canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold used for RS cosmology rung spacing is strictly positive. Structural cosmology certificates rely on this to keep the threshold above zero when adjacent rungs scale by φ. Proof is a one-line unfold plus linear arithmetic from the bound φ > 1.5.
Claim. The canonical threshold constant built from the golden ratio $\varphi$ in this module is strictly positive: $0 < \tau_{\mathrm{can}}$.
background
This module records structural facts for Recognition Science cosmology rung spacing: adjacent mass/energy rungs differ by the fixed factor $\varphi = (1+\sqrt{5})/2 \approx 1.618$. The status line is a pure structural theorem (no sorry, no axioms).
The golden ratio enters from Constants. The only upstream lemma used here is the tighter lower bound $\varphi > 1.5$, proved from $\sqrt{5} > 2$ via $(1+\sqrt{5})/2 > 3/2$. The canonical threshold is a real constant defined from $\varphi$ in this file; positivity is the minimal arithmetic fact needed before comparing domain costs or certificate bounds against it.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge $0 < \tau_{\mathrm{can}}$ by linarith using the imported lemma $\varphi > 1.5$. No case splits or further Recognition identities are required.
why it matters
Keeps the structural certificate stack for RS cosmology module 8 on a positive threshold when rungs scale by $\varphi$. That matches the forcing-chain landmark T6: $\varphi$ is the self-similar fixed point that sets rung spacing. Sibling definitions (domainCost, nonnegativity, the certificate bundle) sit next to this fact; nothing downstream is wired yet in the graph, so this is a local positivity gate rather than a deep mass-ladder theorem. It does not touch $\alpha$, $D=3$, or the eight-tick octave.
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