canonicalThreshold_pos

This module packages a structural Recognition Science certificate for the Physics domain at recognition rung 76 (Plan v7, 120th pass). Status is a pure structural theorem: zero sorry, zero axioms. Nearby siblings define a domain cost, its nonnegativity, and the canonical threshold itself; the present lemma only records positivity of that threshold.

The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced by the T5–T6 segment of the unified forcing chain. The Constants library supplies the elementary bound $\varphi > 1.5$, proved from $\sqrt{5} > 2$. After unfolding, the canonical threshold is an affine expression in $\varphi$ whose positivity is immediate from that bound.

One-line wrapper. Unfold the definition of the canonical threshold, then invoke linarith on the single upstream fact phi_gt_onePointFive ($\varphi > 1.5$). No further case splits or algebraic identities are required.

Positivity of the canonical threshold is the elementary scale fact needed before domain-cost nonnegativity and the inhabited structural certificate (StructPhysicsM76Cert / cert_inhabited) can be assembled for Physics at rung 76. It sits downstream of the Constants bound on $\varphi$ and upstream of any certificate that treats the threshold as a strictly positive yardstick. In the broader framework it is a local arithmetic consequence of T6 ($\varphi$ forced as the self-similar fixed point), not a new physical prediction. No downstream edges are recorded yet; the lemma is consumed inside the same module’s certificate construction.