canonicalThreshold
plain-language theorem explainer
Defines the canonical numerical threshold as φ − 3/2 in real units. Falsifiability certificates and domain-cost comparisons in the RS master theorem cite this constant as the fixed cutoff. The body is a one-line real abbreviation of the golden-ratio constant minus three halves.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden ratio fixed by the Recognition self-similarity equation.
background
The surrounding module states a structural falsifiability theorem for Recognition Science: any measurement lying outside the RS prediction band at 3σ falsifies the framework. Named external falsifiers include Λ outside (1.88, 2.03), α⁻¹ outside (137.030, 137.039), and BTFR slope outside (3.8, 4.2).
φ enters from the Constants import as the unique positive self-similar fixed point forced by the J-cost uniqueness chain (T5–T6). The Cost import supplies the non-negative domain cost against which thresholds are compared. This definition simply freezes the concrete real cutoff φ − 3/2 for those comparisons.
proof idea
Pure definitional abbreviation: the real constant is written as the difference of the imported golden-ratio symbol and the rational 3/2. No lemmas or tactics are required.
why it matters
Supplies the fixed numerical gate used by the RS falsifiability master theorem (v3). Sibling positivity and certificate constructions (canonicalThreshold_pos, RSFalsifiability3Cert) rely on this exact value so that domain-cost tests remain comparable across the prediction bands listed in the module header. It sits downstream of the forcing of φ and upstream of any concrete 3σ rejection test that quotes the canonical cutoff.
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