Evidence Resolution: Certifying How Much Personalization Finite Evidence Can Support

Flexible treatment-effect learners can propose action rules more finely than finite randomized evidence can defend. We formalize evidence resolution: the finest clinically worthwhile action granularity supportable by a representation and prespecified evidential criterion. A symmetric one-signal oracle yields the worst-case frontier $np{d}^2=\Theta (\log M)$; instance-dependent theory separates exact localization from value-tolerant localization and yields a search-versus-multiplicity crossover against exhaustive certification. HonestER freezes representation choices upstream and independently certifies refinements with family-local backoff. A prospectively locked Criteo model for exact reference-best recovery plus certification failed as specified. The decomposition explains why: at the finest depth, selected regions certified in 94% of runs but matched the empirical reference-best bin only 40%, while the leading bins were only 0.35 standard errors apart. Post hoc, a zero-fit certification-resolution prediction from frozen reference geometry matches the observed $R_{80}$ at 8 of 11 sample sizes and misses the other three by one bit. This supports a central distinction: certifiable resolution, exact localization, and deployed value are different statistical objects.