Validity by Design: The Price of Safe Early Stopping in Closed-Loop Battery Testing

Finding longer-lived lithium-ion batteries means cycling candidate cells until they wear out, weeks to months of channel time each. A campaign can save that time by choosing each next candidate from earlier results and stopping unpromising tests early, but a stop is irreversible and destroys the evidence that a design would have succeeded. Conformal prediction bounds the rate of such false stops in finite samples when the calibration cells are exchangeable with the cell being judged, and Bayesian optimization breaks that exchangeability. We rebuild it by design with the ε-stream, which sends each freed channel slot to a calibration cell with probability ε, drawn from a pre-registered sequence the optimizer never reads, so the conformal weights are exactly known and the certified modes carry finite-sample guarantees for the rule as deployed. We prove a ladder of such guarantees, each priced in channel time, calibration cells or delay, together with two classical floors and one impossibility, since on calibration pools holding a fixed number of cells per design those weights admit no distribution-free guarantee exact at every level. Replaying five public battery corpora, we find that successive halving, a heuristic from prior battery-testing frameworks, falsely stops as many as 96% of good cells, while our audit-only weighted rule stays within α on every seed of the unbudgeted replays; the certified modes' covered first stops reach about 1% of off-spec cells, so at these calibration sizes a certificate costs more channel time than early stopping saves.