canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold on the D=3 recognition configuration space is strictly positive. Anyone comparing domain costs or setting cutoffs on C_3 would cite it. Proof is a one-line unfold of the threshold definition followed by linear arithmetic from φ > 1.5.
Claim. The canonical threshold (the explicit real cutoff built from $\varphi$ in the $D=3$ configuration-space module) is strictly positive: $0 < \tau_{\mathrm{can}}$.
background
The ambient module fixes the Recognition Science configuration space at spatial dimension three: $C_3=\mathbb{R}^3$ equipped with the recognition metric $ds^2=J(dx/x)$ on the positive orthant. That metric is the J-cost Riemannian structure; the module records it as positive definite for all $x>0$, and the whole file is marked a structural theorem (zero sorry, zero axiom).
The golden ratio $\varphi=(1+\sqrt{5})/2$ is the self-similar fixed point forced earlier in the chain. The only upstream fact used here is the tighter numerical bound $\varphi>1.5$, obtained from $\sqrt{5}>2$. The canonical threshold is the named real constant in this module against which domain costs are compared; positivity is the elementary gate before any comparison lemmas fire.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge the resulting linear inequality by linarith supplied with the lemma $\varphi>1.5$. No further Recognition identities are required.
why it matters
Supplies the positivity gate for the D=3 configuration-space certificate package (siblings ConfigSpaceD3Cert, cert, cert_inhabited). Without $0<\tau_{\mathrm{can}}$, domain-cost comparisons and threshold cuts on $C_3$ are ill-posed. It sits under the structural D=3 layer (forcing landmark T8) and the J-cost metric on the positive orthant; it does not itself invoke the Recognition Composition Law or the eight-tick octave. The dependency graph currently shows no downstream consumers, so the lemma is infrastructure waiting on later cost or certificate arguments.
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