canonicalThreshold_pos

Module RS_STD_Structural_009 sits in the Standard Model layer of the Recognition Science forcing chain (T5 J-uniqueness through T8, D = 3). It packages a handful of elementary positivity and evaluation facts about a domain cost and a canonical threshold built from φ, then wraps them in a structural certificate with zero sorry and zero axioms.

The only external arithmetic fact used here is the tighter lower bound φ > 1.5 from Constants: since √5 > 2 one has (1 + √5)/2 > 3/2. That bound is strong enough for linear arithmetic once the threshold definition is unfolded. Sibling declarations in the same file introduce the domain cost, its non-negativity, and the threshold itself; this lemma is the positivity half of that package.

One-line wrapper. Unfold the definition of the canonical threshold, then invoke linarith on the single lemma phi_gt_onePointFive (φ > 1.5). No case splits, no induction, no further Recognition lemmas.

Positivity of the canonical threshold is a trivial but necessary gate for any later comparison of domain cost against that threshold inside the structural certificate RSSTDStructural009Cert. The module itself is marked STRUCTURAL THEOREM and sits on the T5–T8 forcing spine (φ uniqueness, eight-tick octave, D = 3). No downstream theorems currently list this lemma as a direct dependency, so its role is local: keep the certificate inhabited and the threshold usable as a strict lower cut. It does not itself advance mass formulae, α bounds, or the Recognition Composition Law.