canonicalThreshold_pos
plain-language theorem explainer
The canonical restoration threshold used in RS ethics is strictly positive. Anyone invoking the partial-repair bound (acceptable when the J-cost stays below the golden-ratio scale) cites this fact. The proof is a one-line wrapper: unfold the threshold definition and finish by linear arithmetic from φ > 1.5.
Claim. The canonical ethics threshold is strictly positive: $0 < \tau$, where $\tau$ is the acceptable partial-restoration cutoff in the RS restorative-justice calculus (the scale set by the golden ratio $\varphi$).
background
The module develops RS ethics as restorative justice: restore sigma balance. Full repair is the zero of the J-cost, $J(\mathrm{harm_repaired}/\mathrm{harm_done}) = 0$. Partial restoration is allowed when the residual cost stays positive yet below the golden-ratio scale $J(\varphi)$ (the acceptable threshold).
$J$ is the unique nonnegative cost forced by the Recognition Composition Law (T5): $J(x) = (x + x^{-1})/2 - 1$. The constant $\varphi = (1+\sqrt{5})/2$ is the self-similar fixed point (T6). The threshold itself is a named real built from $\varphi$; positivity is the first structural fact needed before certificates can compare residual costs against it.
Upstream, phi_gt_onePointFive supplies the tight decimal bound $\varphi > 1.5$ (from $\sqrt{5} > 2$).
proof idea
One-line wrapper. Unfold the definition of the canonical threshold, then apply linarith to the single lemma $\varphi > 1.5$. No further cost identities or case splits are required; the unfolded expression is an affine form in $\varphi$ whose positivity is immediate from that lower bound.
why it matters
Places a strictly positive cutoff inside the RS ethics layer so partial-restoration comparisons are well-posed. The module status is structural theorem (0 sorry, 0 axiom). Sibling certificates (RestorationJust4Cert, cert, cert_inhabited) sit on the same threshold; without positivity those comparisons are vacuous.
Framework landmarks: T5 J-uniqueness and T6 forcing of $\varphi$ fix the scale; the eight-tick and $D=3$ steps are not used here. No downstream edges are recorded yet, so this is a leaf positivity fact waiting on the restoration-certificate chain.
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