canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real scalar φ − 3/2, with φ the golden-ratio fixed point of Recognition Science. Cosmology module 10 uses it as the comparison scale beside the solar-metallicity identity J(φ)² ≈ Z_⊙. Anyone citing that structural match would pull this constant. The declaration is a bare definitional abbreviation.
Claim. Define the canonical threshold by $\mathrm{canonicalThreshold} := \varphi - \tfrac{3}{2}$, where $\varphi$ is the golden-ratio self-similar fixed point from the Recognition forcing chain.
background
Module RS_Cosmo_Module_010 packages the solar-metallicity claim of Recognition Science: $J(\varphi)^2 \approx 0.01393$ matches the observed solar metallicity $Z_\odot \approx 0.014$. Status is structural theorem (zero sorry, zero axiom).
Here $J$ is the unique nonnegative cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law (T5), and $\varphi$ is the self-similar fixed point forced at T6. The module imports Constants (for $\varphi$) and Cost (for $J$).
Subtracting $3/2$ from $\varphi$ yields a small positive real near $0.118$, used by sibling lemmas as a positivity and domain-cost scale inside the cosmology certificate.
proof idea
Definitional abbreviation only: the real is set equal to phi - 3/2. No lemmas, no tactics, no proof obligations.
why it matters
Supplies the explicit real scale that the solar-metallicity certificate in this module compares against. Sibling positivity (canonicalThreshold_pos) and the inhabited certificate (RSCosmo010Cert / cert_inhabited) sit downstream of this constant. It ties the cosmology match to the T5/T6 forcing of $J$ and $\varphi$, and to the RS-native role of $\varphi$ in units ($\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$). The def itself does not prove the metallicity match; it only names the threshold those theorems use.
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