Identities, Not Pairs: Distribution-Free False-Accept Control for Embedding-Based Verification

Embedding-based verification often calibrates a false-accept threshold from all impostor pairs among $m$ identities, although these pairs share identities. We characterize a worst-case limit: when hub identities score highly against a fraction $ρ$ of the population, a calibration-only threshold with marginal false-accept rate (FAR) at most $α$ under every identity-exchangeable law reaches the hub score on hub-free calibration sets with probability at most $(m+2)α/(2ρ)$. Uniformly accepting near that score at levels well below $ρ/m$ therefore requires trial information. We propose COVE, which ranks the trial pair among all $N=\binom{m+2}{2}$ pairs formed by augmenting the calibration units with the probe and reference. Under identity exchangeability, its marginal FAR is at most $\lfloorαN\rfloor/N$, with first possible acceptance at $1/N=O(1/m^2)$. The rule also retains this guarantee with a fixed symmetric cohort-normalized score using an independent cohort. On 6 benchmarks and 8 frozen encoders, realised FAR was consistent with the exact bound. Where both valid calibration-only baselines accepted nothing, COVE retained a median $100\%$ of the sampled oracle's true-accept rate over reliable comparisons. In contrast, an empirical quantile over dependent pairs reached 2.87$\,α$ FAR, and a binomial upper confidence bound over pairs missed its nominal 95\% conditional-FAR target in up to 55\% of calibration draws. Symmetric CSLS raised COVE's true-accept rate by up to 4.3-fold in the tested settings. The code is available in https://github.com/salimkhazem/Cove.git