canonicalThreshold_pos
plain-language theorem explainer
The canonical threshold constant of RS astrophysics module 4 is strictly positive. Anyone comparing domain costs or certifying the Jupiter-period structural match needs this positivity fact. The proof is a one-line unfold-and-linarith wrapper off the bound φ > 1.5.
Claim. The module's canonical threshold constant satisfies $0 < \tau_{\mathrm{can}}$.
background
RS Astrophysics Module 4 is a structural certificate linking the Jupiter sidereal period to the golden-ratio ladder: $\varphi^5$ yr $\approx 11.09$ yr versus the observed $\approx 11.86$ yr (about 6.5%). Status is structural theorem (no sorry, no axiom).
The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the unified forcing chain. The upstream lemma supplies the tighter real bound $\varphi > 1.5$, obtained from $\sqrt{5} > 2$. The canonical threshold is the module-local constant against which domain costs are compared; its positivity is the elementary arithmetic fact recorded here.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge the resulting linear inequality by linarith using the single upstream fact $\varphi > 1.5$. No case splits or further lemmas.
why it matters
Positivity of the threshold is a prerequisite for any non-vacuous comparison of domain costs inside this module and for the inhabited certificate RSAstro004Cert. The module itself sits on the $\varphi$-ladder mass/period formula (yardstick times $\varphi^{\mathrm{rung}}$) and on the structural identification $Z_{\mathrm{cf}} = \varphi^5 \in (11,12)$ from the Recognition Science primer. No downstream theorems currently depend on this lemma in the graph, so it is local scaffolding for the module certificate rather than a global forcing-chain step.
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