canonicalThreshold
plain-language theorem explainer
The canonical materials threshold equals φ − 3/2 in RS-native reals. Anyone comparing domain costs to a fixed cutoff in the copper Debye-temperature module cites this constant. It is a one-line arithmetic definition from the golden ratio and the rational 3/2.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden-ratio fixed point of self-similarity.
background
Recognition Science forces a unique dimensionless cost $J$ and a unique self-similar scale $\varphi$ (forcing steps T5–T6). In RS-native units lengths, energies, and temperatures are measured on the $\varphi$-ladder; ordinary SI values appear only after a yardstick conversion.
This module is the second materials block. Its structural claim is that copper’s Debye temperature sits near $\varphi^{12},\mathrm{K}\approx 321.9,\mathrm{K}$ (about 6% from the experimental 343 K). Domain costs built from $J$ are compared against a single fixed real cutoff; that cutoff is the present definition.
The constant is therefore pure arithmetic: subtract the rational $3/2$ from $\varphi$. No further analytic identity is required at the definition site.
proof idea
Pure definition. The right-hand side is the real expression $\varphi - 3/2$ drawn from the Constants import; there is no proof body, tactic, or lemma application.
why it matters
Supplies the numerical gate used throughout Materials RS Module 2. Sibling positivity and certificate declarations (threshold positivity, the inhabited RSMatl002 certificate) read this constant directly when they assert that a domain cost lies above or below the cutoff. In the broader framework it is a materials-scale avatar of the same $\varphi$ fixed by T6; the eight-tick and $D=3$ landmarks are not invoked here. The module remains structural: the 6% Debye offset is recorded, not derived from a dynamical model.
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