canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in RS-native units. Structural Module 4 (gap-45, minimum rung for stable self-reference at D = 3) uses this constant as the comparison level for domain cost. The body is a one-line real abbreviation of the golden-ratio fixed point minus three halves.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the unique self-similar fixed point forced by the Recognition Composition Law (T6).
background
Module RS_MTH_Structural_004 treats the structural gap $D^2(D+2)=45$ at spatial dimension $D=3$ (the T8 value). That gap is the minimum rung index at which stable self-reference is possible on the $\varphi$-ladder.
The constant $\varphi$ is imported from Constants and is the unique positive solution of the self-similarity fixed-point equation forced at T6; numerically $\varphi=(1+\sqrt{5})/2$. Domain cost (sibling domainCost) is the non-negative cost functional against which this threshold is compared.
The threshold itself is simply the real shift $\varphi-3/2\approx 0.118$, sitting between zero and the Berry creation scale $\varphi^{-1}$.
proof idea
Pure definition: the real constant is introduced by the abbreviation $\varphi-3/2$. No lemmas, tactics, or proof obligations appear; positivity and comparison facts are left to sibling theorems such as canonicalThreshold_pos.
why it matters
Supplies the explicit comparison level used throughout Structural Module 4 when testing whether domain cost clears the gap-45 self-reference floor at $D=3$. The module status line records a complete structural theorem (0 sorry, 0 axiom); this constant is the numeric anchor for those inequalities. It sits downstream of T6 ($\varphi$ forced) and T8 ($D=3$), and upstream of any certificate that domain cost meets or exceeds the stable-self-reference rung.
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