canonicalThreshold_pos
plain-language theorem explainer
The RS gravity canonical threshold is strictly positive. Gravity structural arguments that gate domain-cost comparisons or cutoffs on this constant can cite the inequality directly. The proof is a one-line unfold of the threshold definition followed by linear arithmetic from the bound φ > 1.5.
Claim. The canonical RS gravity threshold is strictly positive: $0 < T_{\mathrm{can}}$, where $T_{\mathrm{can}}$ is the real constant defined from the golden ratio $\varphi$ in this structural module.
background
Module RS_GRV_Structural_010 is a structural gravity layer in Recognition Science: $E_{\mathrm{coh}}$ is fixed once from the electron mass, and subsequent predictions are parameter-free. Status is a structural theorem block (zero sorry, zero axiom).
The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the unified forcing chain. Upstream, phi_gt_onePointFive records the elementary bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$. The canonical threshold is a real constant built from $\varphi$ in this module (sibling of the domain-cost definitions); positivity is the elementary gate needed before nonnegativity or comparison lemmas for domain cost can be used safely.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge $0 < T_{\mathrm{can}}$ by linarith using the upstream lemma $\varphi > 1.5$. No case split and no further Recognition identities are required.
why it matters
Structural gravity certificates in this module (the RSGRVStructural010 cert and its inhabited instance) need a positive cutoff before domain-cost comparisons are meaningful. The result sits in the gravity domain of the RS mirror and inherits the parameter-free calibration story: once $E_{\mathrm{coh}}$ is fixed by the electron, thresholds built from $\varphi$ are not free parameters. It does not itself invoke the Recognition Composition Law, the eight-tick octave, or $D=3$, but it keeps the $\varphi$-ladder arithmetic available to later GRV structural claims. No downstream edges are recorded yet; the immediate consumers are the sibling certificate constructions in the same file.
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