canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as φ − 3/2 in RS-native units. Structural Module 4 (gap-45) uses it when fixing the minimum rung for stable self-reference at D = 3. The body is a one-line real constant, not a derived equality.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
Foundation Structural Module 4 packages the gap-45 identity $D^2(D+2)=9\cdot 5=45$ as the minimum rung count for stable self-reference when spatial dimension is forced to $D=3$ (forcing chain T8). The module imports the global constant $\varphi$ and the J-cost infrastructure.
$\varphi$ is the unique positive self-similar fixed point forced at T6; numerically $\varphi=(1+\sqrt{5})/2$. Subtracting $3/2$ yields a small positive scale that sits below the unit rung and above the Berry creation floor $\varphi^{-1}$ in the same units. Sibling declarations bind a domain cost to this threshold and prove non-negativity and positivity.
proof idea
Pure definition: the identifier is bound to the real expression $\varphi - 3/2$. No lemmas, tactics, or algebraic reduction.
why it matters
Supplies the numeric cut used by the gap-45 structural certificate in this module (siblings canonicalThreshold_pos, RSFDNStructural004Cert). Gap-45 is the combinatorial count $D^2(D+2)$ at the forced dimension $D=3$, read as the lowest rung supporting stable self-reference on the $\varphi$-ladder. The threshold itself is not a forcing-chain step (T0–T8); it is a local scale marker that lets the certificate compare domain cost against a fixed positive level built only from $\varphi$ and rationals.
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