canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2 built from the golden ratio. Workers on the RS stellar-metallicity module use it as the fixed comparison scale for domain cost. The declaration is a bare definition with no proof body; positivity and certificate wiring live in sibling lemmas.
Claim. Define the canonical threshold by $T := \varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of Recognition Science.
background
RS Astrophysics Module 7 treats stellar metallicity as a structural match: $J(\varphi)^2 \approx 0.0139$ against solar $Z_\odot \approx 0.014$, with status claimed as a zero-sorry theorem. The module imports the global constants and the cost layer.
Here $\varphi$ is the unique self-similar fixed point forced at T6, and $J$ is the unique nonnegative cost $J(x)=(x+x^{-1})/2-1$ fixed by T5 and the Recognition Composition Law. Domain cost in this file is the local cost functional against which metallicity scales are compared.
The number $\varphi-3/2$ is the named threshold those comparisons use; it is not itself the metallicity value, only the RS-native cutoff placed beside domain cost.
proof idea
Bare definition: the identifier is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no obligations. Related facts (positivity, certificate packaging) are separate sibling declarations.
why it matters
Gives the metallicity module a single named real scale tied to $\varphi$ rather than an empirical fit. The module doc frames the headline match $J(\varphi)^2 \sim Z_\odot$ as structural; this constant is the threshold those cost comparisons sit against. Sibling certificate objects (RSAstro007Cert and the inhabited cert) package the module claim; this definition is the numeric anchor they share. Landmark link is T6 ($\varphi$ forced) and T5 ($J$ uniqueness), not the eight-tick or $D=3$ steps.
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