canonicalThreshold
plain-language theorem explainer
Defines the canonical materials threshold as the golden ratio minus 3/2. Materials and creep analyses in Recognition Science cite this constant when comparing domain costs against a fixed positive cutoff. It is a pure definitional abbreviation, not a derived inequality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Recognition Science forces $\varphi$ as the unique self-similar scale factor (T6) and $D=3$ spatial dimensions (T8). The materials module treats power-law creep with exponent $n=D=3$ as an exact structural identification.
The golden ratio enters RS-native units and ladder formulae throughout the monolith (via Constants). Subtracting $3/2$ places the threshold slightly above zero ($\varphi-3/2\approx 0.118$), so it can serve as a strict positive cutoff when comparing non-negative domain costs.
Local setting: Module 7 is marked STRUCTURAL THEOREM (0 sorry, 0 axiom) and packages creep-related cost identities around this constant.
proof idea
Pure definition: the real constant is introduced by the single equation $\varphi-3/2$. No lemmas or tactics are involved; positivity and downstream comparisons are proved in sibling declarations.
why it matters
Supplies the fixed numerical cutoff used by the materials creep package (Module 7), whose structural claim is that the creep exponent equals $D=3$. Ties the materials layer to the forcing-chain landmarks $\varphi$ (T6) and $D=3$ (T8). Sibling positivity and certificate results build on this value; no separate paper proposition is attached beyond the module's exact creep identification.
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