canonicalThreshold
plain-language theorem explainer
Defines the canonical recognition threshold as φ − 3/2 in real units. Structural Physics certificate work at rung 86 cites it when comparing domain costs to a fixed cutoff. The body is a one-line abbreviation of that real constant; no proof obligations.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the golden-ratio fixed point of the Recognition self-similarity relation.
background
Module Structural_Physics_mod86 packages a structural Recognition Science certificate for the Physics domain at recognition rung 86 (Plan v7, status: structural theorem, zero sorry, zero axiom). It imports Constants (for φ) and Cost (for the J-cost and related domain cost functionals).
In the RS forcing chain, T6 fixes φ as the unique self-similar scale; costs and mass rungs are measured on the φ-ladder. Sibling definitions in this file introduce a domain cost functional and prove it is nonnegative; the threshold here is the fixed real cutoff those costs are compared against.
Numerically φ ≈ 1.618 so φ − 3/2 ≈ 0.118, a small positive scale sitting between the Berry creation threshold φ⁻¹ and ordinary O(1) cost values.
proof idea
Bare definition: the name is bound to the real expression φ − 3/2. No tactics, no lemmas, no hypotheses. Downstream positivity is handled by the sibling lemma that this quantity is strictly positive.
why it matters
Gives the Physics-domain structural certificate a single named cutoff against which domain costs are judged at rung 86. That keeps the certificate's comparison arithmetic uniform and φ-native rather than an ad hoc numeric magic constant.
It sits downstream of T6 (φ forced) and the Cost layer, and upstream of the certificate packaging (StructPhysicsM86Cert / cert). It does not itself close a forcing-chain step; it is local infrastructure for the mod-86 structural prediction.
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