canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2, with φ the Recognition self-similarity fixed point. Cosmology certificates and domain-cost comparisons in this module cite it as a fixed positive scale. The body is a one-line definitional assignment from Constants.
Claim. The canonical threshold is the real constant $T_{\mathrm{can}} := \varphi - 3/2$, where $\varphi > 0$ is the unique solution of $x = 1 + 1/x$ (the golden ratio forced by Recognition self-similarity).
background
Recognition Science forces a unique dimensionless scale φ via the self-similar fixed-point step (T6) of the unified forcing chain. The Constants import exposes that φ; the Cost import supplies the J-cost and related nonnegativity infrastructure used by sibling lemmas in this file.
This module is Cosmology RS Module 2. Its structural target is the dimensionless combination $\Lambda \ell_P^2$, asserted equal to $8\varphi^5/45$ and to lie in $(1.88, 2.03)\times 10^{-122}$, against the Planck value $\sim 1.99\times 10^{-122}$. The threshold $\varphi - 3/2 \approx 0.118$ is a pure φ-derived comparison scale used next to domainCost in the module's certificates.
proof idea
Definitional, not a proof. The real is assigned by the closed form phi − 3/2, with phi taken from IndisputableMonolith.Constants. No tactics, no lemmas, no sorry.
why it matters
Gives a parameter-free positive yardstick built only from φ, so domain-cost inequalities and the module certificate can stay inside the RS native unit system. Sibling canonicalThreshold_pos will assert positivity; RSCosmo002Cert and cert package the structural claim for $\Lambda \ell_P^2 = 8\varphi^5/45$. Lands in the cosmology layer that converts T6 (φ forced) and the Cost apparatus into a dimensionless vacuum-scale prediction without free fits. No open scaffold: claim_status is definition.
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