LLMs can solve hard math now， but checking whether a proof is actually correct is still shaky， and verification sits at the center of every math agent workflow and RL loop. Rule-based checks miss open-ended proofs； LLM verification is unreliable and expensive， sometimes thousands of API calls for one IMO-level problem.🤔 Pessimistic Verification from @TsinghuaNLP （OpenBMB member）， to appear at ICML 2026， pins the real bottleneck on error detection and builds a simple fix around it. Paper： https://arxiv.org/abs/2511.21522 Code： https://github.com/THUNLP-MT/pverify

1⃣️ The core idea： verify one proof many times in parallel and reject it the moment any run reports an error. Detecting an error is a low-probability event， so aggregating pessimistically amplifies it； since models reason soundly before flagging errors， true false negatives are rare. Majority voting， by contrast， barely helps here. 2⃣️ Three variants from whole-proof to fine-grained. Simple （pes@n） repeats standard verification in parallel； vertical （vp@k） splits the proof into k-line chunks for focused review； progressive （prog@n/k） does multi-scale checking， filtering obvious errors first then drilling into steps， with natural pruning. Progressive gives the best performance and efficiency. 3⃣️ It lifts TNR and Balanced F1 across IMO-GradingBench， Hard2Verify， and their new QiuZhen-Bench， and its token efficiency beats long CoT. At matched performance， progressive uses roughly a quarter of the tokens， runtime， and cost of the parallel verification common in agent workflows. 4⃣️ The twist： most false negatives from GPT-5-mini and stronger models are real critical errors the dataset annotators missed， so benchmarks underestimate strong verifiers. On IMO 2025 with Gemini 3 Pro， a verification-based workflow goes 13 → 22 points with progressive， using fewer tokens than simple parallel verification.