canonicalThreshold
plain-language theorem explainer
The canonical materials threshold is the real number φ − 3/2, with φ the golden-ratio fixed point of Recognition Science. Materials authors compare domain costs against this dimensionless cutoff when certifying structural transitions such as iron melting. The declaration is a closed-form definition with no proof body.
Claim. The canonical threshold is the real constant $\varphi - 3/2$, where $\varphi$ is the golden ratio.
background
Recognition Science forces $\varphi$ as the unique self-similar scale (forcing chain T6). Materials modules import that constant together with the J-cost infrastructure and build dimensionless domain costs that are then compared to fixed numerical gates.
Module 5 is the iron-melting certificate: it reports the $\varphi$-ladder prediction $\varphi^{15}\cdot\varphi^{0.7},\mathrm{K}\approx 1814,\mathrm{K}$ against the experimental $1811,\mathrm{K}$ (0.2 percent). The offset $3/2$ from $\varphi$ itself yields a small positive real near $0.118$, used as the structural cutoff in that comparison.
Sibling facts record positivity of the threshold and nonnegativity of the associated domain cost; those facts sit downstream of this definition alone.
proof idea
Definitional abbreviation only. The real is introduced by the closed expression $\varphi-3/2$; no tactics, lemmas, or rewriting are involved.
why it matters
Gives the numerical gate consumed by the iron-melting materials certificate and its inhabited cert record in the same module. In the RS materials program such thresholds mark the boundary between negligible recognition cost and allowed structural change (here melting). The value inherits $\varphi$ from the global forcing chain and therefore sits on the same ladder used for mass and temperature formulas; it does not itself invoke the Recognition Composition Law or the eight-tick octave.
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