canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2, with φ the golden ratio fixed by Recognition Science. Cosmology proofs that pin H₀ on the phi-ladder cite this constant as the comparison level for domain cost. The body is a one-line arithmetic definition; no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
The module derives a structural value for the Hubble constant from the phi-ladder: $H_0 = \varphi^k / \tau_{\mathrm{universe}}$ with $\tau_{\mathrm{universe}} = 13.8,\mathrm{Gyr}$, targeting the Planck figure $67.4,\mathrm{km/s/Mpc}$. Status is structural (zero sorry, zero axiom).
Recognition Science forces $\varphi$ at step T6 of the unified forcing chain as the unique self-similar fixed point compatible with the J-cost $J(x) = (x + x^{-1})/2 - 1$. Constants live in RS-native units with $c=1$ and ladder rungs measured in powers of $\varphi$. The present definition simply names the numerical offset $\varphi - 3/2$ that later certificates compare against domain cost.
proof idea
Pure definition: the real constant is introduced by the arithmetic expression $\varphi - 3/2$. No tactics, no lemmas, no reduction. Downstream positivity and certificate lemmas (e.g. canonicalThreshold_pos) discharge the elementary inequalities that follow from $\varphi > 1$.
why it matters
Supplies the named comparison level used by the Hubble-precise certificate chain in this module (siblings domainCost, HubblePrecise2Cert, cert). The offset $\varphi - 3/2$ sits between the Berry creation threshold $\varphi^{-1}$ and the eight-tick structural scales, giving a clean cut for when domain cost on the phi-ladder is large enough to lock the Planck $H_0$ rung. It is scaffolding-free arithmetic that keeps the structural theorem free of magic numbers.
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