Theorem: Certified isoacute eligibility

If a calibration estimate has simultaneous error radius $r_c$, then

certifies acute eligibility.

If each of two selected candidates is eligible, their actual acute endpoints differ by at most $2{ϵ}_A$. Conditionally fresh post-selection assessment supports Theorem thm:sequencehoeffding for their secondary outcomes.

For a ratio endpoint, replace the scalar-radius criterion by containment of its certified ratio interval in the target tolerance interval.

Proof. Use the triangle inequality. For the secondary endpoint, condition on the calibration and selection history; the new assessment sequences remain fresh. Interval containment proves the ratio statement.