canonicalThreshold_pos

This module is a Recognition Science structural certificate for a domain-coverage milestone (Plan v7, 109th pass). It sits in the physics layer and imports only Mathlib, the RS constants, and the cost functional. Status is fully proved: zero sorry, zero axioms.

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 used here records the tighter numerical bound $\varphi > 1.5$, which follows at once from $\sqrt{5} > 2$.

Sibling definitions in the same file introduce a domain cost, the canonical threshold itself, and a milestone certificate bundle. Positivity of the threshold is the elementary arithmetic fact needed before any comparison of costs to that cutoff can be stated.

One-line wrapper. Unfold the definition of the canonical threshold, then apply linarith to the single upstream fact $\varphi > 1.5$ (phi_gt_onePointFive). No further case splits or RS identities are required; ordinary real linear arithmetic closes the goal.

The declaration is a local arithmetic lemma inside the FinalModule_1398 milestone certificate. That module packages a structural theorem asserting domain-coverage readiness for the Recognition framework. Without a strictly positive threshold, later comparisons of domain cost against the cutoff would be ill-posed.

No downstream dependents are recorded yet; the lemma exists to discharge the positivity obligation inside the sibling certificate constructors (MilestoneCert, cert, cert_inhabited). It does not itself touch the forcing chain T0–T8, the Recognition Composition Law, or the mass ladder, but it keeps the physics-layer milestone free of sorry.