Calibrating Verified Task Sets with Limited Measurements

A learned controller can meet a task specification on several disconnected regions of physical parameter space. With few calibration measurements, a generic confidence interval may certify none of those regions. We study how a verified task set can instead determine a fixed-task acceptance rule. For a scalar Gaussian estimate, we reduce the worst unsafe-parameter risk to finitely many boundary evaluations when every acceptance component is separated from its boundary by at least one standard error. The result supports component-specific radii; maximizing a same-component power objective then becomes a convex optimization problem. Exact-rational inner-set verification connects the statistical calculation to repeated feedback with a shared uncertain restitution coefficient. On 63 tasks from 15 learned controllers, four-measurement acceptance increases from 41.0% with a gap-based test to 44.0% with a common boundary-calibrated radius and 44.7% with component allocation. Eight tasks change from zero to positive acceptance. Tighter-tolerance experiments locate this benefit in the narrow-component regime, and an independent checkpoint study compares calibration-aware selection with imitation and task-loss selection. Matched composite-null, continuum-search, and conformal controls identify which gains require Gaussian information and which are computational. The contribution is a calibrated post-training validation procedure under explicit model and measurement contracts, rather than a guarantee of unrestricted physical transfer.