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REVIEW 2 major objections 5 minor 14 references

An open agentic Lean 4 prover with a Planner-Worker-Verifier loop beats a linear Lean-calling baseline on ProofNet.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-13 04:37 UTC pith:HSVTNPCZ

load-bearing objection Useful open Lean-integrated agentic prover with a real interactive TUI; the ProofNet lift is real but the baseline is too thin to pin the gain on the architecture. the 2 major comments →

arxiv 2607.09217 v1 pith:HSVTNPCZ submitted 2026-07-10 cs.AI cs.MS

OpenProver: Agentic and Interactive Theorem Proving with Lean 4

Mat\v{e}j Kripner , Milan Straka This is my paper
classification cs.AI cs.MS
keywords automated theorem provingLean 4agentic LLMsPlanner-Worker-VerifierProofNetinteractive theorem provingformal verification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

OpenProver is an open-source system that turns a reasoning language model into a theorem prover by wrapping it in a Planner-Worker-Verifier loop that talks to Lean 4. A Planner keeps a short Whiteboard of the current plan and a Repository of checked intermediate results, then spawns parallel Workers that explore lemmas, counterexamples, or formalizations without seeing one another’s traces; each Worker’s output is independently checked by a Verifier before the Planner continues. The same system can run fully autonomously for reproducible measurement or in an interactive terminal where a human can interrupt agents, edit the plan, and accept or reject actions. On 185 ProofNet theorems under a fixed 100k-token budget, the architecture lifts success rates over a linear chain-of-thought baseline that may also call Lean: 57.3% versus 36.8% with one model and 28.1% versus 21.1% with another. The authors present the system so that agentic theorem proving can be measured by automatic formal verification and steered by humans when research needs judgment rather than pure search.

Core claim

Under a fixed token budget, the Planner-Worker-Verifier architecture with Lean 4 formal verification finds more ProofNet proofs than a linear rollout of the same models that can also perform unlimited Lean checks, while remaining open-source and interactively steerable.

What carries the argument

Planner-Worker-Verifier loop: a single Planner that maintains a compact Whiteboard and an unbounded Repository of Lean-checked items, spawns independent Workers on plaintext tasks, and receives independent Verifier critiques before the next step.

Load-bearing premise

That the linear chain-of-thought baseline is a fair non-agentic comparator under the same token budget and model, so the measured gains can be attributed to the multi-agent design rather than unstated differences in prompting or tool scaffolding.

What would settle it

Re-run the same 185 ProofNet theorems under an identical 100k-token budget with the linear baseline given the same tool interface, Whiteboard-style memory, and parallel-call opportunities; if its success rate then matches or exceeds OpenProver’s, the architectural claim collapses.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Automatic Lean verification of every intermediate Lean item and of the final proof makes quantitative ablations of agentic designs reproducible across runs.
  • Interactive terminal control lets a human interrupt unpromising Workers, inject plan feedback, or gate Planner actions, combining autonomous search with expert judgment.
  • Because most control logic lives in prompts rather than hard-coded rules, the same evaluation loop can later serve as a reward signal for prompt or code self-improvement.
  • Formalization remains harder than informal proof; the gap is expected to shrink as Mathlib and related libraries grow.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same Whiteboard-plus-Repository memory pattern could transfer to other long-horizon formal tasks (program synthesis, verified refactoring) where intermediate artifacts must survive formal checks.
  • Independent Verifiers that never see a Worker’s chain of thought may reduce correlated failure modes that plague single-trace agents on hard math.
  • Public release of both the scaffolding and the evaluation harness invites head-to-head comparison of planner designs under identical Lean oracles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. OpenProver is a system paper presenting an open-source LLM-driven automated theorem prover for Lean 4. It uses a Planner-Worker-Verifier architecture (inspired by Aletheia) in which a Planner maintains a compact Whiteboard and a Repository of intermediate Markdown/Lean items, spawns independent Workers on subtasks, and receives independent Verifier feedback. The system supports both autonomous search and an interactive TUI for human steering, with Lean verification of intermediate and final proofs. On 185 ProofNet theorems under a 100k-token budget, OpenProver reports higher success rates than a linear Chain-of-Thought baseline that can also call Lean: 57.3% vs 36.8% (Kimi-K2.5) and 28.1% vs 21.1% (Leanstral).

Significance. The work is a useful systems contribution: it is fully open-source, couples agentic search to automatic Lean 4 verification (enabling reproducible evaluation), and provides an interactive interface motivated by human-AI code-generation practice. The Whiteboard/Repository design and independent Workers/Verifiers are concrete engineering choices that other groups can reuse or ablate. The quantitative comparison on ProofNet, while limited, is checkable in principle via the released code and formal verification. If the architecture gains hold under fairer controls, the paper supplies a practical scaffold for both autonomous ATP research and interactive mathematical tooling.

major comments (2)
  1. [Section 4 / Table 2] Section 4 / Table 2: The central quantitative claim attributes the lift over the linear-rollout baseline (57.3% vs 36.8%; 28.1% vs 21.1%) to the Planner-Worker-Verifier architecture. The baseline is described only as unrolling each model in a linear conversation under the same 100k-token budget with unlimited Lean verifications. The manuscript does not specify whether the baseline receives the same lean_search / lean_store tools and Mathlib retrieval that Workers use, how parallel Worker/Verifier tokens are counted against the shared budget versus sequential baseline tokens, or whether system prompts, formalization scaffolding, and post-error retry loops are matched. Without these controls (or an ablation that isolates them), the measured gains cannot be confidently attributed to the multi-agent design rather than richer tooling or different token accounting. This is load-bearing because
  2. [Section 4] Section 4 and Abstract: The paper states that automatic formal verification enables quantitative ablation experiments, yet the evaluation reports only a single end-to-end comparison against a linear baseline, with no ablations of Whiteboard, Repository, Verifiers, Worker independence, or tool surface, and no multiple seeds or error bars. A minimal ablation (e.g., Planner+Workers without Verifiers, or OpenProver without lean_search) would make the architecture claim substantially stronger and would match the paper's own framing of what the system enables.
minor comments (5)
  1. [Figure 1] Figure 1 is described in the text but the rendered figure is hard to parse from the manuscript source alone; ensure the published version clearly labels the Planner actions, Whiteboard, Repository, and Verifier feedback paths.
  2. [Table 1] Table 1 lists literature_search as unavailable in isolation mode; a one-sentence definition of isolation mode would help readers who only read the system description.
  3. [Algorithms 1-2] Algorithms 1-2 are high-level pseudocode; a short note on how token budget B is decremented across parallel Workers and Verifiers would clarify the experimental protocol.
  4. [Section 1] Related work mentions Aletheia and OpenGauss but does not discuss other recent Lean-oriented agentic provers or tool-use frameworks; a brief positioning paragraph would help.
  5. [Section 4] ProofNet size is given as 185 formal theorems; state the exact subset or filtering criterion so that replications match the reported numbers.

Circularity Check

0 steps flagged

No circularity: empirical systems evaluation on external ProofNet with automatic Lean verification; measured rates are not forced by definition or fit.

full rationale

OpenProver is a system paper whose load-bearing quantitative claim is an empirical comparison (Table 2, §4): under a fixed 100k-token budget on 185 ProofNet theorems, the Planner-Worker-Verifier architecture with Lean 4 yields higher success rates than a linear Chain-of-Thought baseline that can also call Lean (57.3% vs 36.8% for Kimi-K2.5; 28.1% vs 21.1% for Leanstral). Those percentages are obtained by running the system and baseline on an external benchmark and checking proofs with Lean; they are not algebraic identities of the architecture, not parameters fitted to a subset and re-reported as predictions, and not uniqueness claims imported from the authors’ prior work. Inspiration from Aletheia and related citations is architectural background, not a self-citation chain that forces the measured lift. Concerns about baseline fairness (tool surface, token accounting, prompt parity) are experimental-design risks, not circular reductions of outputs to inputs. Per the analyzer rules, a self-contained external-benchmark evaluation scores 0 with empty steps.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 2 invented entities

Systems paper whose central empirical claim rests on standard assumptions about LLM tool use and Lean soundness, plus a few design and evaluation choices. No physical constants or fitted scientific parameters appear; free parameters are engineering knobs (token budget, model choice). Invented entities are software components, not postulated physical objects.

free parameters (2)
  • token_budget_B = 100000
    Fixed at 100k tokens per problem for the reported experiments; the success rates are defined relative to this cutoff.
  • underlying_LLM_choice = Kimi-K2.5 / Leanstral
    Results are reported only for Kimi-K2.5 and Leanstral; absolute numbers depend on these specific models.
axioms (3)
  • standard math Lean 4 correctly decides the validity of submitted proof terms (no soundness bugs in the kernel for the fragments used).
    Invoked throughout §2.4 and whenever lean_verify or Repository Lean items are accepted.
  • domain assumption A linear multi-turn conversation with unlimited Lean calls is a reasonable non-agentic baseline under the same token budget.
    Defines the comparison in §4 / Table 2; if the baseline is under-engineered the gains are overstated.
  • ad hoc to paper Independent Workers that do not see each other’s traces explore meaningfully distinct proof directions.
    Stated design rationale in §2.1; not independently validated by ablation.
invented entities (2)
  • Whiteboard (compact Markdown scratchpad maintained by Planner) no independent evidence
    purpose: Persist high-level plan, failed attempts, and notes across Planner steps without overflowing context.
    Software design choice introduced in §2.2; no external falsifiable prediction beyond system performance.
  • Repository of slug-addressed Markdown/Lean items no independent evidence
    purpose: Store longer intermediate results while exposing only summaries to the Planner.
    Software design choice in §2.2; Lean items are filtered by formal verification.

pith-pipeline@v1.1.0-grok45 · 10730 in / 2574 out tokens · 44077 ms · 2026-07-13T04:37:25.620980+00:00 · methodology

0 comments
read the original abstract

In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification. OpenProver integrates a Planner-Worker-Verifier architecture inspired by recent ATP agentic systems such as Aletheia. A Planner agent maintains a compact Whiteboard scratchpad and an unbounded Repository of intermediate findings, and decomposes mathematical work into parallel Workers. OpenProver is fully open-source, offers reproducible evaluation through automatic formal verification of generated proofs, and provides an interactive terminal interface for human-guided proof search. In interactive mode, OpenProver allows the human operator to monitor and steer the proof search process, motivated by the established human-AI synergy in interactive code generation. To showcase the potential for quantitative ablation experiments enabled by automatic formal verification, we evaluate OpenProver on ProofNet and compare it with a simple baseline. OpenProver is publicly available at https://github.com/kripner/OpenProver.

Figures

Figures reproduced from arXiv: 2607.09217 by Mat\v{e}j Kripner, Milan Straka.

Figure 1
Figure 1. Figure 1: Overview of the OpenProver proof search loop. Planner iterates on the high￾level plan, manages persistent state, and delegates mathematical work to Workers. A Verifier provides independent feedback to each Worker contribution. OpenProver is an automated theorem prover utilizing a reasoning LLM executed in an agentic scaffolding, with integration of the Lean 4 formal verifier. The system operates in an iter… view at source ↗
Figure 2
Figure 2. Figure 2: High-level pseudocode of OpenProver: the main loop (Alg. 1) repeatedly invokes PlannerStep (Alg. 2). Additionally, the Planner occasionally needs to store longer text or Lean snippets such as detailed failed proof attempts, proofs of lemmas, literature summaries, and similar. To prevent overflowing the Whiteboard, OpenProver manages a Repository of items where each Item is either a Markdown file or a Lean … view at source ↗

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Reference graph

Works this paper leans on

14 extracted references · 6 linked inside Pith

  1. [1]

    Asher, J.: LeanExplore: A search engine for Lean 4 declarations (2025), https://arxiv.org/abs/2506.11085

    Pith/arXiv arXiv 2025

  2. [2]

    Azerbayev, Z., Piotrowski, B., Schoelkopf, H., Ayers, E.W., Radev, D., Avi- gad, J.: ProofNet: Autoformalizing and Formally Proving Undergraduate- Level Mathematics (2023),https://arxiv.org/abs/2302.12433

    Pith/arXiv arXiv 2023

  3. [3]

    Feng, T., Trinh, T.H., Bingham, G., Hwang, D., Chervonyi, Y., Jung, J., Lee, J., Pagano, C., hyun Kim, S., Pasqualotto, F., Gukov, S., Lee, J.N., Kim, J., Hou, K., Ghiasi, G., Tay, Y., Li, Y., Kuang, C., Liu, Y., Lin, H., Liu,E.Z.,Nayakanti,N.,Yang,X.,Cheng,H.T.,Hassabis,D.,Kavukcuoglu, K., Le, Q.V., Luong, T.: Towards autonomous mathematics research (202...

    arXiv 2026

  4. [4]

    org/abs/2602.02276

    KimiTeam:KimiK2.5:VisualAgenticIntelligence(2026),https://arxiv. org/abs/2602.02276

    Pith/arXiv arXiv 2026

  5. [5]

    Lee, Y., Boen, J., Finn, C.: Feedback Descent: Open-Ended Text Opti- mization via Pairwise Comparison (2025),https://arxiv.org/abs/2511. 07919

    2025

  6. [6]

    https://github.com/math-inc/OpenGauss(2026), gitHub repository

    Math Inc.: OpenGauss: LLM-based Interactive Theorem Proving System. https://github.com/math-inc/OpenGauss(2026), gitHub repository

    2026

  7. [7]

    Mistral AI: Leanstral: Open-Source Foundation for Trustworthy Vibe- Coding (2026),https://mistral.ai/news/leanstral

    2026

  8. [8]

    In: International Conference on Automated Deduction

    Moura, L.d., Ullrich, S.: The Lean 4 theorem prover and programming lan- guage. In: International Conference on Automated Deduction. pp. 625–635. Springer (2021)

    2021

  9. [9]

    Novikov, A., V˜ u, N., Eisenberger, M., Dupont, E., Huang, P.S., Wagner, A.Z., Shirobokov, S., Kozlovskii, B., Ruiz, F.J.R., Mehrabian, A., Kumar, M.P., See, A., Chaudhuri, S., Holland, G., Davies, A., Nowozin, S., Kohli, P., Balog, M.: AlphaEvolve: A coding agent for scientific and algorithmic discovery (2025),https://arxiv.org/abs/2506.13131

    Pith/arXiv arXiv 2025

  10. [10]

    Schick, T., Dwivedi-Yu, J., Dessì, R., Raileanu, R., Lomeli, M., Hambro, E., Zettlemoyer, L., Cancedda, N., Scialom, T.: Toolformer: Language models canteachthemselvestousetools.Advancesinneuralinformationprocessing systems36, 68539–68551 (2023)

    2023

  11. [11]

    In: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

    The Mathlib Community: The Lean mathematical library. In: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs. p. 367–381. CPP 2020, Association for Computing Machin- ery, New York, NY, USA (2020).https://doi.org/10.1145/3372885. 3373824,https://doi.org/10.1145/3372885.3373824

    doi:10.1145/3372885 2020

  12. [12]

    Wei, J., Wang, X., Schuurmans, D., Bosma, M., Ichter, B., Xia, F., Chi, E., Le, Q., Zhou, D.: Chain-of-Thought Prompting Elicits Reasoning in Large Language Models (2023),https://arxiv.org/abs/2201.11903

    Pith/arXiv arXiv 2023

  13. [13]

    arXiv preprint arXiv:2506.14245 (2025)

    Wen, X., Liu, Z., Zheng, S., Ye, S., Wu, Z., Wang, Y., Xu, Z., Liang, X., Li, J., Miao, Z., et al.: Reinforcement learning with verifiable re- wards implicitly incentivizes correct reasoning in base LLMs. arXiv preprint arXiv:2506.14245 (2025)

    Pith/arXiv arXiv 2025

  14. [14]

    org/abs/2602.03773

    Wu, I., Qu, Y., Setlur, A., Kumar, A.: Reasoning Cache: Continual Improve- ment Over Long Horizons via Short-Horizon RL (2026),https://arxiv. org/abs/2602.03773

    arXiv 2026