canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold constant as φ − 3/2 on the real line. Structural Module 8 uses it as the comparison level for domain cost along the RS rung ladder (adjacent rungs scale by φ). Pure definitional abbreviation of the golden-ratio offset; no proof content.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
Mathematics RS Structural Module 8 treats rung spacing on the Recognition ladder: adjacent rungs differ by the multiplicative factor $\varphi \approx 1.618$. The module is marked structural (zero sorry, zero axiom) and imports the global Constants and Cost layers.
Here $\varphi$ is the unique positive self-similar fixed point forced at T6 of the Unified Forcing Chain. The Cost import supplies the J-cost and related domain-cost functionals used by sibling declarations (domainCost, nonnegativity). The threshold itself is a fixed real offset of $\varphi$ by $3/2$, sitting slightly above zero since $\varphi > 3/2$.
proof idea
Definitional; no proof. The body is the closed-form real expression $\varphi - 3/2$ drawn from the Constants module. Downstream positivity is handled by the sibling lemma canonicalThreshold_pos, not by this def.
why it matters
Supplies the named comparison level against which domain cost is measured in Structural Module 8 (rung spacing by $\varphi$). Siblings package nonnegativity of domain cost and a certificate (RSMTHStructural008Cert) that the structural claims hold. In the broader RS picture the constant sits next to other $\varphi$-native scales (Berry threshold $\varphi^{-1}$, eight-tick octave, mass ladder yardstick), giving a single real cut for cost-versus-threshold arguments on the ladder. No paper proposition number is attached in the module doc; the role is local scaffolding for the structural certificate.
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