canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold constant of the rung-96 structural physics certificate is strictly positive. Anyone assembling domain-cost comparisons or the Physics structural certificate at that rung cites this positivity. The argument is a one-line wrapper: unfold the threshold and finish by linear arithmetic from the bound φ > 1.5.
Claim. The canonical threshold $T$ used by the structural physics certificate at recognition rung 96 satisfies $0 < T$.
background
The ambient module is the Recognition Science structural certificate for the Physics domain at recognition rung 96 (Plan v7, 120th pass). It is marked as a structural theorem block: zero sorry, zero axioms. Sibling definitions introduce a domain cost functional and a canonical threshold against which that cost is compared.
The only external arithmetic input is the golden ratio $\varphi = (1+\sqrt{5})/2$, the self-similar fixed point forced at T6 of the unified forcing chain. The upstream lemma phi_gt_onePointFive records the elementary bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$. That lower bound is enough to force the unfolded threshold expression to be positive by linear arithmetic.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then invoke linarith on the single hypothesis that $\varphi > 1.5$. No further case splits or Recognition-Composition identities are required.
why it matters
Positivity of the canonical threshold is a local hygiene lemma for the Physics structural certificate at rung 96. Without it, comparisons of the domain cost against the threshold would be ill-typed or meaningless as strict inequalities. The module presents that certificate as a structural RS prediction (0 sorry, 0 axiom). No downstream consumers are recorded yet; the lemma sits inside the certificate infrastructure rather than on the main T0–T8 forcing spine. It does not itself force $\varphi$, the eight-tick octave, or $D=3$; it only uses the already-established bound $\varphi > 1.5$.
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