canonicalThreshold
plain-language theorem explainer
The canonical threshold is the real constant φ − 3/2. It sits in RS Physics Module 3 (neutron lifetime φ^17·0.246 s ≈ 878.5 s vs PDG). Cite it when fixing the numeric gate for domain-cost comparisons in this module. The declaration is a bare definition equal to that closed form.
Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).
background
RS Physics Module 3 records a structural neutron-lifetime match: $\varphi^{17}\cdot 0.246,\mathrm{s}=878.5,\mathrm{s}$ against PDG $878.4,\mathrm{s}$, status STRUCTURAL THEOREM (no sorry, no axiom). The module imports Constants (for $\varphi$) and Cost (J-cost and related defect machinery).
In Recognition Science, $\varphi$ is forced at T6 as the unique self-similar fixed point after J-uniqueness (T5: $J(x)=(x+x^{-1})/2-1$). Thresholds built from $\varphi$ set dimensionless gates for when a cost or defect is treated as active. The sibling domainCost and the positivity lemma on this threshold live in the same file; this definition supplies the numeric cut those statements use.
proof idea
No proof. The declaration is a one-line definition: the real constant equal to $\varphi-3/2$. Downstream lemmas (e.g. positivity) reason about that value; nothing is derived here.
why it matters
Gives a single named real gate for Module 3 physics comparisons instead of scattering the literal $\varphi-3/2$. The module’s neutron-lifetime certificate and the sibling positivity/domainCost facts are the natural consumers. Framework-wise it is a local φ-scale threshold, not a forcing-chain step (T0–T8) and not the Berry creation threshold $\varphi^{-1}$. It keeps the structural neutron-lifetime claim numerically tidy without adding axioms.
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