By: Kaapo Seppänen <seppanenkaapo@gmail.com>
certify signed radial roots with binary64 bounds first Write the directed affine-energy enclosures once over a DirectedBound trait. MPFR at 2048 bits remains the reference certificate; binary64 bounds (nearest rounding stepped one ulp outward) run the same isolation, convex origin check and bracket sign checks first. Anything binary64 leaves unresolved falls back to the unchanged reference pass before any Newton solve, so uncertainty is still never read as an absent root. Natively equal velocities share one radical at r = infinity, and the MPFR helpers use sign-case products and shared endpoint data. Binary64 brackets may differ from reference brackets, so a lane can return certified roots where the reference bracket would fail and escalate precision (about 3e-5 of synthetic thermal rays, none at integrand points). Thermal QCD vector NLO runs about 25x faster per sample (6.44 -> 0.246 ms and 29.5 -> 1.18 ms at two fixed points), Quad-only about 9x and vacuum about 3x, with bit-identical results and fixed-seed integrations. Validation: fmt, Clippy, docs check/build, and the ci-optim nextest selection (1727 passed; the two known raised_cross_section_tests LU host-plan failures are pre-existing).