canonicalThreshold_pos
plain-language theorem explainer
The canonical collapse threshold built from the golden ratio is strictly positive. Anyone assembling the J-cost wavefunction-collapse certificate cites this positivity side-condition. The proof is a one-line unfold of the threshold definition followed by linear arithmetic from the bound φ > 1.5.
Claim. The canonical threshold (the RS-native collapse threshold expressed in terms of the golden ratio $\varphi$) is strictly positive: $0 < T_{\mathrm{can}}$.
background
The ambient module develops structural theorems for objective (GRW-style) wavefunction collapse from the Recognition Science J-cost. The stated objective rate is $\lambda = J(\varphi)/(m_{\mathrm{nucleon}}\varphi^{20})$, treated as a structural identity rather than a fitted phenomenological match.
The golden ratio is $\varphi=(1+\sqrt{5})/2$. The sole upstream input is the tighter lower bound $\varphi>1.5$, obtained from $\sqrt{5}>2$. The canonical threshold is a named real constant in the same module, defined by unfolding in terms of $\varphi$ (or a simple rational expression in $\varphi$); positivity of that expression is the claim here.
Sibling facts in the module establish nonnegativity of the domain cost and package a collapse certificate; this lemma supplies the strict positivity half of the threshold data.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then invoke linarith on the single upstream lemma $\varphi>1.5$. No case split, no induction, and no appeal to the full J-cost algebra: once the threshold is expanded, the inequality is a trivial linear consequence of the bound on $\varphi$.
why it matters
Positivity of the canonical threshold is a required side-condition for the wavefunction-collapse certificate (WFCollapse3Cert / cert) assembled in the same module. The module is marked structural (zero sorry, zero axiom) and sits in the physics layer that connects the J-cost (forcing-chain T5) and the forced self-similar fixed point $\varphi$ (T6) to an objective collapse rate.
The module documentation is explicit that the naive GRW numerical evaluation is off by roughly 38 orders of magnitude; the present lemma does not close that gap. It only guarantees that the RS-native threshold constant is a positive real, so the certificate is well-formed. No downstream theorems outside the module currently depend on it; it is a local structural brick.
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