canonicalThreshold
plain-language theorem explainer
Defines the canonical cost threshold as φ − 3/2 for the structural physics certificate at recognition rung 96. Anyone checking domain-cost bounds or the M96 structural cert cites it. The body is a one-line arithmetic definition from the golden ratio constant.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of Recognition Science.
background
Recognition Science forces a unique dimensionless cost $J$ and a unique self-similar scale $\varphi$ (forcing chain T5–T6). Structural certificates package domain-level predictions at fixed recognition rungs; this module is the physics certificate at rung 96 (Plan v7, structural theorem, zero sorry).
Sibling definitions introduce a nonnegative domain cost and compare it against a fixed real cutoff. The cutoff used throughout the module is this canonical threshold, built directly from the imported constant $\varphi$ (from Constants) rather than from an ad-hoc numerical band.
proof idea
Definition only: the real is definitionally equal to $\varphi - 3/2$. No lemmas, tactics, or proof obligations. Downstream positivity or comparison facts (e.g. that the threshold is positive) are separate declarations.
why it matters
Gives the single numeric gate used by the structural physics certificate at rung 96. It ties the local cost comparison to the same $\varphi$ that appears in the mass ladder, eight-tick octave, and RS-native constants, so the M96 cert stays inside the forced scale rather than an external cutoff. Parent usage is the module certificate and any lemma that needs a positive threshold against domain cost; no external paper proposition is attached beyond the module’s structural claim.
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