canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real number φ − 3/2, with φ the golden ratio fixed by self-similarity. Cosmology and dark-matter analyses in the RS stack cite it as the structural cutoff against which domain costs are compared. The declaration is a one-line definition, not a proved inequality.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
Recognition Science forces a unique dimensionless cost $J$ and a unique self-similar scale $\varphi$ (forcing step T6). In RS-native units the same $\varphi$ sets the mass ladder, the Berry creation threshold $\varphi^{-1}$, and several cosmological cutoffs.
This module (RS Cosmo 006) packages a structural claim about dark-matter mass, stated as $M_W/45 = 1.787,\mathrm{GeV}$ and flagged as a 2026 XENONnT falsifier. The local cost primitives (domainCost and non-negativity) live in the same file; the threshold supplies the numerical bar those costs are measured against.
No external lemmas are required: the value is pure arithmetic in the constants already imported from IndisputableMonolith.Constants.
proof idea
Pure definitional abbreviation. The right-hand side is the difference of the imported golden-ratio constant $\varphi$ and the rational $3/2$; no tactics, no lemmas, no proof obligations.
why it matters
Gives the module a single named real that later certificates (canonicalThreshold_pos, RSCosmo006Cert) can quote without re-deriving $\varphi - 3/2$. In the broader RS cosmology chain it sits beside the eight-tick octave and the $\varphi$-ladder mass formula, supplying a concrete numerical gate for the claimed DM mass window. The module itself is marked TESTABLE against XENONnT 2026, so the threshold is part of the structural skeleton that experiment can hit or miss.
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