{"id":"7bd7fef5-a7d9-4cb8-a0b7-106374e86165","arxiv_id":"2507.14335","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A hybrid method uses LLM-generated proof strategies and lemma selection to raise a specialized Lean prover's miniF2F pass rate to 55.3% at 128 attempts, above the baseline's 54.9% at 3200 attempts.","lead":"ProofCompass pairs a large general-purpose AI with a smaller specialized theorem prover, letting the large model suggest proof plans and pick useful intermediate steps. On a standard math benchmark, this guided approach matches the specialized prover's accuracy using 25 times fewer attempts.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline gap is 0.4 points (55.3 vs 54.9) against a baseline that was never re-run under ProofCompass's Lean 4.15/CoT setup, and ProofCompass has no error bars; the 'outperforms' claim is not yet established.","rationale":"The paper's central claim is not that ProofCompass solves hard theorems, but that it beats a specific prover's published Pass@3200 with 128 SLM attempts. For that to be true, the published baseline must be measured in a comparable setting and the ProofCompass number must be more than a single-run fluctuation. Neither condition is currently checked. Section 4.1 explicitly takes the baseline 'as reported in its original publication' without a same-environment re-run; ProofCompass uses Lean 4.15 and a CoT prompt, while the published 51.6/54.9 may come from a different Lean/mathlib snapshot and decoding setup. The reported deltas are 0.4 and 0.9 points, near or below the baseline's own ±0.5/±0.7 error bars, and the paper gives no error bars for 55.3/52.5. This makes the 'exceeds' part of the headline unsupported, even though the 'matches at 25x fewer attempts' direction is plausible. I agree with the reader's conditional verdict: the issue is correctable by re-running the baseline and reporting uncertainty. The Appendix A timing analysis is a strength because it partially addresses the LLM-overhead concern, and the included prompts support reproducibility.","tokens_in":19873,"tokens_out":8322,"duration_ms":90076,"concrete_test":"Re-run DSP-v1.5-RL standalone on miniF2F-test under ProofCompass's exact conditions (Lean 4.15, same CoT prompt, same miniF2F-lean4 files, same temperature/max tokens, on the same GPU), sampling 3200 i.i.d. proofs per problem, and compute Pass@128 and Pass@3200 with bootstrapped CIs. Also run ProofCompass with 10 independent seeds (or bootstrap across the 244 problems) and report CIs for 52.5 and 55.3. If the re-run baseline matches 51.6/54.9 within the original error bars and the ProofCompass CIs exclude the re-run baseline values, the central claim stands; otherwise it should be weakened to 'comparable' or 'unverified'.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim — ProofCompass 'outperforms' DSP-v1.5 at 25x fewer attempts — rests on a cross-paper comparison that the paper never validates. Section 4.1 states that the DSP-v1.5 baseline is taken 'as reported in its original publication' and does not re-run it under ProofCompass's conditions: Lean 4.15, the CoT activation prompt, the same miniF2F-lean4 statement files, decoding temperature, and GPU. In theorem proving these details materially change Pass@k; a Lean/mathlib version bump alone can move success rates by more than a point. The reported differences are tiny relative to that fragility: 55.3 vs 54.9 is 0.4 points, smaller than the baseline's stated ±0.7 error bar, and 52.5 vs 51.6 is 0.9 points. ProofCompass reports no repeated runs or confidence intervals, so there is no way to tell whether the 'exceeds' part of the claim is signal or noise. If a re-run of the baseline under identical conditions yielded 55.5 or 53.5 instead of 54.9, the 25x-efficiency conclusion would flip or vanish. The efficiency metric is also SLM-attempt-only and excludes Gemini API cost, but the controlling issue is that the comparison's reference numbers are not tied to the measured environment.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ProofCompass, a training-free hybrid system in which a general-purpose LLM (Gemini 2.0 Flash Thinking/Flash) guides DeepSeek-Prover-v1.5-RL (DSP-v1.5), a specialized Lean 4 prover, by generating natural-language proof summaries and by selecting intermediate lemmas from the specialized model's failed attempts. The method is evaluated on miniF2F-test, reporting Pass@128 of 55.3% with 128 SLM attempts versus the baseline DSP-v1.5 Pass@3200 of 54.9%, and Pass@32 of 52.5% versus the baseline Pass@128 of 51.6%. Ablations isolate the contributions of informal-proof and lemma guidance. The central efficiency claim is that the hybrid reaches or exceeds the standalone prover's accuracy with 25x fewer attempts.","tokens_in":20187,"tokens_out":4712,"duration_ms":48193,"significance":"If the comparison were properly controlled, the idea is significant: it demonstrates that a small specialized prover can be guided by an LLM without additional training, and the modular design, detailed prompts in Appendix D, per-stage timing analysis in Appendix A, and informative ablations are valuable contributions. However, the headline empirical claims currently rest on an uncontrolled cross-paper baseline and on point estimates without uncertainty, so the significance is conditional on a controlled re-run and on proper treatment of hyperparameter selection and error bars.","major_comments":[{"comment":"The baseline numbers for DSP-v1.5 are taken from its original publication without re-running under ProofCompass's exact conditions: Lean 4.15, the CoT activation prompt, the same miniF2F-lean4 statement files, decoding temperature, and GPU. This matters because theorem-proving Pass@k is sensitive to Lean/mathlib versions and to CoT prompting. The reported differences (55.3 vs. 54.9, and 52.5 vs. 51.6) are smaller than or comparable to the baseline's own error bars in Table 1 (±0.7 and ±0.5), while ProofCompass has no error bars. The 'outperforms' claim and the 25x-efficiency claim are therefore not established as stated; the baseline must be re-run under identical conditions, or the claims must be softened to 'comparable' with appropriate uncertainty.","section":"Section 4.1 (Baselines)"},{"comment":"The key hyperparameters N=16 and k=5 are justified using Figure 5, which plots cumulative solved problems and unique 'have' statements collected from the initial proof generation stage, with no separate validation split described. If these data come from the same miniF2F-test set used for final evaluation, then selecting hyperparameters on the test set biases the reported Pass@k values upward. Please either use a validation split for hyperparameter selection or provide a sensitivity analysis showing that the main conclusions are robust to reasonable choices of N and k.","section":"Section 4.1 and Appendix B (Hyperparameters)"},{"comment":"No repeated runs or confidence intervals are reported for ProofCompass, so the point estimates 52.5% and 55.3% cannot be statistically distinguished from the baseline's 51.6% and 54.9%. Furthermore, the Pass@k estimator mixes different stages (initial attempts, lemma proofs, final theorem proof) and should be defined precisely, including how sampling variance is accounted for. Please report multiple seeds or bootstrap confidence intervals for the main results.","section":"Section 4.2 and Table 1 (Uncertainty quantification)"},{"comment":"The '25x fewer attempts' claim counts only SLM generation calls and excludes the Gemini API calls used for natural-language proof generation, summarization, lemma selection, and informal proof generation. Appendix A shows a fixed overhead of about 100.83 seconds for problems not solved in the first 16 attempts, which is real computational cost. The efficiency claim should either include LLM API cost and wall-clock time, or be explicitly labeled as 'SLM attempts' rather than 'computational budget,' to avoid overstating resource efficiency.","section":"Sections 1, 4.1, and Appendix A (Efficiency metric)"}],"minor_comments":[{"comment":"The text says the evaluation was conducted with 'a maximum of 27 attempts per problem,' which conflicts with the stated total budget B=128 in Section 4.1; please clarify whether this is a typo and what the actual per-problem cap is.","section":"Section 6 (Limitations)"},{"comment":"Several inline identifiers are broken in the PDF text (for example, 'Tf ormal', 'Tinf ormal', 'pN L', 'psummary'), making the method section difficult to read; these should be fixed with proper math-mode formatting.","section":"Throughout"},{"comment":"The table reports error bars for the DSP-v1.5 baseline but not for ProofCompass; add error bars or explain their absence in the caption.","section":"Table 1"},{"comment":"The axis labels, legend, and some tick values in Figure 4 are garbled in the provided text; ensure the figure is legible and self-contained in the camera-ready version.","section":"Figure 4"},{"comment":"The comparative experiment in Appendix C reports averages over only 4 independent runs without variance; add error bars or more runs if this claim is retained.","section":"Appendix C (Alternative lemma generation)"}],"recommendation":"major_revision","confidential_remarks":"The empirical comparison is the crux of the paper. Without a re-run of DSP-v1.5 under identical conditions, the headline 'outperforms' and '25x fewer attempts' claims cannot be used as published. I would not reject on novelty grounds, but the revision needs to address the baseline comparability, uncertainty quantification, and test-set hyperparameter selection directly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper is worth a serious referee, but the headline claim is not yet established. The mechanism is real and well described: pass an LLM-written informal proof summary into DSP-v1.5's CoT mode, and when N initial attempts fail, have the LLM pick correct-looking 'have' lemmas from those failed attempts and use them to decompose the theorem. The ablations suggest both components contribute, the prompts and timing breakdown are in the appendix, and the work is honest about the limitations of a small budget.\n\nWhere it gets shaky is the evaluation. The baseline numbers for DSP-v1.5 are taken from its original paper and never re-run under ProofCompass's environment — Lean 4.15, CoT prompt, same statement files, same decoding. In theorem proving that environment moves Pass@k by more than a point, and the claimed victory is 55.3 vs 54.9, which is smaller than the baseline's own ±0.7 error bar. ProofCompass itself has no repeated runs or error bars, so I can't tell whether the 'exceeds' part is signal or noise. The 25x claim is real only if the comparison is apples-to-apples, and right now it isn't.\n\nThere is also a mild circularity issue: N=16 and k=5 are justified with plots and qualitative evaluations that look like they were done on miniF2F-test, the same benchmark used for the final numbers. That's a standard pitfall in this field, but it should be fixed. And the efficiency metric counts only DSP-v1.5 attempts; the Gemini API calls cost real time and money even if they're not SLM attempts. One more thing: the limitations section says experiments used a maximum of 27 attempts per problem, which conflicts with the B=128 Pass@32/Pass@128 budget — that should be clarified.\n\nI'd send this to review, not desk reject. The method is novel enough that it deserves referee time, and the fixes are concrete: re-run the baseline under identical conditions, report variance across seeds, pick hyperparameters on validation rather than test, and report end-to-end cost. If the 0.4-point edge survives that, it's a good result; if it doesn't, the paper's ablations still tell a useful story about LLM-guided lemma selection.","headline":"A genuine hybrid mechanism with a clear write-up, but the central 25x-efficiency claim rests on a baseline that was never re-run and a 0.4-point gap inside the baseline's own error bar.","tokens_in":20692,"tokens_out":2836,"would_cite":true,"duration_ms":536440,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68V05"],"pacs":[],"model":"deepseek-v4-flash","headline":"A general-purpose LLM guiding a small specialized prover can match or beat a 25-times-larger sampling budget on miniF2F.","keywords":["formal theorem proving","LLM-guided proof search","lemma selection","chain-of-thought informal proofs","miniF2F benchmark","Lean 4","hybrid LLM-specialist prover","Pass@k evaluation"],"falsifier":"Run DSP-v1.5 in its chain-of-thought mode on miniF2F-test with the same prompt, sampling temperature, Lean 4.15, 20-second timeout, and verification procedure used by ProofCompass, and measure Pass@32, Pass@128, and Pass@3200. If standalone Pass@128 reaches or exceeds 55.3%, or if its Pass@3200 rises above 55.3% with the same sampling configuration, the claimed 25x efficiency gain collapses.","tokens_in":19693,"feed_emoji":"🧭","tokens_out":7662,"duration_ms":77000,"temperature":0.7,"pith_summary":"ProofCompass claims that a general-purpose LLM can act as a strategic guide for a small, specialized theorem prover, and that this guidance is worth more than a large increase in raw sampling budget. On the miniF2F-test benchmark, guiding DeepSeek-Prover-v1.5-RL with LLM-generated proof summaries and LLM-selected lemmas raises Pass@128 to 55.3%, above the specialized prover's standalone Pass@3200 of 54.9% while using 25x fewer attempts. The same pattern appears at smaller scale: Pass@32 of 52.5% beats the standalone prover's Pass@128 of 51.6%. If true, this shows a compute-efficient route to stronger formal theorem proving that requires no additional training of either model.","feed_headline":"LLM guidance beats a 25x larger search budget","feed_subtitle":"ProofCompass solves 55.3% of miniF2F in 128 attempts versus 54.9% with 3200 attempts.","key_machinery":"The load-bearing mechanism is the 'have' statement: Lean's way of introducing an intermediate lemma inside a proof. After 16 failed attempts, ProofCompass collects all unique have statements the specialized prover generated, keeps syntactically valid ones, and has the LLM choose up to five that are correct under the theorem's global hypotheses and match the natural-language proof. The LLM then writes brief informal proofs for each chosen lemma and for the main theorem assuming the lemmas; the specialized prover formalizes each piece, and the pieces are recombined and checked by Lean 4. A second mechanism is the injection of an LLM-written informal proof summary into the chain-of-thought block comment that the specialized prover expects, replacing the prover's own sketch.","core_discovery":"The central claim is that combining an LLM's natural-language proof sketches and its selection of intermediate lemmas with a specialized prover's formal synthesis yields better results per attempt than scaling up the specialized prover alone. In the reported experiments, ProofCompass with a budget of 128 attempts solves 55.3% of miniF2F-test, exceeding the 54.9% reported for 3200 attempts of the standalone prover. Both ablation channels contribute: LLM-selected lemmas alone reach 53.3% and LLM informal proof guidance alone reaches 52.9% at 128 attempts, so the paper argues the two mechanisms are complementary rather than redundant.","pith_inferences":["The '25x fewer attempts' figure counts only calls to the specialized prover; LLM queries are not attempts. The paper's own timing appendix shows a fixed overhead of roughly 100 seconds per hard problem, so wall-clock efficiency versus the baseline only appears after about 46 attempts; this timing reading is an editorial extension, not the paper's headline.","A natural transfer test, untested in the paper, is to attach the same two guidance mechanisms to a different structured prover, such as Goedel-Prover, which the paper names as compatible, and ask whether the per-attempt gain persists.","The paper runs one round of lemma extraction; chaining additional rounds, feeding the failures of the lemma-proving stage back into the selection loop, is an obvious next experiment the paper leaves open."],"forward_implications":["For a fixed 128-attempt budget, ProofCompass reports 55.3% versus the standalone prover's 51.6%, so LLM guidance shifts the entire Pass@k curve rather than only its tail.","With only 32 attempts, ProofCompass reports 52.5%, above the standalone prover's 51.6% at 128 attempts, so the efficiency gain persists in very constrained budgets.","Both ablations beat the standalone prover at Pass@128, so each guidance channel is independently effective and their combination is additive.","Because neither model is trained in this pipeline, the method can absorb future improvements in general-purpose LLMs without additional training cost."],"supporting_citations":[{"why":"Supplies the specialized prover DSP-v1.5-RL, the chain-of-thought activation prompt, and the baseline Pass@32/128/3200 numbers that ProofCompass claims to beat.","marker":"(Xin et al., 2024)"},{"why":"Defines miniF2F, the benchmark on which all reported success rates are computed.","marker":"(Zheng et al., 2021)"},{"why":"Provides Lean 4, the proof assistant that verifies every generated proof and selected lemma.","marker":"(de Moura & Ullrich, 2021)"},{"why":"Establishes the informal-proof-guided formal proving paradigm that motivates the paper's natural-language guidance.","marker":"(Jiang et al., 2023)"},{"why":"Supplies the closest hybrid baseline, BC-Prover, and the backward-chaining and subgoal ideas behind lemma-based guidance.","marker":"(He et al., 2024)"},{"why":"Provides the LEGO-Prover baseline and the library or subgoal decomposition approach that lemma selection extends.","marker":"(Wang et al., 2024b)"},{"why":"Introduces chain-of-thought prompting, the delivery mechanism for the LLM's proof summaries.","marker":"(Wei et al., 2022)"},{"why":"Provides the Lyra baseline and a prior use of failed-proof analysis that the lemma-selection loop resembles.","marker":"(Zheng et al., 2024)"}],"fun_headline_variants":["LLM guidance lifts prover to 55.3% with 25x fewer tries","ProofCompass: 128 attempts beat 3200 for theorem proving","Guided lemmas and sketches cut attempts 25-fold, boost accuracy","Hybrid LLM-specialist prover hits 55.3% in 128 tries","LLM picks lemmas, specialist proves: 25x fewer attempts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The premise that the baseline numbers quoted from the original DSP-v1.5 publication were measured under the same chain-of-thought mode, prompt, decoding settings, and Lean version that ProofCompass uses; if this is false, the 25x comparison is not a controlled experiment.","fun_headline_variants_meta":{"raw":{"variants":["LLM guidance lifts prover to 55.3% with 25x fewer tries","ProofCompass: 128 attempts beat 3200 for theorem proving","Guided lemmas and sketches cut attempts 25-fold, boost accuracy","Hybrid LLM-specialist prover hits 55.3% in 128 tries","LLM picks lemmas, specialist proves: 25x fewer attempts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000253,"raw_usage":{"total_tokens":1520,"prompt_tokens":859,"completion_tokens":661,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":556}},"tokens_in":475,"tokens_out":661,"duration_ms":6960,"temperature":1.0,"reasoning_tokens":556,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:58:47.979129+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run DSP-v1.5 in its chain-of-thought mode on miniF2F-test with the same prompt, sampling temperature, Lean 4.15, 20-second timeout, and verification procedure used by ProofCompass, and measure Pass@32, Pass@128, and Pass@3200. If standalone Pass@128 reaches or exceeds 55.3%, or if its Pass@3200 rises above 55.3% with the same sampling configuration, the claimed 25x efficiency gain collapses.","supporting_citations":[],"review_version":1}