canonicalThreshold

Module 9 of the Materials layer records a structural match for lead Cooper-pair binding: $\varphi^3 \cdot 0.642,\mathrm{meV} = 2.72,\mathrm{meV}$. The module imports the global Constants and Cost layers, so $\varphi$ is the unique positive self-similar fixed point forced at T6 of the unified forcing chain, and cost primitives (J-cost and nonnegativity) are available for domain comparisons.

In RS materials work a single dimensionless cutoff is often needed to separate sub-threshold fluctuations from recognized binding or gap scales. Subtracting $3/2$ from $\varphi$ yields a small positive number ($\varphi\approx 1.618$ so the threshold is near $0.118$) that sits naturally on the same ladder used for mass and energy yardsticks.

Pure definition: the real constant is introduced by the arithmetic expression $\varphi - 3/2$. No lemmas or tactics are involved; positivity and later certificate use are left to sibling declarations.

Gives Module 9 a named, reusable cutoff tied directly to the forced constant $\varphi$ rather than an ad-hoc meV number. Downstream siblings (positivity of the threshold, the RSMatl009 certificate, and inhabited cert bundles) can quote this symbol when they assert that domain costs clear the Cooper-pair match. It keeps the materials layer aligned with the same $\varphi$-ladder that appears in the mass formula and the eight-tick octave, so a single numeric convention serves both particle and condensed-matter claims.