A test set may already be in the training data: accurate evaluation is possible only when the distribution concentrates on few points
Large-model training corpora often cover public benchmarks, so evaluators can no longer assume a fresh test set. This work formalizes evaluability without assuming the test set was held out and without constraining the model or its training algorithm, showing that accurate evaluation from model outputs on the test set alone is feasible if and only if the distribution is close to small support, with sample-complexity bounds tight up to logarithmic factors; allowing extra queries to the model, via self-correctors from program testing, widens the evaluable distributions.