canonicalThreshold
plain-language theorem explainer
Defines the canonical materials threshold as φ − 3/2 in RS-native units. Materials and structural-forcing arguments cite it as the fixed comparison level against domain costs. The body is a one-line real definition from the golden ratio constant.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the unique self-similar fixed point forced by the Recognition Science chain.
background
In Recognition Science, $\varphi$ is the unique positive fixed point of the self-similarity relation forced at T6 after J-uniqueness (T5). Numerically $\varphi=(1+\sqrt{5})/2\approx 1.618$, so $\varphi-3/2\approx 0.118$.
This module sits in the materials structural layer and inherits the forcing spine T5→T6→T7 (eight-tick)→T8 ($D=3$). The local setting is a zero-sorry structural certificate package that compares a domain cost functional to a single fixed threshold built from $\varphi$.
Sibling facts in the same file establish nonnegativity of the domain cost and positivity of this threshold; the present declaration only names the threshold value.
proof idea
Bare definition: the identifier is bound to the real expression $\varphi - 3/2$ using the imported Constants value of $\varphi$. No lemma applications or tactics.
why it matters
Gives the materials layer a single φ-native cutoff against which domain costs are judged inside RS_MAT_Structural_009. That cutoff is the comparison level for the module’s structural certificate (siblings such as the positivity lemma and the inhabited cert). It sits downstream of the T5–T6 forcing of φ and keeps materials thresholds inside the same constant system as c, ħ, and G in RS units. No open scaffold: the declaration is a closed definition.
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