canonicalThreshold
plain-language theorem explainer
The canonical recombination threshold is the real number φ − 3/2. Cosmologists in Recognition Science cite it when comparing domain J-cost against a fixed scale that places z_rec between successive φ-powers. It is a bare numeric definition with no proof body.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio.
background
The module treats recombination redshift from J-cost. Observed $z_{\mathrm{rec}} \approx 1100$ sits on the $\varphi$-ladder: $\log(1100)/\log(\varphi) \approx 14.7$, so $z_{\mathrm{rec}}$ lies between $\varphi^{14}\approx 843$ and $\varphi^{15}\approx 1364$. Status is structural (zero sorry, zero axiom).
$\varphi$ is the self-similar fixed point forced at T6 of the unified forcing chain. The J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) measures recognition defect under the Recognition Composition Law. Sibling definitions in the file introduce a domain cost and its nonnegativity; the present constant is the comparison scale those costs are measured against.
proof idea
Bare definition: the symbol is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Anchors the numeric scale used by the recombination certificate and positivity lemmas in the same module (domain-cost nonnegativity, certificate inhabitation). Links the cosmology layer to the forced constant $\varphi$ from T6 and to the structural claim that $z_{\mathrm{rec}}=1100$ is consistent with a pure $\varphi$-power placement between rungs 14 and 15. Does not itself close an open forcing step; it is infrastructure for the J-cost comparison that makes the redshift window checkable.
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