canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2, with φ the golden-ratio fixed point of the Recognition cost. Foundation and gap-45 arguments cite it as the numerical cutoff tied to D = 3 self-reference depth. The body is a one-line constant definition from Constants.phi.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio self-similar fixed point.
background
Module 3 of the RS forcing chain records the structural gap $g_D = D^2(D+2)$. At spatial dimension $D = 3$ this equals $9 \cdot 5 = 45$, stated as the minimum depth for self-reference. The module is marked a structural theorem (no sorry, no axioms).
The constant $\varphi$ is imported from IndisputableMonolith.Constants: it is the unique positive fixed point forced by T6 of the unified forcing chain (self-similarity of the J-cost). The Cost import supplies the Recognition cost $J$ and related nonnegativity facts used by sibling lemmas in the same file.
This definition simply packages the real shift $\varphi - 3/2$ as a named threshold for later positivity and comparison lemmas (e.g. canonicalThreshold_pos).
proof idea
Pure definition: the real constant is set equal to $\varphi - 3/2$ by abbreviation of the imported $\varphi$. No tactics, no lemmas.
why it matters
Gives a single named real that later certificates in RS_Forcing_Chain_Module_003 can compare against domain costs. It sits inside the D = 3 / gap-45 structural layer of the forcing chain (T8 forces three spatial dimensions; gap $g_3 = 45$ is the self-reference depth). Downstream siblings such as canonicalThreshold_pos and the module certificate RSForcingChain003Cert are the natural consumers; the definition itself carries no theorem content.
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