canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real number φ − 3/2 used as the fixed comparison level in this materials module. Anyone checking domain-cost gates or the Module-11 water specific-heat certificate would cite it. The declaration is a pure definitional binding to the golden-ratio constant from RS constants.
Claim. Define the canonical threshold by $T_{\mathrm{can}} := \varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Recognition Science materials modules pin macroscopic constants to the φ-ladder. This file (Module 11) targets the specific heat of water, stated as the exact identity $\varphi^{19}\cdot 0.447 = 4179,\mathrm{J/kg/K}$, with structural status (no sorry, no axioms).
The constant $\varphi$ is imported from the RS constants layer and is forced in the foundation as the self-similar fixed point (T6). The cost layer supplies the J-cost $J(x)=(x+x^{-1})/2-1$ used by sibling domain-cost definitions. The threshold $\varphi-3/2$ is a φ-native scale sitting a half-unit below $\varphi$, against which domain cost is compared in the surrounding lemmas of the module.
proof idea
Definitional, not a proved statement. The body is the arithmetic difference of the imported constant $\varphi$ and the rational $3/2$; elaboration is by rfl at use sites. No lemmas are applied.
why it matters
Gives the numeric gate referenced by the positivity sibling and the module certificate that packages Module 11. In the materials track it keeps cutoffs on the same φ-native scale as the water specific-heat ladder rather than an external SI cutoff. It does not itself state the heat-capacity identity; that is the module-level structural claim. Framework landmarks in play are T6 (φ forced) and the φ-ladder mass/constant pattern used across RS materials modules.
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