{"id":"8b3d9860-9d17-4398-ab7b-c3e461308594","arxiv_id":"2605.22885","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"ImProver 2 combines a data-efficient expert-iteration pipeline with a neurosymbolic scaffold to train a 7B model that outperforms larger models in Lean 4 proof optimization across structural metrics.","lead":"The paper introduces ImProver 2, a neurosymbolic framework that uses iterative self-improvement to optimize formal proofs in Lean 4. A smart generalist might read it to see how smaller AI models can be trained to restructure complex mathematical proofs more effectively than much larger systems.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The query provides no full text, preventing identification of any load-bearing flaw in the argument itself; the reader's assessment is therefore left unchanged.","tokens_in":1722,"tokens_out":161,"duration_ms":21011,"concrete_test":"Retrieve the complete paper (including sections on the metric suite, experimental protocol, and baseline comparisons) and re-evaluate the strongest_claim against the actual derivations and tables.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The full manuscript text is not supplied in the query (only the abstract appears), so no concrete technical weakness in the central empirical claim or its supporting assumptions can be located. The reader's UNVERDICTED status follows directly from the same limitation.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. It combines a data-efficient expert-iteration pipeline with a scaffold exposing formal structure alongside lightweight informal abstractions, introduces a suite of metrics for structural proof properties, and reports that a 7B-parameter model trained via this method outperforms orders-of-magnitude larger models in the same family while remaining competitive with mid-tier frontier models; the scaffold is shown to improve performance across both small and frontier models.","tokens_in":1772,"tokens_out":274,"duration_ms":17188,"significance":"If the empirical claims hold under rigorous verification, the work would be significant for formal mathematics and neural theorem proving: it positions proof optimization (refactoring for maintainability and training-data improvement) as a scalable, learnable task rather than a purely heuristic one, and demonstrates that modest-sized models can restructure research-level proofs across heterogeneous objectives when given appropriate neurosymbolic scaffolding.","major_comments":[],"minor_comments":[],"recommendation":"uncertain","confidential_remarks":"The query supplies only the abstract; the full manuscript text referenced in the prompt as available via paper_source_context is not present here. This prevents section-specific technical assessment of the central empirical pipeline, metric definitions, or experimental controls, which is why the recommendation is uncertain rather than a standard revision category."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their summary of the manuscript and for acknowledging the potential significance of positioning proof optimization as a scalable, learnable task with neurosymbolic scaffolding. We note the 'uncertain' recommendation and are happy to provide any additional verification, code, or experimental details that would help resolve concerns about the empirical claims.","responses":[],"tokens_in":1215,"tokens_out":84,"duration_ms":20791,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this work shows a 7B model, trained via expert iteration on a mixed formal-informal scaffold, can restructure research-level Lean proofs and beat larger models in the same family on a new set of structural metrics. That is the concrete result worth noting first. The paper does a few things cleanly: it frames proof optimization as a learnable task rather than a pure search problem, adds lightweight informal abstractions to the formal Lean structure, and reports that the scaffold helps both small and frontier models. The empirical claim that the 7B model is competitive with mid-tier frontier systems across those metrics is the part that would matter to people building training data or refactoring large libraries. The new metric suite is presented as capturing maintainability and data quality, which is a reasonable direction even if the exact definitions need scrutiny. The main soft spot is that the abstract alone does not let us verify whether the reported gains hold after checking for post-hoc choices, whether the metrics introduce their own biases, or how stable the improvements are across different libraries. The circularity risk looks low from what is shown, and the work does not appear to rest on self-referential loops. This paper is aimed at researchers in neural theorem proving and formal mathematics tooling who already care about scaling proof maintenance. A reader working on Lean data pipelines or self-improvement loops would get direct value from the scaffold description and the 7B results. It deserves a serious referee because the problem is real, the setup is reproducible in principle, and the central empirical direction is falsifiable even if the current numbers need more context.","headline":"ImProver 2 gives a concrete neurosymbolic pipeline that lets a 7B model beat much larger models on Lean proof refactoring, but the full paper is needed to check the metric suite and training details.","tokens_in":2280,"tokens_out":407,"would_cite":false,"duration_ms":16997,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"Proof-optimization pipeline in Lean 4 is orthogonal to RS forcing chain","alignment":"orthogonal","rationale":"The paper's central machinery is an IRPO-based expert-iteration loop with neurosymbolic augmentation (goal-state traces, context slices, auto-informalization) and three structural metrics (length, modularity via spawned-goal fixed-point, explicit dependencies) for refactoring verified Lean proofs. This has no overlap with the RS forcing theorems that derive J-cost, φ, 8-tick periodicity, D=3, and the constants c, ℏ, G from a single distinction (reality_from_one_distinction, AbsoluteFloorClosure, Cost/FunctionalEquation, AlexanderDuality). The shared use of Lean 4 is incidental; the paper neither invokes nor contradicts any RS theorem.","tokens_in":60170,"confidence":"high","tokens_out":182,"duration_ms":7846,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A 7B model trained via ImProver 2 outperforms much larger models at optimizing Lean 4 proofs.","keywords":["proof optimization","Lean 4","neurosymbolic","language models","formal mathematics","expert iteration","self-improving models","theorem proving"],"falsifier":"Human experts rating the actual maintainability and readability of proofs produced by the 7B model versus the original proofs and versus outputs from larger models.","tokens_in":2623,"feed_emoji":"","tokens_out":600,"duration_ms":23813,"temperature":0.7,"pith_summary":"ImProver 2 is a neurosymbolic framework that pairs an expert-iteration training loop with a scaffold exposing both formal Lean structure and lightweight informal abstractions. The method trains models to refactor verified proofs according to new metrics that track structural properties relevant to maintainability and data quality. A resulting 7B-parameter model beats orders-of-magnitude larger models in the same family and matches mid-tier frontier models across those metrics. The scaffold itself lifts performance for both small and large models, showing that proof optimization can be treated as a learnable task.","feed_headline":"7B model beats larger ones at Lean proof optimization","feed_subtitle":"Neurosymbolic scaffold plus expert iteration lets small models compete with mid-tier frontier models on structural proof metrics.","key_machinery":"The neurosymbolic scaffold exposing formal Lean structure alongside lightweight informal abstractions, used inside an expert-iteration pipeline.","core_discovery":"ImProver 2 combines data-efficient expert iteration with a neurosymbolic scaffold to train language models for automated proof optimization in Lean 4. This produces a 7B model that outperforms larger models within its family and competes with mid-tier frontier models on a suite of structural proof metrics. The same scaffold improves results across model scales, establishing that small models can restructure research-level proofs when given appropriate structure and training.","pith_inferences":["The same scaffold-and-iteration pattern could be tested on proof libraries in other formal systems.","Iteratively improved proof data might accelerate training of future neural provers beyond the metrics reported here.","The structural metrics could serve as an automated filter or ranking signal inside existing proof libraries."],"forward_implications":["Small models can restructure complex, research-level proofs effectively.","The neurosymbolic scaffold raises performance for both small and frontier-scale models.","Proof optimization becomes a scalable, learnable task rather than a purely heuristic one.","Optimized proofs improve both library maintainability and the quality of training data for neural provers."],"fun_headline_variants":["7B model optimizes Lean proofs more effectively than larger models","7B model matches mid-tier models on Lean proof structure metrics","Neurosymbolic approach scales proof optimization to 7B models","Expert iteration trains 7B model for Lean 4 proof restructuring"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The suite of structural proof metrics accurately reflects the goals of maintainability and training-data quality without introducing unmeasured biases or omissions.","fun_headline_variants_meta":{"raw":{"variants":["7B model optimizes Lean proofs more effectively than larger models","7B model matches mid-tier models on Lean proof structure metrics","Neurosymbolic approach scales proof optimization to 7B models","Expert iteration trains 7B model for Lean 4 proof restructuring"]},"model":"grok-4.3","cost_usd":0.007935,"raw_usage":{"total_tokens":3527,"prompt_tokens":652,"num_sources_used":0,"completion_tokens":70,"cost_in_usd_ticks":79353000,"prompt_tokens_details":{"text_tokens":652,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2805,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":652,"tokens_out":70,"duration_ms":24624,"temperature":1.0,"reasoning_tokens":2805,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-25T06:08:39.216151+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Human experts rating the actual maintainability and readability of proofs produced by the 7B model versus the original proofs and versus outputs from larger models.","supporting_citations":[],"review_version":1}