{ "counts": { "adjacent": 13, "core": 9, "errors": 0, "negative": 65, "total": 87 }, "date": "2026-07-13", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-13T17:31:46Z", "items": [ { "age_days": 3, "arxiv_id": "2607.09217", "authors": [ "Matěj Kripner", "Milan Straka" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09217", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-07-10", "score": 16.9, "source": "arxiv-ai4math-core", "summary": "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.", "title": "OpenProver: Agentic and Interactive Theorem Proving with Lean 4", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09217" }, { "age_days": 6, "arxiv_id": "2607.06341", "authors": [ "Shuangxiang Kan", "Shuanglong Kan", "Sebastian Ertel" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06341", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-07", "score": 9.5, "source": "arxiv-ai4math-core", "summary": "Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort. Large language models (LLMs) promise to generate these proofs automatically, yet existing approaches wire a fixed, human-designed proof strategy into the system and constrain the model to follow it (retrieving premises and predicting tactics one step at a time, or splitting goals by divide-and-conquer), and still prove only a fraction of their target theorems. We show that imposing such a strategy is unnecessary and limiting. Handing the whole lemma to a general LLM code agent (for example, Claude Code), free to choose its own approach, and wrapping it in a verification harness is both simpler and more effective, achieving full coverage: every targeted lemma proved, with no failures and no Coq expert intervention. The agent writes the proofs under feedback and hard constraints from the harness that keep each one sound (accepted only when the prover's kernel closes it), complete (no obligation left unproved or silently dropped), and terminating (no divergent tactics). We evaluate this harness plus code agent along three dimensions. (1) Core logic: on Iris, the state-of-the-art separation logic for concurrent and memory-manipulating programs, Aria proves all 4,257 lemmas of the four core modules and the 217 lemmas verifying Rust's standard libraries built on it, fully automatically. (2) Comparison with prior LLM provers: on reglang, where prior provers manage barely one in eight, Aria proves all 318. (3) Generality: on iris-lean, the unfinished Lean 4 port of Iris, it proves 72 not-yet-ported lemmas, showing the approach is not specific to Coq. A state-of-the-art model (Claude Opus 4.7) can write proofs for verified software development fully and automatically.", "title": "Harnessing Code Agents for Automatic Software Verification", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06341" }, { "age_days": 6, "arxiv_id": "2607.06820", "authors": [ "Pavel Snopov", "German Magai" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06820", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-07-07", "score": 9.3, "source": "arxiv-ai4math-core", "summary": "Recent advances in AI for Mathematics have focused largely on autoformalization and theorem proving, leaving the role of Computer Algebra Systems (CAS) in agentic LLM workflows underexplored. We propose a ReAct-style agentic setup that combines LLM reasoning with verifiable feedback from SageMath, together with Context7 for the up-to-date documentation. We evaluate this agentic setup across frontier models for solving research-level mathematical problems from the RealMath benchmark in a setting that emulates a computational-mathematics research loop. We also propose a refinement to the RealMath benchmark by introducing a multi-step post-processing procedure and a multi-stage validation pipeline, both of which improve the quality and reliability of the extracted problem set. Our experiments reveal substantial performance gains from SageMath access across all evaluated models on +9.7~pp on average, the gains range from 1.5~pp to 27.8~pp and narrow the gap between open-weight and closed models. Qwen~3.7-Max benefits from SageMath the most, while GPT-5.5 achieves the highest solve rate of $75.2\\%$ and the lowest token usage among tool-enabled configurations. Our findings suggest that CAS-augmented agents represent a promising direction for assisting mathematicians in computational exploration, and we believe that this work is a step towards automated conjecture discovery. The project repository is available online.", "title": "Evaluating SageMath-Augmented LLM Agents for Computational and Experimental Mathematics", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06820" }, { "age_days": 7, "arxiv_id": "2607.04655", "authors": [ "Haocheng Wang", "Baiyu Huang", "Yingjia Wan", "Xiao Zhu", "Xiaoyang Liu", "Yinya Huang", "Zhijiang Guo" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "arxiv:2607.04655", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-07-06", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "The veracious semantic alignment in autoformalization is significant for formal mathematical reasoning. However, existing evaluations provide only opaque binary verdicts or scalar scores, offering no interpretable insight into where or why translations fail. This opacity severely limits both human understanding and automated system improvement. To bridge this gap, we introduce FormalRx, a comprehensive diagnostic evaluation framework that transforms autoformalization assessment from black-box judgments into actionable feedback. At its core is SCI Error Taxonomy, a hierarchical classification scheme decomposing autoformalization errors into 28 distinct categories with strict priority ordering. Building on this taxonomy, FormalRx provides four critical diagnostic capabilities: alignment verdicts, error categorization, error localization, and correction. We instantiate the framework with a diagnostic model FormalRx-8B, trained on 56,287 NL-FL pairs with fine-grained diagnostic annotations, and release FormalRx-Test as the first fine-grained diagnostic benchmark. FormalRx-8B achieves F1-scores of 0.88 (verdict) and 0.71 (categorization), along with accuracies of 0.75 (localization) and 0.73 (correction), substantially outperforming both general-purpose LLMs and specialized baselines. By connecting evaluation with actionable insights, FormalRx enables systematic diagnosis and improvement of autoformalization systems.", "title": "FormalRx: Rectify and eXamine Semantic Failures in Autoformalization", "updated": "2026-07-06", "url": "https://arxiv.org/abs/2607.04655" }, { "age_days": 5, "arxiv_id": "2607.07779", "authors": [ "Eric Jiang", "Xiao Liang", "Yikai Zhang", "Yingjia Wan", "Mengting Li", "Haikang Deng", "Alexander K. Taylor", "Justin Baker", "Rushil Raghavan", "Junyi Zhang", "Ying Nian Wu", "Andrea L. Bertozzi", "Kai-Wei Chang", "Raghu Meka", "Matthew Sottile", "Nanyun Peng", "Amit Sahai", "Terence Tao", "Wei Wang" ], "content_date": "2026-07-08", "freshness": "fresh", "id": "arxiv:2607.07779", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents", "seed_author:Nanyun Peng" ], "published": "2026-07-08", "score": 7.5, "source": "arxiv-ai4math-core", "summary": "Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages. However, current systems remain fundamentally limited in tackling frontier research mathematics, such as discovering new theorems or resolving open conjectures, which are often open-ended, under-specified, and involve multiple layers of abstraction. We argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning. In this position paper, we provide a systematic review of the field, covering datasets, auto-formalization, and proof synthesis. More importantly, we identify core limitations of existing systems in serving as mathematical research agents, examining issues across datasets, relational structure, mathematical exploration, tool ecosystem, and human-AI collaboration, outlining a strategic road-map for the future of AI4Math.", "title": "From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier", "updated": "2026-07-08", "url": "https://arxiv.org/abs/2607.07779" }, { "age_days": 3, "arxiv_id": "2607.09632", "authors": [ "Chengkai Zhu", "Ziao Tang", "Guocheng Zhen", "Yimeng Cao", "Yusheng Zhao", "Ranyiliu Chen", "Xuanqiang Zhao", "Lei Zhang", "Xin Wang" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09632", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error correction. Formalizing its coding theorems requires connecting finite-block protocols, analytic inequalities, and asymptotic limits within a unified machine-checked framework. Existing developments, however, lack a reusable operational layer that defines codes, error criteria, achievable rates, and capacities independently of their information-theoretic characterizations. In this work, we present LeanQIT, a Lean 4 library for finite-dimensional QIT. It provides composable, kernel-checked interfaces for quantum states and channels, source and channel codes, finite-block performance criteria, hypothesis testing, one-shot quantities, and asymptotic rate constructions. Using this infrastructure, we formalize Schumacher's quantum source-coding theorem, the Holevo--Schumacher--Westmoreland classical-capacity theorem, and the entanglement-assisted classical-capacity theorem together with its strong converse. By separating operational definitions from analytic characterizations and exposing reusable achievability, converse, and asymptotic components, Lean-QIT provides a machine-readable foundation for formal QIT and a compositional knowledge substrate for emerging AI-assisted formalization, automated proof search, and agentic reasoning in quantum information and computation.", "title": "Lean-QIT: Towards a Formal Infrastructure for Quantum Information Theory", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09632" }, { "age_days": 3, "arxiv_id": "2607.09072", "authors": [ "Seongmin Lee", "Yaoxuan Wu", "Miryung Kim" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09072", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "As the cost of code generation becomes cheaper with AI, the new bottleneck in software engineering has shifted to intent specification and validation. Overcoming this durability crisis of AI-driven coding requires more than traditional fuzzing: each candidate property must be proven correct over a model and shown to hold on the real implementation, making formal proof and systematic property-based testing (PBT) complementary. However, validating properties this way at scale requires solving two subproblems: verifying candidate properties and operationalizing PBT without AI hallucination. We hypothesize that recurring property patterns, cast as property templates--abstract, parameterized forms with holes--address both at once. This paper investigates recurring property patterns in Apache Spark. In data-intensive scalable computing systems, correctness properties arise from the principles of data partition, computation decomposition, and dataflow computation. For instance, aggregation decomposition relates a global function executed on the entire dataset to a local function followed by a recombiner. We design an agentic, dual-track validation framework that uses property templates to formally verify correctness in the Lean 4 theorem prover and instantiate PBT templates as executable PySpark tests. Our evaluation shows that property templates increase agentic proof engineering success by up to 2.6x (1.6x on average) and reduce proof hallucinations by 59%. Template-guided PBT synthesis reduces intent misalignments from 22 to 1 and cuts synthesis cost by up to 5.7x (3.8x on average). Template-guided synthesis further exceeds a state-of-the-art Spark fuzzer and approaches unguided LLM-based PBT on code coverage. Finally, comparing the two tracks is informative: when a proof succeeds yet a PBT finds a counterexample, the mismatch identifies a gap between the formal model and implementation.", "title": "Agentic Proof and Property-Based Testing via Property-Templates in Data-Intensive Computing", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09072" }, { "age_days": 4, "arxiv_id": "2607.08692", "authors": [ "Arthur F. Ramos", "Tulio Soria" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08692", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-09", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We present a metagame analysis of the competitive Pokemon Trading Card Game, machine-checked in Lean 4 over real tournament data. The headline game-theoretic results, including Nash equilibrium, replicator dynamics, and the matrix-level type-bridge computation, rely on native_decide, which trusts Lean's compiler rather than its kernel; the trust boundary is made explicit. The artifact spans approximately 31,900 lines, 87 files, and 2,627 theorems, of which roughly 200 directly verify empirical claims, with no sorry, admit, or custom axioms. Analyzing Trainer Hill data from January to February 2026 for events with at least 50 players, over 14 archetypes and their full pairwise matchup matrix, we prove a popularity paradox: the most played deck, Dragapult, with 15.5% metagame share, has only 46.7% expected win rate, while Grimmsnarl, with 5.1% share, achieves 52.7%. A machine-checked Nash equilibrium of the raw game assigns Dragapult 0% weight; exhaustive enumeration over all nonempty support subsets confirms a unique symmetric Nash equilibrium of the constant-sum symmetrization with seven-deck support. Against this equilibrium mix, Dragapult falls 40.4 permil below the game value. Single-step replicator dynamics indicate downward fitness pressure on Dragapult, upward pressure on Grimmsnarl, and strongest extinction pressure on Alakazam. A 10,000-iteration sensitivity analysis confirms qualitative stability, with core support decks appearing in more than 96% of resampled equilibria. The primary contribution is methodological: a reproducible case study showing how formal verification can turn qualitative metagame narratives into machine-checkable, re-runnable strategic science.", "title": "From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08692" }, { "age_days": 6, "arxiv_id": "2607.06693", "authors": [ "Pedro Abdalla", "Jaume de Dios Pont", "João P. G. Ramos", "Mitchell A. Taylor" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06693", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "lean_formal_proving_agents" ], "published": "2026-07-07", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We prove that, after $L^2$ normalization, stable phase retrieval holds over the $L^2$-spans of independent real-valued centered random variables if and only if all but possibly one coordinate satisfies a uniform two-sided $L^1$ bound. This provides a complete characterization of stable phase retrieval for such subspaces, building upon the pioneering work of Calderbank--Daubechies--Freeman--Freeman and confirming the conjectured characterization communicated to us by those authors. We provide two different proofs of this fact, both based on a decomposition of the $\\ell^2$-coefficients of each random variable. The first is a compactness proof, which makes use of the infinite divisibility of limit laws of tail sums. The second is a quantitative proof, which substitutes the compactness step with an explicit dichotomy based on anticoncentration estimates of Sperner type. This latter proof was partially LLM generated based on the ideas in the first proof and a considerable amount of guidance by the authors. An autoformalization of our main result in Lean 4 is also provided, following the ideas in the quantitative proof.", "title": "Stable Phase Retrieval for Spans of Independent Random Variables", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06693" }, { "age_days": 6, "arxiv_id": "2607.05810", "authors": [ "Yueke Zhang", "Yifan Zhang", "Zihan Fang", "Kevin Leach", "Wei Zhang", "Yu Huang" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.05810", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation", "verifier_guided_reasoning" ], "published": "2026-07-07", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Code generation with large language models (LLMs) remains unreliable because generated programs can appear correct while still violating key semantic requirements in the natural language specification. Existing feedback-based methods improve over coder-only generation, but they often rely on unstructured critique or execution signals that do not explicitly identify what the code is semantically missing. We present SCOPE, a prover-initialized subgoal critic for code generation. SCOPE adapts a Lean-oriented prover model to produce three parseable feedback fields for downstream code generation: subgoals, gap analysis, and a robustness checklist. Our approach combines supervised fine-tuning, process-aligned reinforcement learning (RL), and feedback-guided inference, with two complementary rewards during RL: a dense reward for structured critique quality and a sparse reward based on whether the critique improves the coder's execution score. Experiments show that SCOPE improves over the compared feedback baselines. On LiveCodeBench V6, SCOPE achieves 39.4% pass@1, compared with 36.6% for Reflexion and 20.6% for the coder-only baseline. On BigCodeBench (Hard), it reaches 42.6%, surpassing Reflexion at 36.5% and coder-only generation at 34.5%. Further analysis shows that SCOPE's gains are concentrated in tasks with concrete semantic constraints and that its code corrections are more localized than Reflexion's.", "title": "SCOPE: Leveraging Subgoal Critiques for Code Generation", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.05810" }, { "age_days": 3, "arxiv_id": "2607.09383", "authors": [ "Yichen Xu", "Oliver Bračevac", "Cao Nguyen Pham", "Yaoyu Zhao", "Martin Odersky" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09383", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Substructural type systems give strong static control over aliasing. Examples include uniqueness, separation, and borrowing. How can such control be brought to established languages whose programming models rely on higher-order abstraction, unrestricted aliasing, and pervasive sharing? We study this problem in the context of Scala. We show how to retrofit these guarantees selectively instead of globally: ordinary code keeps Scala's usual aliasing discipline, while stronger guarantees can be enforced where they matter. Our starting point is Scala's capture checking, whose treatment of capabilities is inspired by the object-capability tradition: capabilities are ordinary values, and capture sets record, in a value's type, which capabilities the value may use. We develop System Capybara, which adds a selective alias-control layer to this mechanism. By tracking separation, consumption, freshness, and read-only access for capabilities, Capybara recovers key reasoning principles from substructural and ownership-based disciplines without global invariants. We give a type-preserving translation from the surface calculus Capybara to CoreCapybara, a core calculus extending System Capless, the earlier foundation for capture checking. The translation uses quantifiers for capture polymorphism and freshness, and constraint-indexed modal types for separation. We prove a semantic soundness result for the core calculus in Lean 4 and derive type safety, memory safety (no use-after-free or double-free), immutability of read-only computations, and data-race freedom for well-typed programs. Finally, we implement Scala 3's new separation checker, which brings higher-order separation reasoning about effects, capabilities, and resources to ordinary Scala, including fearless concurrency.", "title": "System Capybara: Tracking Capabilities for Separation and Freshness (Extended Version)", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09383" }, { "age_days": 3, "arxiv_id": "2607.09014", "authors": [ "Patrick White" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09014", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A proper sub-box of $A=\\{0,1,2\\}^d$ is a product $S_1\\times\\dots\\times S_d$ with each $\\varnothing\\neq S_i\\subsetneq\\{0,1,2\\}$. A double cover is a finite multiset of proper sub-boxes covering every point of $A$ exactly twice; write $f(d)$ for the minimum size of a double cover. Leader, Milicevic and Tan asked whether $f(d)\\ge 2^d$ for all $d$ (Question 4.1 of the PatternBoost paper of Charton-Ellenberg-Wagner-Williamson), analogous to the Alon-Bohman-Holzman-Kleitman partition bound $2^d$. No better than the trivial volume bound was previously known, for any $d\\ge 2$. We prove the first nontrivial lower bounds. A modular refinement of the parity argument gives $f(d)\\ge 2^{d+1}/(d+1)$; a slicing argument gives $f(4)\\ge 19$, $f(5)\\ge 33$, both above $2^d$, resolving the question for $d=4,5$ -- the first cases beyond the trivially known $d\\le 3$. A finer \"line rigidity\" argument yields $f(6)\\ge 60$, breaking the profile-statistic barrier (capped at $57$, shown here). This is formally verified in Lean 4: $f(6)\\ge 60$ is machine-checked on the three standard Mathlib axioms alone. On the upper-bound side, a dimension-lifting construction $f(r+3)\\le 6\\cdot 2^r+3f(r)$ gives $f(6)\\le 81$ (improving the known $82$) and $f(d)\\le(\\tfrac65+o(1))2^d$ asymptotically; a refinement improves the constant to $\\tfrac87$. This makes partial progress on PatternBoost's problem of reducing their constant $1.28$, and refutes the closed-form guess $f(d)=5\\cdot 2^{d-2}+1$ from $d=7$ on. Together, $60\\le f(6)\\le 81$. Finally we isolate the construction-side obstruction -- an \"S+c=2^j+1\" phenomenon, every skeleton sitting exactly one box past the partition bound -- and show it is of a piece with the Leader-Milicevic-Tan question itself.", "title": "New bounds for double covers of the discrete box {0,1,2}^d", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09014" }, { "age_days": 4, "arxiv_id": "2607.08656", "authors": [ "Jaume de Dios Pont", "Lukas Liehr", "Mitchell A. Taylor" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08656", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the Cantor measure with base $b$ does not admit a Fourier frame whenever $b > 1$ is an odd integer. In particular, this answers a question of Strichartz on the existence of a Fourier frame for the middle third Cantor measure. A formalization of our main result in Lean 4 is also provided.", "title": "Cantor measures with odd base do not admit Fourier frames", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08656" }, { "age_days": 4, "arxiv_id": "2607.08986", "authors": [ "Joseph K. Miller" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08986", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game. The objective is to turn a LaTeX document into Lean. The game is won when the development compiles, contains no sorry, and a machine check shows the target theorems rest on Lean's foundational axioms alone. Reuse is a second check, by a definition we introduce: whether the development yields a self-contained layer of general mathematics the wider library could absorb. The case study is a complete, axiom-clean formalization of well-posedness for the nonlinear Vlasov equation via Dobrushin's mean-field route -- existence, uniqueness, the stability estimate and mean-field limit, and a short-window superposition principle (weak solutions are Lagrangian). The human's role was to direct, not to write proofs: to scope the definitions, steer the decompositions, and triage the library's gaps; the AI agent executed. The formalization certifies the proof of each statement as written; whether the written statement is the intended theorem stays the mathematician's judgment. The optimal-transport machinery that fell out of the build (in particular, properties of the Wasserstein-1 metric and the Kantorovich-Rubinstein duality theorem) separates into a self-contained layer that compiles against Mathlib alone: about a sixth of the development (49 of 299 declarations), behind a 22-declaration interface with no reverse dependency. The headline theorems ran in about a week, the full development in about a month. We report the quantitative claims as observations of one game, not as general laws. The game's rules name no particular system, so the methodological framing is meant to outlast the tools of any one run.", "title": "A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08986" }, { "age_days": 5, "arxiv_id": "2607.07857", "authors": [ "Sirui Lu", "Erickson Tjoa", "J. Ignacio Cirac" ], "content_date": "2026-07-08", "freshness": "fresh", "id": "arxiv:2607.07857", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-07-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration. The agents, coordinated through a structured mathematical blueprint and periodic human review, orchestrated and executed the full formalization autonomously. For some statements, the agents were able to explore new proof routes that are not part of the standard literature. Along the way the agents produced extensive tensor-network and quantum-information libraries not previously available in Mathlib, Lean's mathematical library. As a physical application, the formalization also extends towards symmetry-protected topological phases in one dimension. We find that the main bottleneck in large-scale autoformalization is enforcing mathematical intent and we provide a detailed study of the full process and various subtleties involved. We release the codebase as the library \\href{https://github.com/LionSR/TNLean}{TNLean}, together with a \\nChapters{}-chapter \\href{https://lionsr.github.io/TNLean/blueprint/}{blueprint} of the formalization effort.", "title": "Multi-agent Autoformalization of Tensor Network Theory", "updated": "2026-07-08", "url": "https://arxiv.org/abs/2607.07857" }, { "age_days": 6, "arxiv_id": "2607.05987", "authors": [ "Yuwei Lyu", "Kai Li" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.05987", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We formalize in Lean 4 a complete combinatorial route from Scarf's theorem to Brouwer's fixed point theorem and to the existence of mixed Nash equilibria in finite games. The development follows Ivanov's indexed-order formulation of Scarf's theorem, formalizes the room--door incidence structure and parity argument, instantiates the theorem on finite grids of the standard simplex, and carries out the compactness and continuity argument needed to obtain a fixed point. We then extend the result to finite products of simplices by an explicit embedding--projection construction and use this product theorem to prove mixed Nash equilibrium existence via the Nash map. As a secondary by-product, we derive BrouwerBench, a preliminary 80-item Lean-grounded benchmark for probing proof-structure understanding within this single formal development.", "title": "Formalizing Scarf, Brouwer, and Nash in Lean", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.05987" }, { "age_days": 6, "arxiv_id": "2607.06089", "authors": [ "Serhii Zabolotnii" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06089", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We study binary classification under shared-generator elliptical class-conditional distributions. The log-likelihood ratio is an additive function of the two squared Mahalanobis radii, with radial link $\\varphi=\\log g$; QDA is recovered only when this link is affine. We derive the Bayes radial-link family from the within-class radius law and estimate it by a finite fractional-power stochastic-polynomial projection instead of tuning a generic spline. The link is identifiable from the radius law, the plug-in estimator is $\\sqrt{n}$-consistent and asymptotically normal under finite-moment regularity conditions, and the induced classifier is asymptotically Bayes-optimal in an iterated sieve limit. The structural bridge, GAM membership, and identity-link/affine-generator dichotomy are verified in Lean 4 without unproven placeholders. Against the global Mahalanobis-GAM of Ghosh et al. (2025), reimplemented with mgcv REML splines at equal input budget, the derived link is never significantly worse on three UCI benchmarks and is decisively better on breast_cancer ($[+0.009,+0.021]$ global, $[+0.109,+0.136]$ global+local). Across six real financial series under temporal-dependence-robust validation, it is never significantly worse than the fitted GAM and is significantly better on three of five heavy-tailed series plus the light-tailed control. Relative to QDA, it improves the heaviest-tailed series (oil $[+0.024,+0.070]$, S&P 500 $[+0.038,+0.126]$, JPY/USD $[+0.009,+0.047]$) and ties elsewhere. A closed-form rate simulation corroborates the $\\sqrt{n}$ rate and the predicted excess-risk dichotomy between QDA's approximation-limited floor and the derived link's vanishing excess risk. The contribution is no significant loss relative to a tuned global GAM without spline smoothing-parameter selection, plus improved accuracy over QDA where generator curvature matters.", "title": "Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06089" }, { "age_days": 6, "arxiv_id": "2607.06379", "authors": [ "Michael R. Douglas" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06379", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Mathematicians have embraced interactive theorem provers with growing enthusiasm -- building large shared libraries and machine-checking a string of landmark results. Theoretical physics is different: most of its results are not theorems but justified by arguments the community trusts without a rigorous proof. For many -- the one we treat here among them -- no rigorous proof is within reach. For 4d Yang--Mills theory, deriving exact rigorous results from first principles would first require constructing the interacting theory nonperturbatively, which is a sizable piece of one of the Clay Millennium prize problems. We argue here that an interactive theorem prover can be used to verify some non-rigorous physics arguments. The method is to postulate a short list of explicit, named physical postulates, which imply the physical results by virtue of a machine-checkable proof. The trust that remains then rests on that short, inspectable list, and the prover can report, for any downstream result, exactly which assumptions it used. We carry this out for the Seiberg--Witten solution of ${N}=2$ $SU(2)$ super-Yang--Mills -- the genus-one case -- formalized in Lean 4; the higher-genus $SU(N)$ generalization is developed in the same repository as an axiomatized skeleton and left to future work. We describe what is proved, what is assumed, how the assumptions are checked -- external review and an independent numerical oracle -- and why this discipline is a sound standard for validating AI-generated results in theoretical physics. What we offer is a discipline, reviewable on its own terms: a reader may take the Seiberg--Witten mathematics on trust and still assess the formalization method.", "title": "Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06379" }, { "age_days": 7, "arxiv_id": "2607.05492", "authors": [ "Kazumi Kasaura", "Kei Tsukamoto", "Kento Mori", "Risa Mizuno", "Takahiro Namatame", "Yuta Oriike", "Masaya Taniguchi", "Sho Sonoda", "Hayata Yamasaki" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "arxiv:2607.05492", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Quantum information theory is built on entropic quantities; among them, the sandwiched Rényi relative entropy is a fundamental divergence with various applications, and its data processing inequality (DPI) under quantum channels is a cornerstone result. In this work, we present a Lean 4 library for quantum information, designed as a reusable formal infrastructure for theoretical analysis. As a central demonstration of the library, we formalize the DPI for the sandwiched Rényi relative entropy for positive semidefinite operators on finite-dimensional quantum systems. The library provides a basis-independent operator-theoretic framework for finite-dimensional quantum mechanics compatible with the standard mathematical library Mathlib, including reusable interfaces for finite-dimensional systems, states, channels, tensor products, partial traces, Choi operators, Kraus representations, and Stinespring representations. It also builds infrastructure for noncommutative trace inequalities, including operator monotonicity and convexity via the real continuous functional calculus, block-operator positivity, Hilbert-Schmidt operator spaces, Jensen's operator inequality, generalized perspectives, operator power means, and Lieb-Ando trace inequalities. On top of this framework, we formalize entropy-specific ingredients for the DPI: variational formulas for the sandwiched quasi-entropy via Young and reverse-Young inequalities, tensor-product compatibility of real powers, and Haar measures on unitary groups. Together, these components yield a Lean formalization of the DPI, give strong subadditivity as a corollary, and provide the last missing component needed to complete the Lean formalization of the generalized quantum Stein's lemma. More broadly, the development provides machine-checkable foundations for future formalized and AI-assisted research in quantum information theory.", "title": "Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information", "updated": "2026-07-06", "url": "https://arxiv.org/abs/2607.05492" }, { "age_days": 4, "arxiv_id": "2607.08366", "authors": [ "José A. R. Fonollosa" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08366", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-09", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Fix $n \\ge 2$. A set $A = \\{a_0 < a_1 < \\dots < a_{n-1}\\}$ of $n$ residues in $\\Z_N$ is \\emph{valid mod $N$} if the all-ones multiset is the \\emph{only} size-$n$ multiset drawn from $A$ whose sum is $p := \\sum_i a_i \\pmod N$. For the super-increasing set $A = \\{2^k - 1 : 0 \\le k \\le n-1\\}$ we determine the least valid modulus exactly: $\\Nmin(n) = 2^{\\,n} - 2^{\\lfloor \\log_2 n \\rfloor}$ for all $n \\ge 2$. Both directions of the proof are elementary, resting on a sharp minimal-digit-sum estimate for representations by binary coins, and the full theorem has been machine-checked in Lean~4/Mathlib for all $n$ (https://github.com/jarfo/min-modulus). We conjecture that no size-$n$ residue set admits a smaller valid modulus. This validity condition is exactly what makes the permanent of an $n \\times n$ matrix equal to a single coefficient of a row-product polynomial modulo $x^N - 1$, extractable by a size-$N$ discrete Fourier (or number-theoretic) transform; the theorem thus identifies the smallest transform, $N \\approx 2^n$, for which this evaluation is exact. That application -- and the resulting common framework for the classical formulas of Ryser and Glynn and this transform -- is developed in a companion paper [2].", "title": "Minimum modulus for the unique multiset-sum problem", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08366" }, { "age_days": 5, "arxiv_id": "2607.06944", "authors": [ "Shanwen Wang", "Yijun Yuan" ], "content_date": "2026-07-08", "freshness": "fresh", "id": "arxiv:2607.06944", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-08", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let $p$ be a prime number. We introduce a sparseness condition on the supports of $p$-adic Hahn series, and prove that this condition implies transcendence over $\\breve{\\mathbf Q}_p$, the completed maximal unramified extension of $\\mathbf{Q}_p$. As an application, we prove the order-type conjecture of $\\mathbf{Q}_p$-algebraic $p$-adic Hahn series with bounded support under the condition that the support has only finitely many accumulation points. All results in this paper have been fully formalized in the Lean theorem prover (v 4.31.0), building over Mathlib.", "title": "$p$-adic Hahn series with sparse support", "updated": "2026-07-08", "url": "https://arxiv.org/abs/2607.06944" }, { "age_days": 6, "arxiv_id": "2607.05739", "authors": [ "Ken Ono" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.05739", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "For $n\\ge1$, we let $$x_n:=\\tan\\bigl(\\sum_{k=1}^{n}\\arctan k\\bigr).$$ In 2008, Amdeberhan, Medina, and Moll conjectured that $x_n\\not \\in \\mathbb{Z}$ for every $n\\ge5$. This was known for a set of positive integers of density $\\tfrac{120}{817}\\approx0.1469$. We prove that an integer value $x_n=m$ satisfies $|m|\\ge e^{(1/2+o(1))\\,n\\log n}$, which we use to deduce that $$\\#\\{\\,1\\leq n\\le N:x_n\\in\\mathbb{Z}\\,\\}=O(\\log N). $$ In particular, the conjecture holds for a density-one set of $n$. The results in this note were formalized in Lean/Mathlib and produced autonomously by AxiomProver from natural-language statements.", "title": "Integer values of $\\tan(\\arctan 1+\\arctan 2+\\cdots+\\arctan n)$ are rare", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.05739" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:0d2a4847435e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: clarify warning for semireducible definitions of class type (#14196)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/0d2a4847435ef95e2aa2eba0a7783ab945e44b76" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:373c37ead3c0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/373c37ead3c0dd57f3a7ab0329157088e0907adb" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:8bcd02e578d7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: disable grind_bitvec2 benchmark (#14377)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/8bcd02e578d7479fa0eb52e64015b54873619da7" }, { "age_days": 0, "authors": [ "Salvatore Mercuri" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a3364faec429", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(NumberTheory): make `InfinitePlace.Completion` a one-field structure (#41543)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/a3364faec42918fcd84a03a255b50570129f9ead" }, { "age_days": 0, "authors": [ "Thomas R. Murrills" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b118b5f12c2e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(scripts/runSkimmer): only `lake update skimmer` (#41662)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/b118b5f12c2e678fada5704d29a60351692365b1" }, { "age_days": 0, "authors": [ "Yongxi (Aaron) Lin" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:46931f419bdd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: function composition preserves boundedness (#33126)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/46931f419bdd637d3b9db8c6232646f21fb519c4" }, { "age_days": 0, "authors": [ "Anatole Dedecker" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f65b4ad3395c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: convenience API for strict linear maps (#41250)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/f65b4ad3395cc684112fd1d1c633681822fec13c" }, { "age_days": 0, "authors": [ "Eric Wieser" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b883e5758cef", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Multiset): add the Multiset version of `List.find?` (#40326)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/b883e5758cefe396784b08a8444fbdc322737b5f" }, { "age_days": 0, "authors": [ "Hagb (Junyu Guo 郭俊余)" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5715d56e4663", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Finsupp/MonomialOrder): weaken `IsOrderedCancelAddMonoid` to `IsOrderedAddMonoid` (#32829)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/5715d56e4663ff3c48097b3c24d10a5c5bab7ece" }, { "age_days": 0, "authors": [ "teorth" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:11c7f27fb4ff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/BoxIntegral): minor API additions to BoxIntegral and BoxIntegral.BoxAdditiveMap (#41592)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/11c7f27fb4ff943700fc58bb89b3ad8789e250b3" }, { "age_days": 0, "authors": [ "Nailin Guan" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d6b248061c64", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Module): lemma for `spanFinrank` eq one (#40813)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/d6b248061c64ee3aff51e28de440294ac185a6dc" }, { "age_days": 0, "authors": [ "Junyan Xu" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a7a0864217d0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra): localization preserves unique factorization (#33832)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/a7a0864217d023035b6915bf6fcd07cc9e3161d0" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4a7edd35ec64", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-07-13 (#41687)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/4a7edd35ec64de7117995da659e9d4d80e6cca19" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b86f7b9ebe47", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: tweak bench suite (#41692)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/b86f7b9ebe47ff9bc2db86b38a6b7f3fac59febb" }, { "age_days": 0, "authors": [ "Kevin Buzzard" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:22e2625af6b5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: simplify `show _ from by _` to `show _ by _` (#41493)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/22e2625af6b5248de5323d0026f58b5771833042" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:81a5d257c8e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: bump toolchain to v4.32.0 (#41690)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/81a5d257c8e410db227a6665ed08f64fea08e997" }, { "age_days": 0, "authors": [ "damiano" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9637cdc63e17", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add missing `to_additive` docstrings in category theory files (#41643)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/9637cdc63e1714c89e44dbeb8573b755996809ac" }, { "age_days": 0, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3977924c6317", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/{W}Seq): cleanup flexible linter exceptions (#41672)", "updated": "2026-07-13", "url": "https://github.com/leanprover-community/mathlib4/commit/3977924c63176de352502cfd7f029dcb54efbc0a" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:5c749092faf4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: normalization of bitvector literals in `grind` (#14371)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/5c749092faf4c9c121eaa5ac5071ac93b37fb7e8" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:1d69dd53445e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: bitvec simproc bug (#14370)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/1d69dd53445ef8e60c7ec9728b44383ebb76b5bf" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:7f3f2fd48c70", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: 0 divides constraint in `grind` (#14373)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/7f3f2fd48c70226d9dd15b0f9125c5d8262893e4" }, { "age_days": 1, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:30ff0d59c486", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Util/AddRelatedDecl): error instead of panicking when the target declaration already exists (#41422)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/30ff0d59c48647f4d2f88c55fe92696464019c50" }, { "age_days": 1, "authors": [ "Attila Gáspár" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f34e762642b3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Sets): disjoint `Compacts` form an open set (#40053)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/f34e762642b3470574f0117a100a8fc4eaeae651" }, { "age_days": 1, "authors": [ "Nailin Guan" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7c59a0a6cbff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal): prime avoidance for maximal ideal (#40814)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/7c59a0a6cbff267024f1c701907f704c690782fb" }, { "age_days": 1, "authors": [ "Noah Walker" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6ee55367d7ab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/GroupWithZero): prove that `Is{Left,Right}CancelMulZero` is Dedekind-finite (#41453)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/6ee55367d7ab04d9a9d24751d6b493b7e023e27d" }, { "age_days": 1, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bd2f30dcd35b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-07-12 (#41650)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/bd2f30dcd35b91fe8cf67d333de797947f6173e2" }, { "age_days": 1, "authors": [ "Sebastien Gouezel" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9de183cf4048", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: fix nsmul and zsmul non-reducible diamond in SplittingField (#40708)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/9de183cf4048aa3d2198571106af8d53ac8ff4fd" }, { "age_days": 1, "authors": [ "damiano" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:eb3af393c9d3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add missing `to_additive` docstrings in MeasureTheory.Measure (#41638)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/eb3af393c9d32e9d57fef7aeff7bd266e5ed1d7c" }, { "age_days": 1, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:79aee35d9696", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(scripts): update nolints.json (#41627)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/79aee35d9696d759b73eed71d7dde666750bc35e" }, { "age_days": 1, "authors": [ "Yongle Hu" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2800ac2bd3c2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/Polynomial/Basic): remove unused `haveI` and defeq abuse (#41608)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/2800ac2bd3c2653f48647df6cb15b22c6e6e5039" }, { "age_days": 1, "authors": [ "Scott Carnahan" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c0cbc05a6f61", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/TensorProduct/Map): add symm_lTensor and symm_rTensor (#41550)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/c0cbc05a6f61999c6e6e8afdcbbe0b3daff95a27" }, { "age_days": 1, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b95982f413bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Geometry/Manifold/ContMDiff/Atlas): generalise `mem_maximalAtlas_of_contMDiffOn` and friends (#40720)", "updated": "2026-07-12", "url": "https://github.com/leanprover-community/mathlib4/commit/b95982f413bf08801f23ed434feeb52dad009330" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:2aaf675cfd53", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: try to skip `check` at `applyAbstractResult?` (#14361)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/2aaf675cfd53143c757178c1a5954ded3e930ff5" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:630f130affce", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: inline unsafe term helpers (#14365)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/630f130affce3a7a0065014dd4ea4603c42c06b2" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:12c859a4d735", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: no lib files for exe template (#14366)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/12c859a4d735fbcdb3ebbddb42dcc8619bcc7a7d" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:49a89d6148a4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: `presetup` module facet (#14300)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/49a89d6148a42f82336f1b5cca00a5e67fa67a9d" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:164a94bafecc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: `getLakeSharedDynlib` (#14364)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/164a94bafecc3ff732dc1e2c45ba968c9a70849d" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover/lean4:82ab4ec95682", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove unnecessary `public meta import` on critical rebuild path (#14360)", "updated": "2026-07-11", "url": "https://github.com/leanprover/lean4/commit/82ab4ec9568240c66f8cfeb62ae369c389f59950" }, { "age_days": 2, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5e1cacbae25b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: a map is smooth iff its post-composition with an immersion is (#28865)", "updated": "2026-07-11", "url": "https://github.com/leanprover-community/mathlib4/commit/5e1cacbae25bf77b65215f70f89fe2124bebdd60" }, { "age_days": 2, "authors": [ "Pepa Montero Jimena" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4efb186f102e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Algebra/InfiniteSum/NatInt): hasProd versions of ℕ+/ℕ transfer lemmas (#41502)", "updated": "2026-07-11", "url": "https://github.com/leanprover-community/mathlib4/commit/4efb186f102ebfd2eea1545c151d6fbcfdff0e43" }, { "age_days": 2, "authors": [ "Evgenia Karunus" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:052559c5c957", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(MeasureTheory/Function/EssSup): add iSup_le_essSup, add essSup_le_iSup (#40453)", "updated": "2026-07-11", "url": "https://github.com/leanprover-community/mathlib4/commit/052559c5c957052541d779c79f6c57f78379de8b" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:8006bb040003", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: fsanitize exclusion cleanup (#14349)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/8006bb040003c4e51c57f46af26e3373d5f6b1d0" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:d387212232d5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: add vcgen benchmark over the verina corpus (#14340)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/d387212232d51ff1e8401bc5d4f23eaa4ff282bd" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:0aa1c39b6dde", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: fast path for `grind`'s internal envelope type `Ring.OfSemiring.Q type` (#14358)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/0aa1c39b6dded6d88d07eec27b078ee44ee3e78c" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:dd8e885bf12e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: avoid unnecessary `modifyEnv` (#14354)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/dd8e885bf12ec43c87046fd1484e29384d04ea6c" }, { "age_days": 3, "authors": [ "Potato Hatsue" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:02294f9a2c32", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix incorrect examples of K-like reduction in RecursorVal docstring (#13967)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/02294f9a2c32551fc8a2273076b46ed5d780a2a6" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover/lean4:a586d13e4dae", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: revert \"chore: cmake: disable Lake cache on `PREV_STAGE` use as well\" (#14347)", "updated": "2026-07-10", "url": "https://github.com/leanprover/lean4/commit/a586d13e4dae0b84baab92f5e4ac2ab2782e46e9" }, { "age_days": 3, "authors": [ "Kim Morrison" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c368140668f5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Topology/DiscreteSubset): fix typo eventualy -> eventually in lemma name (#41569)", "updated": "2026-07-10", "url": "https://github.com/leanprover-community/mathlib4/commit/c368140668f5fa16a1bd977448c1f665d48c3df4" }, { "age_days": 4, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:4c1cf2f9806a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: construct `IntModule.OfNatModule.Q type` manually (#14346)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/4c1cf2f9806ac782dc2bcedba9aba7229ce99ac0" }, { "age_days": 4, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:804bb1281b43", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: run shell main on a thread with the configured stack size (#14343)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/804bb1281b4365af2195fb716b7982a7f37eee4d" }, { "age_days": 4, "authors": [ "Joachim Breitner" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:e599b3e12cc3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `partial_fixpoint` error on nested recursive calls (#14335)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/e599b3e12cc3da4f9240cd649529d6edaf03abaf" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:41ace69675a8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lint on `open` statements within `namespace` which do not open all candidate namespaces (#14325)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/41ace69675a807d954d1a6938ced70e26bcded17" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:5ae4723270cd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: error on self-deprecation (#14333)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/5ae4723270cd968db64e8f307ac41a3eaa592466" }, { "age_days": 4, "authors": [ "Garmelon" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:69d6d5229239", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: repeat some benchmarks to avoid outliers (#14342)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/69d6d5229239dadbff0853c8d8629a5097da8a2b" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:387908cb61ec", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: reduce namespace pollution (#14308)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/387908cb61eca4b499242240eda2dde1ebc589f9" }, { "age_days": 4, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:9d4bba94d5ae", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: disable `interpreter.prefer_native` for further build stages as well (#13757)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/9d4bba94d5aeb0de2c3d2236899b2206d3ddba39" }, { "age_days": 4, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "github:leanprover/lean4:1bb99fe3a25e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: show failed tests' output in test summary (#14337)", "updated": "2026-07-09", "url": "https://github.com/leanprover/lean4/commit/1bb99fe3a25e0b93a9a7a518bb1d27475e2f2745" }, { "age_days": 3, "arxiv_id": "2607.09582", "authors": [ "Okezzi Ukorigho", "Opeoluwa Owoyele" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09582", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.", "title": "Entropy-Constrained Machine Learning with Residual Data Augmentation for Modeling Chemical Kinetics", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09582" }, { "age_days": 3, "arxiv_id": "2607.09564", "authors": [ "Andrew Slattery", "Jonathan Sterling" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09564", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Surface syntax in proof assistants like Rocq, Lean, Agda, and Idris is highly implicit, lacking many details that are needed for user-written code to denote precisely defined mathematical objects. Elaboration is an algorithm that accounts for these details by translating surface syntax to an explicit enough core syntax. The reliability and predictability of elaboration relies on several critical properties of the core type system, including decidability of judgemental equality and the injectivity of type constructors; these dependencies are witnessed in a concrete system by explicit calls to conversion checking and weak-head reduction subroutines. We introduce a dependently typed monadic domain specific language for the executable specification of correct-by-construction elaboration algorithms that is abstracted from any particular representation of normal forms or algorithm for conversion checking. In particular, we represent a bidirectionally typed surface language for Martin-Löf type theory by shallow embedding in this DSL so that the translation of surface terms into core terms amounts to elementary equational calculation. This translation is correct by construction in the sense that it cannot produce ill-typed terms, and is automatically stable under judgemental equality of core terms and even under substitution; from the latter property, we obtain a new denotational interpretation of the suspension of elaboration problems. Finally, a concrete elaboration algorithm is extracted by algebraic means from a presheaf model of the DSL built out of the bi-initial natural model of Martin-Löf type theory.", "title": "Bidirectional Elaborators à la Carte", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09564" }, { "age_days": 4, "arxiv_id": "2607.08006", "authors": [ "Naveen Ravi", "Nathan Wichmann", "Md. Wasi-ur- Rahman", "Aurelien Bouteiller", "Yıltan Hassan Temuçin", "Avinash Kethineedi", "Johnathan Alsop", "Brandon Potter", "Shubhendra Pal Singhal", "Jun Shirako", "Akihiro Hayashi", "Vivek Sarkar", "Lawrence C. Stewart", "Michael Beebe", "Benjamin Michalowicz", "Jeongnim Kim", "Thiago Teixeria", "Mark F. Brown", "Aaron Welch", "Oscar Hernandez", "Wendy Poole", "Steve Poole" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08006", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Leadership-class HPC systems are now accelerator-centric, with GPUs providing most floating-point throughput and memory bandwidth. As next-generation systems increasingly integrate accelerators through high-speed memory fabrics and system interconnects, exposing larger tightly coupled device domains, \\ac{PGAS} models such as OpenSHMEM provide a natural abstraction for expressing fine-grained remote memory operations across these devices. While OpenSHMEM 1.x offers a lean PGAS model for irregular communication, atomics, fine-grained synchronization, and collectives, its memory model lacks portable semantics for accelerator architectures. As a result, existing GPU-enabled OpenSHMEM implementations differ in memory management, capability discovery, and operation semantics, limiting portability and ecosystem cohesion. This risks fracturing the community that OpenSHMEM was originally created to unify. This paper proposes an OpenSHMEM Auxiliary Specification for GPU-Aware Communication, designed as a lightweight, backward-compatible extension to OpenSHMEM 1.x. The auxiliary specification introduces a minimal memory model extension via a GPU-scoped memory space abstraction, along with capability queries and well-defined semantics for using \\acs{GPU}-attached buffers in RMA, atomic, synchronization, and collective operations. This is initially conceived through the lens of a host-initiated interface, although it provides a general set of semantics that also allow for optional device-initiated support. A central goal of this effort is to demonstrate that GPU-aware OpenSHMEM semantics can be specified and implemented across GPUs from multiple vendors, providing a practical and rapidly implementable step toward unification under a vendor-neutral specification while informing the design of future OpenSHMEM specifications.", "title": "Toward a Unified GPU-Aware OpenSHMEM Specification", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08006" }, { "age_days": 5, "arxiv_id": "2607.07879", "authors": [ "Peter Lean", "Ewan Pinnington", "Patrick Laloyaux", "Mihai Alexe", "Eulalie Boucher", "Simon Lang", "Tomas Kral", "Paul Poli", "Hans Hersbach", "Niels Bormann", "Matthew Chantry", "Anthony McNally" ], "content_date": "2026-07-08", "freshness": "fresh", "id": "arxiv:2607.07879", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Earth system reanalysis datasets are foundational for weather and climate research and provide the gridded training data used by most machine learning weather prediction systems. Here we show results from a prototype system that suggest that machine learning models trained only on Earth system observations can potentially be used to generate multi-decade global reanalyses without using physics-based numerical models. The resulting gridded fields capture large-scale atmospheric structure and variability across multiple timescales, while exhibiting signs of physical coherence in several key dynamical diagnostics. Evaluations of the prototype against held-out independent atmospheric observations indicate that the root mean square vector error of upper-level winds is close to that of ERA5 when compared at a consistent resolution, and that the standard deviation of the error at the surface is between that of 4th- and 5th-generation ECMWF reanalyses (ERA-Interim and ERA5). Furthermore, while traditional reanalysis production is computationally expensive, typically taking several years to produce, the reanalysis presented here was generated during the course of a single working day. These results suggest that observation-trained machine learning models offer a promising new approach for reanalysis production from observations alone.", "title": "Global reanalysis from observations alone with machine learning", "updated": "2026-07-08", "url": "https://arxiv.org/abs/2607.07879" }, { "age_days": 5, "arxiv_id": "2607.07669", "authors": [ "Jordan Painter", "Dipankar Srirag", "Adarsh Kappiyath", "Diptesh Kanojia", "Aditya Joshi", "Lu Yin" ], "content_date": "2026-07-08", "freshness": "fresh", "id": "arxiv:2607.07669", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Large language models increasingly \\emph{understand} dialectal English, yet still \\emph{produce} only standard, US-leaning English, leaving dialectal generation, the harder half of the problem, largely unaddressed. We introduce \\textbf{DiaLLM}, which continually pretrains three open-weight language model families on the International Corpus of English and applies implicit and explicit post-training paradigms, each combined with three model alignment strategies, giving the first controlled comparison of these components across Australian, Indian, and Northern British English. Our results reveal that dialectal robustness and generation are \\emph{dissociated}: benchmarks are shaped by continual pretraining and SFT, while alignment visibly reshapes generation in ways benchmarks do not capture. Explicit variety-targeted adaptation produces output reliably recognised as dialectal and preferred over broad alignment, yet the method that most aggressively optimises the dialectal reward is not preferred by human evaluators. Independent linguistic analysis corroborates this reward-quality gap, most clearly on two of the three families. No single alignment method dominates, and closing the gap will require richer reward designs and continued investment in dialectal resources. We release all code, checkpoints, and preference datasets.", "title": "DiaLLM: An Investigation into the Robustness-Generation Gap in English Dialect Adaptation", "updated": "2026-07-08", "url": "https://arxiv.org/abs/2607.07669" }, { "age_days": 6, "arxiv_id": "2607.06627", "authors": [ "Bogdan Grechuk", "Jamal Agbanwa" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.06627", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Many Diophantine equations can be reduced to the question of whether, for a given non-degenerate quadratic form $F$ and a univariate polynomial $P$ with integer coefficients, $P(x)$ can be represented by $F$ for infinitely many values of $x$. We develop a method for answering this question for certain cubic and quartic polynomials $P$, as well as for certain polynomials of the form $P(x)=R(Q(x))$, where $R(t)$ and $Q(x)$ are polynomials of degree $3$ and $2$, respectively. Applying this method with $F(y,z)=y^2+z^2$, $R(t)=t^3-4$ and $Q(x)=x^2$, we conclude that $x^6-4$ is a sum of two squares infinitely often. In turn, this implies that the equation $y^2+x^3y+z^2+1=0$ has infinitely many integer solutions. Prior to this work, it was the shortest equation for which it was open whether its integer solution set is finite or infinite. We conclude with a list of the new shortest equations whose finiteness problem remains open. All main results of this paper has been formalized in Lean using Aristotle.", "title": "On the polynomial values represented by quadratic forms", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.06627" }, { "age_days": 6, "arxiv_id": "2607.05874", "authors": [ "Wanli Ma", "Zichen Wang", "Zaiwen Wen" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "arxiv:2607.05874", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Existence proofs for many matrix decompositions share a recursive routine: a local transformation prepares the matrix, a slice is selected, a recursive solution is obtained, and the result is lifted and transported back. Formalizing this routine uniformly in dependent type theory is difficult because recursive subproblems may change index types, and reconstruction must preserve structural predicates across block embeddings and reindexings. We develop a Lean~4 framework that separates decomposition schemas, transformations, reduction strategies, measures, lifting, transport, and subtype induction. The framework uses general index types, packages square and rectangular matrices in universe types, and provides a decomposition driver that assembles strategy data into subtype-induction instances. It has been instantiated across PLU, LU, LDL/Cholesky, QR variants, Gauss rank normal form, Hessenberg reductions, Schur variants, normal spectral decomposition, SVD, bidiagonalization, tridiagonalization, UTV, Smith normal form, rational canonical form, and Jordan-type forms at varying levels of statement strength. Across these instances, repeated decomposition proofs are best treated not as separate tasks but as instances of a more general inductive statement whose interface records a certified proof path compatible with the chosen decomposition statement.", "title": "A Unified Framework for Formalizing Matrix Decomposition Proofs", "updated": "2026-07-07", "url": "https://arxiv.org/abs/2607.05874" }, { "age_days": 7, "arxiv_id": "2607.05626", "authors": [ "Muhammad Rizwan", "David Nabergoj", "Jure Demšar" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "arxiv:2607.05626", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Background: Depression frequently co-occurs with ADHD and autism spectrum disorder (ASD), but population-level differences in symptom expression between these groups remain underexplored. Objective: We examined whether social media users with ADHD and ASD differ in how they express DSM-5 depressive symptoms in their tweets, and whether differences persist across varying levels of depressive-content filtering. Methods: We analysed 1,282,437 tweets from 792 users (622 ADHD; 170 ASD) with self-reported diagnoses on Twitter. Tweets were pre-filtered for depressive relevance using zero-shot NLI, then classified into nine DSM-5 symptoms using MentalRoBERTa fine-tuned on ReDSM5. Profiles were mean-centered per user. We applied L1-penalised logistic regression with cross-validation to distinguish ADHD from ASD users, complemented by Pearson correlations for symptom co-occurrence, and tested robustness across five filtering thresholds using bootstrapping. Results: MentalRoBERTa achieved macro-F1 of 0.901 on a held-out set, outperforming the original ReDSM5 benchmark. ADHD vs ASD classification yielded stable but modest performance (cross-validated ROC-AUC 0.645-0.653). Cognitive issues, sleep issues, appetite change, and fatigue leaned toward ADHD, while suicidal ideation and anhedonia leaned toward ASD. A largely shared symptom co-occurrence structure emerged between groups; no pair met our criterion for a robust disorder-specific difference. Conclusions: Population-level differences in depression-related language between ADHD and ASD social media users were consistently observed across thresholds, reflecting reproducibility rather than clinical validity. Findings are exploratory and do not establish differing phenomenology at the individual level.", "title": "Population-Level Profiling of DSM-5 Depressive Symptoms Among Self-Reported ADHD and ASD Users on Twitter: An Exploratory Study Using Advanced NLP and Statistical Analysis", "updated": "2026-07-06", "url": "https://arxiv.org/abs/2607.05626" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }