canonicalThreshold

Recognition Science fixes a single dimensionless scale $\varphi$, the unique self-similar fixed point of the cost geometry (forcing step T6). In RS-native units many cutoffs and gaps are integer or half-integer shifts of powers of $\varphi$.

This module is Structural Theorem 10: once the coherence energy $E_{\mathrm{coh}}$ is pinned by the electron mass, all further predictions are parameter-free. The local cost objects (domainCost and its nonnegativity) compare a domain cost against a fixed real cutoff; that cutoff is the present constant.

The imports bring Mathlib reals, the RS Constants package (where $\varphi$ lives), and the Cost layer that supplies the J-cost and related defect measures.

Pure definition: the real is introduced as the term $\varphi - 3/2$. No tactic proof, no lemma application. Downstream facts such as positivity of the threshold are separate theorems that unfold this abbreviation.

Gives a single named real that the rest of RS_MTH_Structural_010 can cite when stating that domain cost sits above (or meets) a canonical cutoff. That supports the module certificate RSMTHStructural010Cert and the positivity lemma for the threshold itself. In the broader framework it is a concrete half-integer offset of $\varphi$, consistent with the T6 forcing of $\varphi$ and with the style of other RS cutoffs (Berry threshold $\varphi^{-1}$, eight-tick structure, mass-ladder gaps). It does not itself prove any physical bound; it only freezes the number those bounds use.