canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in RS-native units. Standard-model structural certificates and domain-cost comparisons cite this constant as the fixed cutoff against which J-type costs are measured. The body is a one-line real definition from the golden ratio.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the unique self-similar fixed point forced by the Recognition Science chain.
background
Recognition Science forces a unique dimensionless scale φ via the J-cost fixed-point step (T5–T6 in the unified forcing chain): J(x) = (x + x^{-1})/2 − 1, and φ is the self-similar solution of that structure. Constants and Cost modules supply φ and the non-negative cost functional used throughout the monolith.
This file is StandardModel structural module 9. Its local setting is the RS forcing spine T5 (J-uniqueness) → T6 (φ forced) → T7 (eight-tick octave) → T8 (D = 3), recorded as a structural theorem block with no sorry and no axioms. Sibling definitions introduce a domain cost and prove it is nonnegative; the threshold is the comparison level those costs are measured against.
proof idea
Pure definition: the real constant is written as phi - 3/2. No lemma applications, tactics, or proof obligations. Positivity and certificate packaging live in sibling declarations (canonicalThreshold_pos, RSSTDStructural009Cert).
why it matters
Gives a single named cutoff for structural Standard Model checks in the RS ledger. With φ ≈ 1.618, the value sits near 0.118, a small positive scale consistent with cost defects measured in J-units rather than an ad hoc SM parameter. It sits downstream of T6 (φ forced) and upstream of the module’s certificate inhabitants that assert domain costs clear this bar. No paper proposition number is attached in-source; the landmark link is the T5–T8 forcing chain stated in the module header.
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