canonicalThreshold
plain-language theorem explainer
Defines the canonical real threshold as φ − 3/2 (≈ 0.118). Domain-coverage and milestone certificates in this physics module cite it as the fixed cutoff against which domain cost is compared. The body is a one-line real abbreviation from the RS constant φ.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ is the Recognition Science self-similar fixed point (golden ratio).
background
This module is a Plan v7 structural milestone certificate for domain coverage: zero sorry, zero axioms. It sits in the physics layer and imports RS constants and the cost calculus.
The constant $\varphi$ is the unique self-similar fixed point forced at T6 of the unified forcing chain; numerically $\varphi = (1+\sqrt{5})/2$. Sibling definitions package a domain cost functional and a positivity lemma for this same threshold. In RS units the cost side is built from the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), whose uniqueness is T5.
The threshold value $\varphi-3/2$ is therefore a pure RS-native cutoff expressed in the same units as those cost comparisons, not an external SI constant.
proof idea
No proof. The declaration is a definitional abbreviation: the real canonicalThreshold is definitionally equal to phi - 3/2 from the constants module. Downstream lemmas (e.g. positivity) unfold this equality and reason about the resulting real.
why it matters
Gives the milestone module a single named cutoff so domain-cost comparisons and the MilestoneCert package stay uniform. It is the numeric hinge between the φ-ladder geometry (T6) and the structural domain-coverage certificate this file asserts. Sibling canonicalThreshold_pos and the inhabited certificate cert consume it; without a shared name those comparisons would re-inline φ − 3/2 ad hoc. It does not itself close a forcing-chain step (T0–T8), but it is the local scale against which this physics milestone checks coverage.
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