canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2, with φ the golden-ratio self-similar fixed point. It is the fixed comparison level used beside domain-cost arguments in the φ-uniqueness structural module. Anyone citing the RS structural certificates for φ would reach for it. The declaration is a one-line definitional binding, not a proved claim.
Claim. Define the canonical threshold as the real number $\varphi - 3/2$, where $\varphi$ is the unique positive self-similar fixed point ($\varphi = 1 + 1/\varphi$) of the Recognition forcing chain.
background
Module RS_FDN_Structural_006 packages the structural uniqueness of φ as the infinite continued fraction $1+1/(1+1/(1+\cdots))$, the self-similar fixed point forced at T6 of the UnifiedForcingChain. Status is structural: zero sorry, zero axioms. Imports pull φ from Constants and the cost apparatus from Cost.
Sibling declarations introduce a domain cost, prove it equals its pointwise evaluation, and show nonnegativity. The threshold sits next to those facts as the fixed real against which costs are compared. In Recognition Science, φ also sets the mass ladder, the eight-tick octave, and several native cutoffs; here it appears only through the algebraic shift φ − 3/2.
proof idea
Definitional binding only: the real is set equal to φ minus three-halves. No tactics, no lemmas, no proof obligations.
why it matters
Gives the φ-uniqueness structural module a concrete numeric cutoff for cost comparisons. Sibling positivity (canonicalThreshold_pos) and the module certificate (RSFDNStructural006Cert) sit on top of this binding. Framework landmark is T6: φ forced as the self-similar fixed point. The constant is local scaffolding for domain-cost arguments under the Recognition Composition Law, not a replacement for other RS thresholds such as the Berry scale φ^{-1}. Module claims full structural closure (0 sorry, 0 axiom).
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