canonicalThreshold_pos

FinalModule_1397 is a Recognition Science structural certificate module (Plan v7, 109th pass): zero sorry, zero axioms, aimed at a domain-coverage milestone. Sibling definitions introduce a domain cost and a canonical threshold built from the RS constant $\varphi$.

In RS units $\varphi$ is the golden ratio $(1+\sqrt{5})/2$, forced earlier in the T0–T8 chain as the self-similar fixed point (T6). The only upstream lemma used here is phi_gt_onePointFive: "$\varphi > 1.5$ (since $\sqrt{5} > 2$, so $(1+\sqrt{5})/2 > 1.5$)." That stricter lower bound, rather than the weaker $\varphi > 1$, is what makes the threshold expression positive by linear arithmetic after unfolding.

One-line wrapper. Unfold the definition of the canonical threshold, then discharge $0 < \cdots$ by linarith using the single fact $\varphi > 1.5$. No case splits, no induction, no further RS identities.

Supplies the positivity side-condition for the canonical threshold inside the FinalModule_1397 domain-coverage certificate. The module status line calls the whole package a structural theorem with empty axiom surface; this lemma is the elementary arithmetic hinge that keeps the threshold well-formed as a positive real cutoff.

No downstream consumers are recorded yet (used_by empty), so the result is presently a local certificate ingredient rather than a widely reused lemma. It sits downstream of the Constants layer (φ bounds) and upstream of any milestone certificate that assumes a positive domain threshold. It does not itself touch T5–T8, the RCL, or the mass ladder; it only polices a numeric gate those structures may later use.