbers and ties the threshold to the same φ that appears in the mass ladder, the eight-tick octave, and the α-band. Downstream positivity and inhabitation facts build directly on this value.
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