canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold constant in the J-cost wave-particle module is strictly positive. Duality and complementarity certificates that normalize against this cutoff cite the fact. Proof is a one-line unfold plus linear arithmetic from the bound φ > 1.5.
Claim. The canonical threshold (the real cutoff defined from the golden ratio $\varphi$ in this module) satisfies $0 < \tau$.
background
The module develops wave-particle duality as a structural theorem from the J-cost: pure interference sits at $J=0$, pure detection at $J=1$, and RS complementarity is the continuous transition between those limits in cost space. Status is fully closed (zero sorry, zero axiom).
The golden ratio $\varphi=(1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the foundation chain. The only upstream fact used here is the tighter numerical bound $\varphi>1.5$ (from $\sqrt{5}>2$), which is enough to pin positivity of the module's canonical threshold after unfolding its definition.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge the resulting strict inequality by linarith using the lemma $\varphi>1.5$. No further case splits or cost identities are required.
why it matters
Positivity of the cutoff is the elementary gate for the wave-particle duality certificate built in this file (siblings WPDuality3Cert, cert, cert_inhabited). The parent program treats complementarity as a continuous J-cost transition rather than an on/off postulate, consistent with J-uniqueness (T5) and the forced $\varphi$ (T6). No downstream consumers are wired yet; the lemma is local scaffolding for the structural theorem stated in the module doc.
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