canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, the golden-ratio offset used as a comparison level for domain costs in the D=3 count-law module. Anyone citing positivity or separation of the seven observable categories against a fixed RS scale will reference it. The body is a one-line constant abbreviation; no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the self-similarity relation in Recognition Science.
background
Module 7 of the RS forcing chain records the exact count law $2^D - 1 = 7$ independent observable categories once spatial dimension is fixed at $D = 3$ (T8). The module imports the global constants (including $\varphi$) and the cost calculus.
In RS units the golden ratio $\varphi$ is the unique self-similar fixed point forced at T6. Domain costs are nonnegative real functionals on the recognition side; a fixed numerical threshold is needed to separate trivial from nontrivial cost values when the seven categories are compared.
The expression $\varphi - 3/2$ is the natural offset that sits strictly between 0 and the first positive rung spacings on the $\varphi$-ladder, so it serves as a uniform comparison level inside this structural theorem.
proof idea
Pure definitional abbreviation: the real constant is introduced by the single equation $\mathrm{canonicalThreshold} := \varphi - 3/2$. No tactics, no lemmas, no unfolding obligations beyond the already-imported definition of $\varphi$.
why it matters
Supplies the fixed real scale against which domain-cost positivity and separation statements in the same module (e.g. the companion positivity lemma for this threshold) are measured. The surrounding certificate package asserts a structural theorem with zero sorry and zero axioms for the exact count $2^3 - 1 = 7$.
Within the broader forcing chain the constant sits downstream of T6 ($\varphi$ uniqueness) and T8 ($D = 3$), and upstream of any argument that the seven independent observable categories remain distinguishable once costs are compared to a canonical positive level. It does not itself encode the count law; it only normalizes the cost side of that law.
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