canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2, a fixed positive comparison scale for domain costs on the RS rung ladder. Standard Model structural certificates cite it when checking adjacent-rung separations against a φ-native floor. The declaration is a one-line definition in terms of the golden-ratio constant from Constants.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio.
background
Recognition Science forces the golden ratio $\varphi$ as the unique self-similar fixed point of the cost functional (forcing chain T6). On the mass ladder, adjacent rungs differ by the multiplicative factor $\varphi$. This module records structural facts about that spacing for Standard Model bookkeeping, with status zero sorry and zero axioms.
The module imports Constants (for $\varphi$) and Cost (for the J-cost and domain-cost comparisons). The quantity $\varphi - 3/2$ is an affine shift of $\varphi$ used as a simple positive reference level against which domain costs are measured. Sibling lemmas establish nonnegativity of domain cost and positivity of this threshold.
proof idea
Definitional abbreviation only: the real is set equal to $\varphi - 3/2$. No tactics, no lemmas, no proof obligations.
why it matters
Supplies the numeric floor used by the sibling positivity fact and by the module certificate RSSTDStructural008Cert. Keeps rung-spacing checks native to the forced $\varphi$ of T6 rather than an external cutoff. Sits in the zero-sorry Standard Model structural layer that packages ladder geometry before particle-content claims. Does not itself close any open forcing step; it is infrastructure for those certificates.
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