canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold appearing in the domain-coverage milestone is strictly positive. Structural certificates in FinalModule_1399 cite this fact whenever a cost or coverage bound needs a positive floor. The proof is a one-line wrapper: unfold the definition, then linear arithmetic from φ > 1.5.
Claim. The canonical threshold (the real constant defined from $\varphi$ in this milestone module) is strictly positive: $0 < t_{\mathrm{can}}$.
background
FinalModule_1399 is a Recognition Science milestone module: a structural certificate for domain coverage (Plan v7, 109th pass), with status STRUCTURAL THEOREM (zero sorry, zero axiom). It sits in the Physics layer and imports Constants and Cost.
The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the unified forcing chain. The upstream lemma phi_gt_onePointFive records the tighter numerical bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$. The canonical threshold is a real constant defined in this module from $\varphi$ (sibling of domainCost); positivity is the elementary arithmetic consequence needed before any coverage or cost comparison can fire.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then apply linarith to the resulting arithmetic inequality, feeding in the single upstream fact $\varphi > 1.5$. No case splits or further lemmas.
why it matters
Supplies the positivity floor for the domain-coverage structural certificate packaged in this module (siblings MilestoneCert, cert, cert_inhabited). Without $t_{\mathrm{can}} > 0$, cost comparisons and coverage inequalities in the milestone cannot start. The argument rests only on the T6 constant $\varphi$ and its elementary lower bound; it does not touch the RCL, eight-tick octave, or mass ladder. No downstream consumers are recorded yet; the lemma is local glue inside the milestone certificate.
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