One-Sided Verification Under Limited Expert Review

AI has become increasingly helpful in scientific discovery, yet human expert review remains essential for those problems without reliable automated evaluation, posing a fundamental challenge as candidate generation scales beyond available review capacity. This paper studies verification under limited human effort, where rare valid solutions need to be prioritized while invalid candidates should be filtered out to reduce human workload. We adopt the one-sided verification objective that maximizes the rejection rate of invalid solutions (TNR) under a constraint on the false-rejection rate of valid ones (FNR), making human review cost an explicit term to minimize. Drawing on the intuition that verifying a specific error can be easier than discovering one, we introduce OSVerify, an algorithmic framework that decouples error proposal from error validation. The error proposer searches for errors in solutions across different granularities by hierarchical decomposition, while the validator distinguishes substantial errors from minor or hallucinated ones. Experiments on competition- and research-level benchmarks show that OSVerify reduces the number of human reviews of invalid solutions by 46% on average compared to voting baselines under the same empirical low FNR constraint. Our post-training of the validator further improves the reduction to 57%. As high-impact real-world use cases, we apply OSVerify to identify errors in published research papers that are subsequently confirmed by the original authors and help resolve three Langlands open conjectures that are confirmed by experts, demonstrating its utility to facilitate human-AI research collaboration.