canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as φ − 3/2 in RS-native units. Cosmology and ladder analyses cite it as the comparison scale for domain cost when checking the gap-45 structural bound at D = 3. The body is a one-line real constant built from the forced golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Module RS_COS_Structural_004 packages the gap-45 structural fact: at spatial dimension $D = 3$ one has $D^2(D+2) = 9\cdot 5 = 45$, identified as the minimum rung for stable self-reference. The module is marked structural (zero sorry, zero axiom) and imports the global constants and cost layers.
$\varphi$ is the unique positive self-similar fixed point forced at T6 of the Unified Forcing Chain; in RS it sets the φ-ladder spacing for masses and thresholds. The cost layer supplies the J-cost $J(x) = (x+x^{-1})/2 - 1$ and nonnegativity facts used by sibling domain-cost lemmas. This definition simply names the real scale $\varphi - 3/2$ against which those costs are compared.
proof idea
Pure definition: the real constant is introduced as the arithmetic expression $\varphi - 3/2$. No proof obligations; positivity and comparison lemmas live in sibling declarations.
why it matters
Gives a single named scale for the structural cosmology certificate in this module (gap-45, minimum rung for stable self-reference at $D = 3$). Downstream siblings such as the positivity lemma for the threshold and the inhabited certificate package use it as the cutoff when domain cost is checked. It sits next to other RS threshold landmarks (Berry creation at $\varphi^{-1}$, $Z_{\mathrm{cf}} = \varphi^5$) as a φ-native comparison value, not a derived dynamical bound. Ties the T6 φ-forcing and T8 $D = 3$ landmarks into the cosmology structural layer.
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