canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold constant is strictly positive. Anyone wiring domain-cost gates or threshold comparisons in the RS forcing chain cites this non-degeneracy fact. Proof is a one-line wrapper: unfold the definition, then linear arithmetic from φ > 1.5.
Claim. The canonical threshold $T$ (the real constant defined from the golden ratio $\varphi$ in this module) satisfies $0 < T$.
background
Foundation RS Module 6 packages structural facts for the forcing chain with config dimension $D=3$ read off the eight-tick period $2^3$, forced with no free parameters (status: structural theorem, zero sorry, zero axiom).
The golden ratio $\varphi=(1+\sqrt{5})/2$ is the self-similar fixed point of the Recognition cost calculus (forcing landmark T6). Constants supplies the tighter numerical bound $\varphi>1.5$, proved from $\sqrt{5}>2$. The canonical threshold is a real constant defined from $\varphi$ in this module (sibling of domainCost); positivity is the elementary gate before any strict cost comparison against that threshold.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then close by linarith using the upstream lemma $\varphi>1.5$ (phi_gt_onePointFive). No further case splits or Recognition-Composition identities are required.
why it matters
Supplies the basic positivity fact for the canonical threshold inside Foundation Module 6 of the RS forcing chain. The ambient module is the structural package for $D=3$ from the eight-tick octave (landmarks T7 period $2^3$, T8 spatial dimension three). Sibling certificate objects (RSForcingChain006Cert, cert_inhabited) collect such elementary gates. No downstream dependents are recorded in the graph yet; the lemma is infrastructure for any later comparison that treats the threshold as a strict barrier rather than a soft cutoff. It does not itself force $D=3$ or $\varphi$; those sit upstream in the T0–T8 chain.
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