canonicalThreshold_pos

This module closes the T0–T8 forcing chain as a structural theorem (zero sorry, zero axiom): uniqueness of the J-cost, the Recognition Composition Law, φ as the self-similar fixed point, the eight-tick octave, D = 3, and the derived constants through Λ. The local objects include a domain cost and a canonical threshold against which that cost is compared.

The only upstream fact used here is the tighter lower bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$ so that $(1+\sqrt{5})/2 > 3/2$. In RS-native units φ is the unique positive fixed point forced by self-similarity (T3/T6 in the chain), and positivity of any threshold built linearly from φ is the first arithmetic check before cost comparisons.

One-line wrapper. Unfold the definition of the canonical threshold, then apply linarith to the hypothesis $\varphi > 1.5$ from phi_gt_onePointFive. No further lemmas are required; the inequality is pure real-linear arithmetic once the threshold is expanded in φ.

Positivity of the canonical threshold is a tiny but necessary arithmetic gate in the Forcing Chain Completeness certificate (siblings ForcingChainComp3Cert, cert, cert_inhabited). Without $t > 0$, domain-cost nonnegativity and threshold comparisons in the same module are meaningless. It sits under the structural T0–T8 package that derives the physical constants from J, including φ-forcing and the eight-tick octave. No downstream consumers are recorded yet; the lemma is infrastructure for the local completeness cert rather than a widely reused identity.