canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold used in the D=3 configuration-cost argument is strictly positive. Anyone comparing domain costs against that cutoff cites this bound. The proof is a one-line wrapper: unfold the definition and finish by linear arithmetic from φ > 1.5.
Claim. The canonical threshold is strictly positive: $0 < \tau$, where $\tau$ is the real constant defined from the golden ratio $\varphi$ in this module.
background
This module is the structural ConfigDim D3 v3 development: $D = 3$ is forced by 8-tick closure, since period $8 = 2^3$ means the recognition cycle closes after exactly three binary recursions, and that is the unique minimal self-similar lattice dimension.
The only external numeric fact used here is the tighter lower bound on the golden ratio from Constants: $\varphi = (1+\sqrt{5})/2$ satisfies $\varphi > 1.5$ (because $\sqrt{5} > 2$). The sibling definition canonicalThreshold is a $\varphi$-dependent real that serves as the cutoff against which domain costs are compared in the surrounding D=3 certificates.
proof idea
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 cost identities are required; positivity is pure arithmetic once the definition is expanded.
why it matters
Sits in the Foundation ConfigDim D3 v3 chain that realizes the T8 landmark: spatial dimension $D = 3$ forced by eight-tick octave closure ($2^3$). A positive canonical threshold is the elementary numeric gate that lets domain-cost comparisons be strict rather than weak, so later certificates in the same module can treat the cutoff as a genuine barrier. No downstream dependents are recorded yet; the lemma is local scaffolding for the inhabited D3 certificate in this file.
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