canonicalThreshold_pos
plain-language theorem explainer
The canonical short-GRB threshold constant in this module is strictly positive. Anyone citing the RS short-duration window (φ^{-2}–φ^{-1} s) needs that positivity as a structural side condition. Proof is a one-line unfold of the threshold definition followed by linarith from the bound φ > 1.5.
Claim. The module's canonical threshold (the φ-derived positive real that anchors the short-GRB duration window) satisfies $0 < T_{\mathrm{can}}$.
background
Astrophysics RS Module 6 records the short gamma-ray burst duration band as $\varphi^{-2}$ to $\varphi^{-1}$ seconds (about 0.382–0.618 s, inside the observational 0.1–2 s range). The module is marked a structural theorem stack: zero sorry, zero extra axioms.
The golden ratio $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point forced at T6 of the Recognition forcing chain. The only upstream fact used here is the elementary tightening $\varphi > 1.5$, which follows at once from $\sqrt{5} > 2$. The canonical threshold is the named real constant in this file against which the short-duration window is measured; sibling lemmas also record nonnegativity of the domain cost functional built from the RS J-cost.
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then discharge the resulting inequality by linarith using the imported lemma $\varphi > 1.5$. No further case splits or Recognition-Composition identities are required.
why it matters
Supplies the positivity half of the short-GRB structural certificate (RSAstro006Cert / cert_inhabited in the same module). Without $T_{\mathrm{can}} > 0$ the duration window would be ill-posed as a positive-time interval. The result sits downstream of the T6 forcing of $\varphi$ and the elementary bound $\varphi > 1.5$; it does not itself re-derive the eight-tick octave or the mass ladder. No external used_by edges are recorded yet, so its present role is local certification inside Module 6.
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