canonicalThreshold_pos

This module treats vacuum energy density in Recognition Science units as $\rho_{\mathrm{vac}} = J(\varphi)/\varphi^5$, with the RS vacuum identified as the ground state of the recognition field (all $J = 0$). The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the unified forcing chain.

The only upstream fact used here is the tighter lower bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$. That bound is strong enough for linear arithmetic once the threshold definition is unfolded. Sibling material in the same file introduces a domain cost and nonnegativity lemmas that sit alongside this positivity statement.

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 case splits or field identities are required.

Positivity of the canonical threshold is a structural sign check inside the recognition-field vacuum development (Plan v7, structural theorem status: zero sorry, zero axiom). It underwrites any later comparison that treats the threshold as a strictly positive scale for domain cost or vacuum energy density $\rho_{\mathrm{vac}} = J(\varphi)/\varphi^5$.

In the broader framework it sits downstream of T5–T6 (J-uniqueness and $\varphi$ as fixed point) and the RS-native constants ($c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$). No downstream consumers are recorded yet in the graph; the lemma is local infrastructure for the vacuum certificate in this module.