{"id":"9b8bf464-6e6d-4b73-967d-5cac0788cff5","arxiv_id":"2607.11849","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A 245-problem advanced proof benchmark plus 888 expert-labeled trajectories shows frontier LLMs remain far from reliable advanced proof generation and verification.","lead":"AdvancedMathBench is a new suite for testing whether large language models can write and check advanced math proofs, not just final answers. It shows frontier models still fail often on undergrad and qualifying-exam proofs and are weak at catching subtle errors.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Headline scores for both generation and verification rest on an only partially validated auto-verifier plus a weak gpt-oss-120b meta-verifier, so the reported gaps may partly be judge artifacts.","rationale":"The reader’s weakest-assumption diagnosis is exactly the load-bearing point: the entire empirical narrative is mediated by the trained auto-verifier and the gpt-oss-120b meta-verifier. The paper’s own numbers (Table 3 Meta F1 73.9; gpt-oss-120b’s own 47.9 Meta F1) already quantify the residual gap to perfect human fidelity, and the closed training loop (extra annotation + positive repair + Meta-Ver reward) makes circularity a concrete rather than generic risk. Abstract/body numerical discrepancies (296 vs 245 problems, 75.8/66.1 vs 64.5/48.9) are real presentation defects but secondary once body figures are used; they do not independently falsify the pattern. No stronger internal contradiction or unstated mathematical assumption appears. The CONDITIONAL verdict therefore stands: the suite is a useful process-level resource provided public artifacts appear and the judge-agreement stress test above is passed.","tokens_in":18908,"tokens_out":714,"duration_ms":22793,"concrete_test":"Draw a stratified sample of 40 ProverBench trajectories (20 UG + 20 QE) generated by GPT-5.5-xhigh and DeepSeek-V4-Pro. Obtain independent double-blind PhD re-annotations of binary validity and first-fatal-step under the exact Appendix C protocol. Compute Cohen’s κ against the auto-verifier’s 8-way pessimistic verdicts and the absolute difference in acceptance rate. If κ < 0.65 or the acceptance-rate delta exceeds 8 points, the Table 1 scores (and therefore the unsolved claim) are materially judge-dependent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that AdvancedMathBench remains unsolved (best ProverBench 64.5 UG / 48.9 QE under pessimistic auto-verification; best VerifierBench Meta-Ver Balanced F1 ~65.1 with low TNR) is only as strong as the two judges that produce those numbers. The auto-verifier (Intern-S2-Preview-35B fine-tuned with Meta-Ver-RL rewards, positive repair augmentation, and 8-way pessimistic voting, §4) is the sole scorer for Table 1; gpt-oss-120b is the meta-verifier that both supplies the RL reward (§4.3) and produces every Meta-Verification column of Table 2. On the 94-example held-out set the auto-verifier itself reaches only 73.9 Meta-Ver Bal. F1 (TNR 69.1, Table 3), while gpt-oss-120b scores 47.9 Meta F1 / 32.0 TNR on the full VerifierBench (Table 2). Because positive-sample repair and the reward model both route through these same components, residual polarity bias or incomplete fatal-error localization can systematically shift acceptance rates. Consequently the absolute gaps that underwrite “substantial room for improvement” and “critical error detection remains a major bottleneck” are not yet shown to be free of judge dependence.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper introduces AdvancedMathBench, a suite for process-level evaluation of advanced natural-language mathematical proofs. ProverBench comprises 245 undergraduate (UG, n=200) and doctoral qualifying-exam (QE, n=45) proof problems; model-generated proofs are scored by an expert-aligned automatic verifier (Intern-S2-Preview-35B trained with Meta-Ver-RL, positive repair augmentation, and 8-way pessimistic voting). VerifierBench provides 888 model-generated proof trajectories with full-chain expert labels (fatal vs recoverable errors) and evaluates models on validity polarity plus rationale quality via a gpt-oss-120b meta-verifier. Experiments report that the best generator (GPT-5.5-xhigh) reaches only 64.5 UG / 48.9 QE under pessimistic verification, and the best verifier reaches ~65.1 Meta-Verification Balanced F1 with low true-negative rates, arguing that advanced proof construction and critical error detection remain open.","tokens_in":19400,"tokens_out":1463,"duration_ms":20605,"significance":"If the evaluation pipeline is sufficiently faithful to expert judgment, this is a timely and useful contribution: existing math benchmarks remain largely answer-centric or olympiad-focused, and natural-language proof validity is under-measured. Strengths include multi-source curation with PhD-level QC, a full-chain annotation protocol that separates fatal from recoverable errors, public prompts and annotation fields, and ablations (Table 3) showing that Meta-Ver-RL, extra annotation, positive augmentation, and pessimistic voting each improve held-out verifier quality over the base model and over frontier LLM-as-judge baselines. The UG→QE difficulty gradient and the systematic over-acceptance pattern (high TPR, low TNR) are informative for the field. The work would be more decisive with stronger external validation that reported rankings are not judge-dependent.","major_comments":[{"comment":"Abstract vs body numerical inconsistency is load-bearing for credibility. The abstract states ProverBench has 296 problems and that GPT-5.5-xhigh scores 75.8 / 66.1 on UGD and QE; §3.2 and Table 1 state 245 problems (200 UG + 45 QE) and 64.5 / 48.9. Figure 1 and the introduction repeat the body numbers. These cannot both be correct; the abstract must be reconciled with the tables before any claim about absolute performance or “room for improvement” can be trusted.","section":null},{"comment":"§3.3 and §4.3: gpt-oss-120b is used both as the meta-verifier that produces every Meta-Verification column of Table 2 and as the RL reward judge for the auto-verifier. On the same VerifierBench, gpt-oss-120b itself scores only 47.9 Meta-Ver Balanced F1 and 32.0 TNR (Table 2). Training and evaluating with a meta-judge that systematically fails at true-negative detection risks baking in polarity bias and incomplete fatal-error localization. The paper should either replace or ensemble the meta-verifier with a stronger/human-calibrated judge, or report sensitivity of Table 2 rankings and of the trained auto-verifier to the meta-judge choice.","section":null},{"comment":"§4.4 / Table 3: the auto-verifier is the sole scorer for all ProverBench generator rankings (Table 1), yet on the 94-example held-out set it reaches only 73.9 Meta-Ver Balanced F1 (TNR 69.1). That is better than GPT-5.5-xhigh and DeepSeek-V4-Pro as judges, but still leaves substantial residual disagreement with experts. There is no reported human re-grade of a stratified sample of accepted vs rejected model proofs, no inter-annotator agreement on the expert labels, and no correlation between auto-verifier scores and independent human rankings of generators. Without that, the absolute gaps (e.g., 64.5 UG / 48.9 QE) and the claim that AdvancedMathBench “remains unsolved” remain only partially validated against judge artifacts.","section":null},{"comment":"§3.2 / Table 1: the QE split has only 45 problems. Several models score in the teens or single digits (e.g., Gemini-3.1-Pro-Preview 17.8, gpt-oss-120b 2.2). No confidence intervals, bootstrap variance, or per-subject breakdowns are reported. With n=45 and a binary pessimistic accept/reject, small labeling or sampling shifts can reorder models. Either enlarge QE, report uncertainty, or temper claims that rest on fine QE differences.","section":null}],"minor_comments":[{"comment":"Abstract uses “UGD” and “strong agreement with human experts”; body uses “UG” and reports 73.9 Meta-Ver Bal. F1. Align terminology and tone with the measured agreement.","section":null},{"comment":"Figure 1 caption and intro cite HMMT Feb. 2026 / USAMO 2026 scores from matharena.ai without stating evaluation protocol parity (answer-centric vs process-level). A short caveat would avoid over-reading the ↓41% comparison.","section":null},{"comment":"§4.1–4.2: “approximately 2k” annotated examples and “approximately 1.2k” positive repairs are imprecise; exact counts and train/held-out split construction should be stated.","section":null},{"comment":"Free parameters (reward scale EXACT/BASIC/POOR/WRONG, 8 pessimistic passes, verifier-uncertainty entropy threshold) are fixed without sensitivity analysis; a short appendix on ranking stability under nearby settings would help.","section":null},{"comment":"Appendix A.2 examples and B prompts are useful; ensure LaTeX rendering of the isoperimetric and tempered-distribution examples is consistent with the main text’s claim of careful QC.","section":null},{"comment":"Related Work is thorough; a brief explicit comparison table (coverage, proof vs answer, auto vs human judge) against Open Proof Corpus, IMO-Bench, ProcessBench, and FrontierMath would improve navigability.","section":null}],"recommendation":"major_revision","confidential_remarks":"The abstract/body score and size mismatch is severe enough that I would ask the authors for a clear account of which numbers are current before trusting any absolute claim. The scientific idea is sound and the annotation effort is real; I do not see grounds for reject if the judge-validation and consistency issues are fixed. Scope is appropriate for a methods/benchmark venue in CS/ML; pure math journals may find the contribution less central."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a useful resource paper, not a theory result. The thing worth knowing is that they built a harder natural-language proof suite (UG + QE) and, more importantly, full-chain expert labels that separate fatal from recoverable errors, then used those labels both to train a process verifier and to meta-score model critiques. That combination is what makes the work more than another olympiad dump.\n\nWhat is new is concrete: 245 curated proof problems with a clear UG/QE gradient, 888 expert-annotated model trajectories, a trained auto-verifier (Meta-Ver-RL + positive repair + 8-way pessimistic voting) that beats frontier LLM-as-judge on a 94-example held-out set (82.1 Rough / 73.9 Meta Bal. F1 vs ~70/62 for GPT-5.5-xhigh), and tables that show frontier models still drop hard on QE generation and, on verification, over-accept invalid proofs (best Meta Bal. F1 ~65, TNR often in the 30–55 range). The annotation protocol, prompts, and ablations are written carefully enough that a referee can actually check the design. Citation pattern is normal for this line of work; they place themselves against MATH/Olympiad/NaturalProofs/ProcessBench/IMO-Bench/FrontierMath without pretending those do not exist.\n\nSoft spots, in proportion. First, abstract numbers (296 problems; 75.8/66.1) do not match the body (245; 64.5/48.9). Use the body. Second, the stress-test concern is real but not fatal: Table 1 is scored only by their auto-verifier, and Table 2 Meta columns (and the RL reward) go through gpt-oss-120b, which itself has weak TNR on VerifierBench. Held-out gains over LLM judges help, but absolute “room for improvement” claims still carry some judge dependence. Third, public data/code release is not clearly evidenced in the manuscript, which is the main practical limit for a benchmark paper. None of that erases the empirical pattern that process-level advanced proof is still hard and that binary polarity overstates verification quality.\n\nWho it is for: people building or evaluating LLM math systems who care about proof process rather than final answers. I would bring it to reading group, cite the benchmark and the fatal/recoverable distinction if I work in this area, and send it to peer review. It deserves referee time; the main asks are number consistency, clearer release plans, and more human agreement numbers on the judges.","headline":"Solid advanced-proof benchmark with real process labels; headline gaps are real enough to matter, but partly judge-dependent and the abstract/body numbers disagree.","tokens_in":19997,"tokens_out":619,"would_cite":true,"duration_ms":6142,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Frontier models still fail advanced natural-language math proofs under process-level checks.","keywords":["mathematical proof generation","proof verification","process-level evaluation","LLM benchmarks","undergraduate mathematics","qualifying exams","meta-verification","pessimistic verification"],"falsifier":"On a held-out set of model proofs, independent PhD graders disagree with the automatic pipeline’s accept/reject decisions and fatal-error localizations at rates high enough to reverse the ranking or close the reported performance gap with competition-style benchmarks.","tokens_in":19815,"feed_emoji":"📐","tokens_out":594,"duration_ms":4671,"temperature":0.7,"pith_summary":"This paper argues that high scores on high-school and olympiad answer benchmarks hide a deeper gap: models cannot yet construct or check rigorous proofs at undergraduate and doctoral qualifying-exam levels. It introduces AdvancedMathBench, whose ProverBench holds 245 proof problems (200 undergraduate, 45 qualifying-exam) spanning core mathematical subjects, and whose VerifierBench holds 888 model-generated proof trajectories labeled by experts. Because final answers cannot certify a proof, the authors train an automatic verification pipeline on large-scale expert annotations and use meta-verification of rationales. Under that process-level regime, the best generator reaches only 64.5 on the undergraduate split and 48.9 on the harder split, while the best verifier reaches only about 65 Balanced F1 and routinely misses fatal errors. The claim is that advanced mathematical reasoning must be measured by whether the proof chain itself is valid, not by whether a short answer matches.","feed_headline":"Frontier models score under 65% on advanced math proofs","feed_subtitle":"Process-level checks expose large gaps that final-answer benchmarks hide","key_machinery":"The expert-aligned automatic verification pipeline: large-scale expert labels, positive-sample repair augmentation, reinforcement learning with meta-verification rewards, and 8-way pessimistic voting that accepts a proof only when every pass agrees it is correct.","core_discovery":"Under expert-aligned process verification, AdvancedMathBench remains unsolved for frontier models: the strongest proof generator scores 64.5 on the undergraduate split and 48.9 on the doctoral qualifying-exam split, and the strongest proof verifier reaches only about 65 Meta-Verification Balanced F1, driven by low true-negative rates that show models over-accept plausible but invalid proofs.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Frontier models top out under 65% on advanced math proofs","AdvancedMathBench shows frontier LLMs still lag on hard proofs","Expert process checks leave AdvancedMathBench unsolved for frontier models","Strongest prover hits 64.5 UGD and 48.9 QE under process verification","Proof verifiers top ~65 F1 as models over-accept invalid proofs"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The trained automatic verifier and the meta-verifier are faithful enough proxies for PhD-level human judgment that the reported gaps and rankings are not mainly artifacts of judge bias or annotation skew.","fun_headline_variants_meta":{"raw":{"variants":["Frontier models top out under 65% on advanced math proofs","AdvancedMathBench shows frontier LLMs still lag on hard proofs","Expert process checks leave AdvancedMathBench unsolved for frontier models","Strongest prover hits 64.5 UGD and 48.9 QE under process verification","Proof verifiers top ~65 F1 as models over-accept invalid proofs"]},"model":"grok-4.5","effort":"low","cost_usd":0.005184,"raw_usage":{"total_tokens":1482,"prompt_tokens":831,"num_sources_used":0,"completion_tokens":99,"cost_in_usd_ticks":51840000,"prompt_tokens_details":{"text_tokens":831,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":552,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":831,"tokens_out":99,"duration_ms":4601,"temperature":1.0,"reasoning_tokens":552,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T02:42:09.087959+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"On a held-out set of model proofs, independent PhD graders disagree with the automatic pipeline’s accept/reject decisions and fatal-error localizations at rates high enough to reverse the ranking or close the reported performance gap with competition-style benchmarks.","supporting_citations":[],"review_version":1}