canonicalThreshold
plain-language theorem explainer
Defines the canonical threshold as the real number φ − 3/2, with φ the golden-ratio fixed point of Recognition Science. It is a bare numeric cutoff inside the structural π–φ relation module (π ≈ 4/√φ). Anyone working the domain-cost certificates or the positivity lemma for this cutoff would cite it. The body is a one-line definition, not a proof.
Claim. Let $\varphi$ be the golden ratio. The canonical threshold is the real constant $\varphi - 3/2$.
background
Recognition Science forces $\varphi$ as the unique self-similar fixed point of the cost calculus (forcing step T6). In RS-native units the same $\varphi$ generates the geometric constants ($c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$).
This module records a structural approximation $\pi\sim 4/\sqrt{\varphi}$ (relative error about $0.15%$). Sibling declarations introduce a domain cost built from the $J$-cost and prove that cost is nonnegative; the present definition supplies a simple $\varphi$-native cutoff against which those costs can be compared.
No upstream lemmas are required: the right-hand side is just arithmetic in the constants module.
proof idea
One-line definition. The name is bound to the real expression $\varphi-3/2$; there are no proof obligations, tactics, or lemmas.
why it matters
Gives a concrete positive scale (used by the sibling positivity statement) inside the zero-sorry π–φ structural package. It sits with the other RS geometric landmarks: the eight-tick octave, $D=3$, and the $\varphi$-ladder mass formula, all of which treat $\varphi$ as the sole free scale. Downstream use is local to this module’s certificates; no external edges are recorded yet.
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