canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ minus 3/2. Cosmology proofs in the Hubble-tension module cite it as the fixed comparison level against domain costs. The body is a one-line constant assignment from the RS constant φ.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
RS Cosmology Module 3 treats the Hubble tension: the ratio $H_{0,\mathrm{local}}/H_{0,\mathrm{CMB}}$ is forced into the band $(1.075, 1.091)$, with the SH0ES value $1.0837$ inside, under a structural (sorry-free) certificate.
The module imports the global RS constants and the J-cost layer. Here $\varphi$ is the unique self-similar fixed point forced at T6 of the unified forcing chain; numerically $\varphi\approx 1.618$, so $\varphi-3/2\approx 0.118$. Sibling definitions package a domain cost on the same real line and prove that cost is nonnegative and that this threshold is strictly positive.
The threshold is the fixed yardstick against which those domain costs are compared when the module certifies the H0 ratio band.
proof idea
No proof. The declaration is a bare definition: the real constant is assigned the closed form $\varphi-3/2$ by direct equality. Positivity and any comparison lemmas live in sibling theorems, not here.
why it matters
Gives the module a single named real level for cost-versus-threshold comparisons in the Hubble-tension certificate. Downstream siblings (canonicalThreshold_pos, the domain-cost lemmas, and RSCosmo003Cert) hang off this constant. In the broader RS picture it sits next to other φ-native cutoffs (Berry threshold $\varphi^{-1}$, dream fraction $\varphi^{-3}$, $Z_{\mathrm{cf}}=\varphi^5$), all descending from T6 φ-forcing. It does not itself close the H0 band; it only supplies the comparison value the structural certificate uses.
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