{
  "counts": {
    "adjacent": 19,
    "core": 10,
    "errors": 0,
    "negative": 68,
    "total": 97
  },
  "date": "2026-07-08",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-07-08T16:59:00Z",
  "items": [
    {
      "age_days": 1,
      "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": 8,
      "arxiv_id": "2606.31134",
      "authors": [
        "Arshia Soltani Moakhar",
        "Iman Gholami",
        "Max Springer",
        "Mahdi JafariRaviz",
        "MohammadTaghi Hajiaghayi"
      ],
      "content_date": "2026-06-30",
      "freshness": "fresh",
      "id": "arxiv:2606.31134",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "general_ai_math_reasoning",
        "lean_formal_proving_agents",
        "tool_use_agents"
      ],
      "published": "2026-06-30",
      "score": 9.3,
      "source": "arxiv-ai4math-core",
      "summary": "While Large Language Models (LLMs) have demonstrated exceptional capabilities in mathematical reasoning, they frequently produce subtle errors that evade human detection. Formal mathematical languages like Lean 4 offer mechanical proof checking, strongly motivating the need for autoformalization: the automatic translation of natural language mathematics into verifiable code. Recent trends indicate that general-purpose LLMs, heavily optimized for standard programming, now outperform smaller models explicitly fine-tuned for Lean. Leveraging this shift, we introduce an agentic autoformalization framework powered by general coding LLMs. At the core of our system is an orchestrator that manages a multi-agent pipeline tailored for research-level mathematics. Because cutting-edge research frequently relies on concepts outside the scope of existing libraries like Mathlib, our system dynamically extends necessary type definitions and validates them via a novel Auxiliary Lemma technique before formalizing the primary theorems. We applied our approach to PutnamBench, producing machine-checked Lean proofs for a random sample of 32 problems. Furthermore, we evaluate our system on five papers from the ACM Symposium on Theory of Computing (STOC) spanning combinatorics, communication complexity, mechanism design, and learning theory, successfully formalizing their main theorems and validating the generated formalizations with human experts; for all five we also formalize the proofs alongside the statements, and notably two of them are proved with no axioms beyond Lean's kernel. All of our formalizations are available at https://beyondthelibrary.github.io/formal_arxiv .",
      "title": "Beyond the Library: An Agentic Framework for Autoformalizing Research Mathematics",
      "updated": "2026-07-01",
      "url": "https://arxiv.org/abs/2606.31134"
    },
    {
      "age_days": 2,
      "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": 3,
      "arxiv_id": "2607.04321",
      "authors": [
        "Ján Perháč",
        "Vasyl Khashcha",
        "Samuel Novotný"
      ],
      "content_date": "2026-07-05",
      "freshness": "fresh",
      "id": "arxiv:2607.04321",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-05",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present LogicProof, an interactive web-based theorem prover designed for educational use. The system supports natural deduction and sequent calculus for propositional and first-order logic in both classical and constructive variants. It emphasizes a modern user experience through real-time feedback and interactive visualization of proof trees. We evaluated LogicProof in a study involving 35 students. The results suggest that the system improves understanding of formal proof construction and supports student engagement with logical concepts. Compared to traditional pen-and-paper approaches, students reported faster iteration, easier error correction, and greater confidence in the correctness of their solutions. These findings indicate that LogicProof can serve as a practical supplement to existing teaching methods, particularly in supporting the learning process and reducing barriers associated with formal proof construction.",
      "title": "LogicProof: An Interactive Web-Based Educational Theorem Prover for Natural Deduction and Sequent Calculus across Classical and Constructive Logics",
      "updated": "2026-07-05",
      "url": "https://arxiv.org/abs/2607.04321"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.03963",
      "authors": [
        "Yanjie Zhao",
        "Hongjie Chen",
        "Li Lu",
        "Zhou Yang",
        "Xiao Cheng",
        "Haoyu Wang"
      ],
      "content_date": "2026-07-04",
      "freshness": "fresh",
      "id": "arxiv:2607.03963",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-04",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Ask a large language model (LLM) whether a pointer dereference is safe, and it can often produce a plausible justification for ``yes''. The difficulty is that a fluent justification is not a proof. This gap is precisely where automated vulnerability detection lives: deciding, for a given operation in source code, whether a memory safety defect such as a null dereference, use-after-free, or double free can actually occur. We trace the unreliability of LLM-based vulnerability detection to a mechanism, the premature discharge of safety obligations, and argue that the remedy is not better prompting but a separation of roles: the component that interprets the code must not also be the one that decides a safety obligation is met. In this paper, we present LeanGuard, a neuro-symbolic framework that assigns each act to the side equipped for it. On the neural side, an LLM serves strictly as a semantic filter over candidate facts extracted from the abstract syntax tree (AST): it prunes spurious facts and keeps the real ones, but never discharges an obligation or decides the verdict on its own. On the symbolic side, the surviving facts are compiled into a verification model in Lean 4 (a formal proof assistant whose kernel accepts a conclusion only when it is formally proved), where every dangerous operation must be matched by a guard that provably covers it in scope; absent such a guard, the obligation stays open rather than being argued away. Because a function rarely arrives with full context, this symbolic model is necessarily partial: an unproved obligation is not yet a defect. An evidence-aware adjudicator therefore weighs the symbolic and neural verdicts by the quality of each. We instantiate the framework on five CWE classes to ask how far this division of labor can be pushed.",
      "title": "Neuro-Symbolic Reasoning for Vulnerability Detection",
      "updated": "2026-07-04",
      "url": "https://arxiv.org/abs/2607.03963"
    },
    {
      "age_days": 8,
      "arxiv_id": "2606.31002",
      "authors": [
        "Ke Zhang",
        "Patricio Gallardo Candela",
        "Sudhir Murthy",
        "Yi Xie",
        "Zhi Wang",
        "Maziar Raissi"
      ],
      "content_date": "2026-06-30",
      "freshness": "fresh",
      "id": "arxiv:2606.31002",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-06-30",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Theorem-proving benchmarks evaluate proof search against fixed formal statements, but natural-language-to-Lean formalization must generate the formal statement itself. In this setting, compilation is only a validity check: a Lean declaration may type-check while omitting hypotheses, changing domains, or expressing a vacuous claim. We study faithful statement formalization as both an evaluation problem and a bottleneck-attribution problem. On a 400-entry graduate-level benchmark spanning real analysis, complex analysis, topology, and algebra, our protocol combines Lean compilation, cross-model semantic judging, and human expert calibration. The resulting picture is different from compile-rate evaluation: a full tool-augmented agent reaches 89.5% compilation but only 60.5% consensus faithfulness, exposing a 29.0-point compile-pass but consensus-unfaithful gap. Targeted human audits support the metric as a conservative decision boundary: across available case-level audits, 96.0% of consensus-positive outputs are human-confirmed faithful, while 82.4% of compile-pass consensus-negative outputs are human-confirmed semantic failures. Under this metric, existing one-shot formalizer models and prover-oriented Lean models remain low, suggesting that formal validity, proof-oriented Lean competence, and faithful statement generation should be reported separately. We then use a full $2^3$ factorial design to decompose three recurring interventions in formalization pipelines: parametric expert drafting, Mathlib/context search, and Lean elaboration feedback. Elaboration feedback is the largest validity intervention, but it also exposes a larger compile-pass semantic-failure bucket; search mainly improves grounding and selectivity; and fine-tuned drafting is largely substitutable in this tool stack once feedback and grounding are available.",
      "title": "Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization",
      "updated": "2026-06-30",
      "url": "https://arxiv.org/abs/2606.31002"
    },
    {
      "age_days": 1,
      "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": 8,
      "arxiv_id": "2606.31562",
      "authors": [
        "Quan Quan"
      ],
      "content_date": "2026-06-30",
      "freshness": "fresh",
      "id": "arxiv:2606.31562",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "reasoning_rl_distillation",
        "verifier_guided_reasoning"
      ],
      "published": "2026-06-30",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "Stabilization learning is an interdisciplinary paradigm that bridges control theory and machine learning. Its core idea is to enable systems to adjust their policies under perturbations or environmental changes through real-time feedback and adaptive mechanisms. It takes stability as its primary goal, distinguishing itself from certificate learning, which focuses on formal proofs, and reinforcement learning, which pursues optimality. It encompasses a range of methods, including Lyapunov-based analysis and design, deep feature extraction, and data-driven feedback synthesis, and is applicable to complex high-dimensional, nonlinear systems. This paper elaborates on the two major categories of stability in stabilization learning, as well as three typical application scenarios: control, observation, and recognition. It constructs a unified mathematical framework based on a six-tuple, and expands into two types of seven-tuple models: constrained learning with barrier spaces and tracking problems with targets. It also analyzes the roles, meanings, and implementation choices of key elements such as state space, controlled system, metrics, and policy. Through the formal reformulation of 11 types of problems, including multi-agent cooperative tracking, visual servo robot position stabilization, chess games, and Push-T tasks, this paper illustrates the potential applicability of the framework across multiple domains. Finally, it points out that future stabilization learning will focus on two major directions: constructing a unified problem framework and achieving efficient and robust learning, providing solutions for complex system control that combine theoretical rigor with engineering practicality.",
      "title": "Stabilization Learning: A Paradigm Transition Bridging Control Theory and Machine Learning",
      "updated": "2026-06-30",
      "url": "https://arxiv.org/abs/2606.31562"
    },
    {
      "age_days": 1,
      "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": 1,
      "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": 1,
      "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": 2,
      "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": 3,
      "arxiv_id": "2607.04534",
      "authors": [
        "Manuel Israel Cázares",
        "Wenlin Zhang",
        "Haobo Ma"
      ],
      "content_date": "2026-07-05",
      "freshness": "fresh",
      "id": "arxiv:2607.04534",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-05",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present an empirical study of structural routing failure in large language models (LLMs) over a formally verified algebraic corpus. The task requires selecting the correct proof-mechanism label from a fixed closed template set for compact mathematical objects drawn from the FiberRing formalization in Lean 4, where each item is anchored to a Lean-verified artifact and assigned a label from the corresponding certificate family. Our central finding is a mechanism-level routing ceiling: under blind conditions, gpt-oss-120b achieves 80.3% template accuracy on 22 FiberRing items (n=66; temperature=0, seed=0), while Llama 3.3 70B reaches 68.2%. Exposing a mechanism-bearing Lean verdict/witness cue (Condition A2) raises accuracy to 90.9% and 81.8% -- gaps of +10.6 and +13.6 pp termed cue-induced routing uplift. The dominant failure is a CRT-to-ring-equivalence misroute: gpt-oss-120b misroutes 7 of 12 CRT items (58.3%) blind, zero under A2. A cross-model dissociation in Llama is notable: verdict accuracy is identical in both conditions (95.5%), while template accuracy improves 13.6 pp -- confirming that truth inference and proof-mechanism classification are separable capacities. A cross-corpus extension (Set B; 6 POM/CollisionKernel items, 72 evaluations) provides a small cross-module check: CRT-granularity compression reappears with different labels, and an inverse cross-model dissociation emerges. These findings extend the router hypothesis (Cazares 2026) to formal algebraic structures. The full pipeline, manifest, and results are at https://github.com/bytepro-ai/fiber-routing-eval.",
      "title": "Mechanism-level routing failure in LLMs over Lean-verified algebraic structures",
      "updated": "2026-07-05",
      "url": "https://arxiv.org/abs/2607.04534"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.03406",
      "authors": [
        "Simon Jeanteur",
        "Lorenzo Veronese",
        "Magdalena Solitro",
        "Matteo Maffei"
      ],
      "content_date": "2026-07-03",
      "freshness": "fresh",
      "id": "arxiv:2607.03406",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-03",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Computer-aided formal verification is a widely used approach for the symbolic analysis of cryptographic protocols. However, many modern protocols rely on features that remain challenging for existing techniques. In particular, reasoning about state, time-dependent behavior, inductively defined data structures, unbounded executions, and conditional secrecy requires a level of expressiveness that is difficult to reconcile with effective automation. As a result, protocol verification has largely followed two disjoint paths: fully automated methods with limited expressiveness, or interactive proofs in general-purpose theorem provers that offer flexibility but only limited, non-specialized automation. We present an orthogonal approach that bridges this gap by combining compositional type-based reasoning with trace-based reasoning, enabling modular verification of stateful and unbounded protocols. Guided by the language-and-automation co-design (LAC) principle, our approach delivers protocol-specific automation while retaining high expressiveness. We implement this framework as the LeanDY library for the Lean proof assistant, building on and extending the design of DY*, and combining protocol-specific automation with interactive proofs. Our framework supports, in a unified setting, a broad class of functional and security requirements, including secrecy and authentication for stateful protocols, as well as recursive conditional secrecy for protocols using XOR. We formalize SegWit-style blockchain primitives in LeanDY and demonstrate its expressiveness by carrying out an in-depth formalization of payment channels on top of this blockchain model, verifying punishment mechanisms and properties that depend on chain liveness.",
      "title": "LeanDY: Type-Based and Trace-Based Symbolic Protocol Verification in Lean",
      "updated": "2026-07-07",
      "url": "https://arxiv.org/abs/2607.03406"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.01734",
      "authors": [
        "Simon Guilloud",
        "Sankalp Gambhir",
        "Samuel Chassot"
      ],
      "content_date": "2026-07-02",
      "freshness": "fresh",
      "id": "arxiv:2607.01734",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
      ],
      "published": "2026-07-02",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present a case study in reformalization, a variant of autoformalization in which the input proof is not natural language but a formal development in a different proof assistant. Concretely, we report three reformalizations of the Jordan Curve Theorem: from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. We analyse the results and identify pipeline design choices that matter for practical reformalization tasks.",
      "title": "Reformalization of the Jordan Curve Theorem",
      "updated": "2026-07-02",
      "url": "https://arxiv.org/abs/2607.01734"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.01223",
      "authors": [
        "Michael Saldivar",
        "Ben Slivinski"
      ],
      "content_date": "2026-07-01",
      "freshness": "fresh",
      "id": "arxiv:2607.01223",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-01",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "When should an AI system's answer be trusted? Formal proof assistants offer certainty but cannot reach most of the problem distribution; scalar LLM judges offer coverage but produce opaque scores that cannot be audited after the fact and are subject to the same coherence issues as any LLM. We present Theoria, a verification architecture that closes this gap. A candidate solution is rewritten into a sequence of typed state transitions, each licensed by an explicit justification, whether that be a citation, computation, or problem-given fact, and every transition is independently auditable. The foundational invariant is completeness of change: every difference between consecutive proof states must be accounted for, so hidden premises surface as unlicensed mutations rather than passing silently. On HLE-Verified Gold (185 text-only expert problems), Theoria certifies 105 at 91.4% strict precision (Wilson 95% CI [84.5%, 95.4%]). Every certification produces a human readable proof trace in which each step can be independently challenged. Holistic LLM judges achieve comparable precision at matched coverage but fail on different problems (Jaccard 0.14-0.36), making the approaches complementary. On 95 adversarial poisoned proofs across 15 domains, structured judges catch 94.7% versus 83.2% for holistic judging (p= 0.0017). The overall 11.5 pp gap concentrates in hidden premises (90.6% vs. 62.5%, a 28 pp difference) and fabricated citations (100% vs. 90%), the error classes where the formal analysis predicts an advantage; performance is identical on arithmetic and theorem-misapplication errors, where no advantage is predicted. On GPQA Diamond (n= 65), certified precision is 97.1% (Wilson CI [85.1%, 99.5%]).",
      "title": "Theoria: Rewrite-Acceptability Verification over Informal Reasoning States",
      "updated": "2026-07-02",
      "url": "https://arxiv.org/abs/2607.01223"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.00815",
      "authors": [
        "Stefan Szeider"
      ],
      "content_date": "2026-07-01",
      "freshness": "fresh",
      "id": "arxiv:2607.00815",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-01",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "SAT solvers settle combinatorial problems beyond the reach of interactive theorem provers and produce LRAT certificates for independent verification. We present LRAT-Catcher, a standalone, general-purpose tool that imports a DIMACS formula together with an LRAT certificate into Lean 4 as a theorem. LRAT-Catcher runs the formally verified LRAT checker from Lean core as compiled native code via reflection. This scales to instances where Mathlib's explicit proof-term import exhausts memory. LRAT-Catcher also composes cube-and-conquer solving runs entirely inside Lean. Per-cube refutations are combined with a cover-completeness certificate, itself an LRAT proof, into a single unsatisfiability theorem. Verified encodings connect CNF-level results to the original combinatorial problems. We evaluate the tool against Mathlib's proof-term import and the external checker cake_lpr on establishing the Schur number S(4) = 44 and the Ramsey number R(4,4) = 18 as Lean theorems.",
      "title": "LRAT-Catcher: Importing SAT Solver Certificates into Lean4 by Reflection",
      "updated": "2026-07-01",
      "url": "https://arxiv.org/abs/2607.00815"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.01340",
      "authors": [
        "Iván Blanco-Chacón",
        "Rodrigo Martín Sánchez-Ledesma",
        "Raúl Durán Díaz"
      ],
      "content_date": "2026-07-01",
      "freshness": "fresh",
      "id": "arxiv:2607.01340",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-01",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "In the present work we address some key questions regarding the generalization of root-based attacks presented in a recent work by the authors. In particular, we analyze potential root-based attacks extensions via the construction of explicit isomorphisms from vulnerable instances, and provide a formal proof that this approach will not yield any new vulnerabilities under a fully-split setting. To do so, we first construct an explicit isomorphism between fully-split polynomial rings and polynomial rings where previous attacks apply and show that the application of such an isomorphism will always distort the samples in a way that the resulting samples cannot be used to distinguish. Then, we prove that any isomorphism between fully-split polynomial rings must be of the form of the constructed isomorphism.",
      "title": "An alternative approach towards attacks against fully-split PLWE instances",
      "updated": "2026-07-01",
      "url": "https://arxiv.org/abs/2607.01340"
    },
    {
      "age_days": 8,
      "arxiv_id": "2607.00091",
      "authors": [
        "Aleksandr Semenov",
        "Alexander Fradkov"
      ],
      "content_date": "2026-06-30",
      "freshness": "fresh",
      "id": "arxiv:2607.00091",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-06-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "The paper proposes an approach for verifying integral persistent excitation, which is important in problems of parameter identification and adaptive control in nonlinear dynamical systems. The approach works for conservative polynomial ODEs a priori without knowledge of the parameters. Rigorous proofs of the corresponding theorems are provided. An example of a nonlinear dynamical system with higher-order interactions and the application of the proposed method to it are analyzed. The proof of the main result is formalized in the Lean formal verification language.",
      "title": "A Priori Integral Persistent Excitation in Conservative Polynomial ODEs with Higher-Order Interactions",
      "updated": "2026-06-30",
      "url": "https://arxiv.org/abs/2607.00091"
    },
    {
      "age_days": 9,
      "arxiv_id": "2606.30440",
      "authors": [
        "Haobo Yang"
      ],
      "content_date": "2026-06-29",
      "freshness": "fresh",
      "id": "arxiv:2606.30440",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-06-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present a complete formal proof that transformer architectures, when their internal update mechanisms satisfy a Bayes joint-distribution condition, implement exact Bayesian posterior inference. Working within the measure-theoretic kernel framework, we define a hierarchy of abstractions -- from the core Bayesian transformer, through semantic transformers with explicit update kernels, to full transformer blocks with QKV/attention/residual/MLP pipelines, and finally multilayer stacks -- and prove at each level that the Bayes joint semantics implies the update kernel equals the posterior almost everywhere. For the block-level architecture, we derive the explicit Bayes formula through Radon-Nikodym differentiation and prove its normalization. We additionally prove that the softmax attention mechanism induces a valid probability distribution over keys, establishing the bridge between the abstract kernel framework and concrete attention implementations. The framework makes no architectural assumptions beyond the Markov kernel structure and exposes explicit conditions under which a transformer block is provably Bayesian. In essence, when this joint distribution condition is satisfied, the forward computation of a Transformer is formally equivalent to a rigorous Bayesian posterior update.",
      "title": "Transformer Architectures as Complete Bayes Processes: A Formal Proof in the Measure-Theoretic Kernel Framework",
      "updated": "2026-06-29",
      "url": "https://arxiv.org/abs/2606.30440"
    },
    {
      "age_days": 9,
      "arxiv_id": "2606.30782",
      "authors": [
        "Lars Warren Ericson"
      ],
      "content_date": "2026-06-29",
      "freshness": "fresh",
      "id": "arxiv:2606.30782",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-06-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present a complete machine-checked formalization of Dana Scott's landmark 1972 paper \\emph{Continuous Lattices} \\textbf{[Sco72]}, carried out in Lean 4 against mathlib and including the March 1972 Milner correction in \\textbf{[Sco72]} (pp.~135--136). Scott's paper develops a model for \\(λ\\)-calculus from a topological starting point. He defines \\emph{injective} \\(T_0\\)-spaces -- those with a strong extension property for continuous maps -- and shows that they are exactly the \\emph{continuous lattices}: complete lattices whose Scott topology is determined by the order via the way-below relation (\\(\\ll\\)). On this foundation he studies projections, retractions, products, function spaces, and inverse limits. The capstone (Theorem 4.4) constructs an inverse limit \\(D_\\infty\\) of function-space approximants and proves \\(D_\\infty \\cong [D_\\infty \\to D_\\infty]\\), yielding a purely mathematical model for Church's untyped \\(λ\\)-calculus. Our development formalizes \\textbf{43 numbered results} from Scott's Sections 1--4 (Propositions, Corollaries, Lemmas, and Theorems), each as a sorry-free Lean theorem, together with supporting infrastructure (step functions, the \\(\\Uparrow a\\) basis of Scott opens, Milner's coarser-than-Scott hypothesis, the function-space tower, and the \\(i_\\infty\\)/\\(j_\\infty\\) pair). The formalization is \\textbf{classical} (uses \\texttt{Classical.choice} transitively) and follows Scott's proof dependency order. Where the Lean proof required choices not visible in the original -- or where dead ends were encountered -- we record detailed notes in Section 5. All proofs check with the standard footprint \\(\\texttt{[propext, Classical.choice, Quot.sound]}\\).",
      "title": "A Lean 4 Formalization of Scott's \\emph{Continuous Lattices} (1972)",
      "updated": "2026-06-29",
      "url": "https://arxiv.org/abs/2606.30782"
    },
    {
      "age_days": 1,
      "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": 7,
      "arxiv_id": "2607.01544",
      "authors": [
        "Kenny Lau",
        "Seewoo Lee",
        "Ken Ono"
      ],
      "content_date": "2026-07-01",
      "freshness": "fresh",
      "id": "arxiv:2607.01544",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-07-01",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "The theory of $q$-series and basic hypergeometric series plays a crucial role at the intersection of combinatorics, number theory, and representation theory. From the classical partition identities of Euler and Jacobi to modern developments in class field theory, vertex operator algebras, and the Monstrous Moonshine conjecture, $q$-series provide the analytic framework for a wide range of profound applications. In this paper, we discuss the formalization of this theory in the Lean proof assistant, a process that requires careful design of scalable and versatile structures to reconcile formal algebraic identities with analytic convergence properties. We address these foundational challenges by focusing on the construction of $q$-Pochhammer symbols, $q$-binomial coefficients, Bailey's Lemma and similar primitives. To demonstrate the utility of this work, we provide fully verified proofs of the Jacobi Triple Product formula and the celebrated Rogers-Ramanujan identities, which serve as both historical and technical benchmarks for the field. This work establishes a rigorous computational foundation for the future formalization of mock theta functions, modular forms, and the diverse algebraic structures that underpin their applications across mathematics and physics.",
      "title": "Formalized $q$-series: The Rogers-Ramanujan Identities and Beyond",
      "updated": "2026-07-01",
      "url": "https://arxiv.org/abs/2607.01544"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8554442f92d9",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: replay tactics when only trailing whitespace is changed (#11958)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/8554442f92d900c9f90f0e483244bfa5ec460df4"
    },
    {
      "age_days": 0,
      "authors": [
        "Wojciech Nawrocki"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c1d6de5ef78e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add Insert instances for NameMap/NameSet (#14153)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/c1d6de5ef78e1ef320d89599031ab42bd3d8012d"
    },
    {
      "age_days": 0,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d14ff0ba3412",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: fix namespaceing in `DeprecatedModule` (#14310)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/d14ff0ba34122b569f8e4a19265d5d2458fc00ac"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:306bbbc83e53",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: disable binary stripping in release configuration (#14139)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/306bbbc83e539d7ae6b8ef63cb784e69e5429bc7"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:86b7320a2f2a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: cmake: disable Lake cache on `PREV_STAGE` use as well (#14321)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/86b7320a2f2a8382d711a9bc29a27c2201b65531"
    },
    {
      "age_days": 0,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:81074d12aee3",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: change `UnusedSimpArgs` hint (#14313)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/81074d12aee3c79efdffc5e11bf7fd65b89045b1"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:e90c70fdd7d0",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: skip test stack-overflowing under fsanitize (#14320)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/e90c70fdd7d0cb1b39ab5380a75950b416f11638"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:6405ec1878f8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: re-enable test header snapshots (#14324)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/6405ec1878f8608fa31ed1257b9760d0ba1b2cca"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:fedd162755dd",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: negotiate common objects when pushing PR release tags (#14319)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover/lean4/commit/fedd162755dd5f5ec7a50844b4d5c69d1a7c7ee4"
    },
    {
      "age_days": 0,
      "authors": [
        "Junyan Xu"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:2f35248703f4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: refactor(Algebra): weaken NormalizationMonoid (#34179)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover-community/mathlib4/commit/2f35248703f4824acffd6dce07cc4d44105bc56f"
    },
    {
      "age_days": 0,
      "authors": [
        "Salvatore Mercuri"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:8df0e1b604d1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: perf: make valuation unexposed (#41492)",
      "updated": "2026-07-08",
      "url": "https://github.com/leanprover-community/mathlib4/commit/8df0e1b604d1668165ad022c4bc8be3fe03e6efd"
    },
    {
      "age_days": 0,
      "authors": [
        "Paul Lezeau"
      ],
      "content_date": "2026-07-08",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1c3e8f34a897",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-08",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: implement LMFDB attribute (#41290)",
      "updated": "2026-07-08",
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      "title": "leanprover/lean4: chore: move `ImportCompletion` into `Lean.Lsp` (#14305)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: move `ExceptT` lemmas out of internal module (#14302)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: make builtin simproc helpers private (#14303)",
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      "url": "https://github.com/leanprover/lean4/commit/dacee08d9a95d1c32f97e68aa5ab1ec51543bb1b"
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: fix three spell-check typos (#14312)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: delete unused C++ code (#14203)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: bump softprops/action-gh-release from 3.0.0 to 3.0.1 (#14239)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: bump msys2/setup-msys2 from 2.31.1 to 2.32.0 (#14238)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: bump actions/upload-artifact from 5 to 7 (#12752)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: bump actions/download-artifact from 7 to 8 (#12751)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: CI: bump actions/cache from 5 to 6 (#14237)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: strip mdata from the program in `vcgen` (#14295)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: restore go-to-definition on `mut` variables after a `for` loop (#14296)",
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    {
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      "arxiv_id": "2607.05874",
      "authors": [
        "Wanli Ma",
        "Zichen Wang",
        "Zaiwen Wen"
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      "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"
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    {
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      "authors": [
        "Muhammad Rizwan",
        "David Nabergoj",
        "Jure Demšar"
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      "content_date": "2026-07-06",
      "freshness": "fresh",
      "id": "arxiv:2607.05626",
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      "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"
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    {
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      "authors": [
        "David Victor Feldman"
      ],
      "content_date": "2026-07-05",
      "freshness": "fresh",
      "id": "arxiv:2607.04077",
      "kind": "paper",
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      "matched_signals": [],
      "published": "2026-07-05",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Let $S_N = \\sum_{j=1}^N j^{-3}$ and $R_N = ζ(3) - S_N$. The simple continued fraction of $\\sqrt{R_N}$ has partial quotients of generic size $O(N)$. We prove that at the sequence of indices $N_k = (Q_{2k+1}-1)/2$, where $Q_{2k+1}$ are companion Pell numbers, the continued fraction begins \\[ \\sqrt{R_{N_k}} = \\bigl[0;\\; M_k-1,\\; 1,\\; 6M_k^3+12M_k-2,\\; 1,\\; \\ldots\\,\\bigr], \\] with $M_k = P_{2k+1}$ (Pell numbers), and the third partial quotient grows cubically while generic ones are linear. We determine all partial quotients through the fifth: \\begin{align*} \\PQ_0 &= M_k - 1, & \\PQ_2 &= 6M_k^3 + 12M_k - 2, & \\PQ_4 &= \\Bigl\\lfloor\\frac{10M_k - 261}{261}\\Bigr\\rfloor, \\PQ_1 &= 1, & \\PQ_3 &= 1, & \\PQ_5 &= \\Bigl\\lfloor\\frac{261}{r_k}\\Bigr\\rfloor + ε_k, \\end{align*} where $r_k = (10M_k) \\bmod 261$ satisfies the recurrence $r_{k+1} \\equiv 6r_k - r_{k-1} \\pmod{261}$, and $ε_k = -1$ at the $k$ with $r_k \\mid 261$ (the two residue classes $k \\equiv 57, 62 \\pmod{60}$), and $ε_k = 0$ otherwise. All six formulas follow from the Euler--Maclaurin expansion of $1/\\sqrt{R_{N_k}}$, carried to sufficient precision, combined with the Pell identity $Q_{2k+1}^2 - 2M_k^2 = -1$. The delicate first step, $\\PQ_0 = M_k - 1$, is proved by rationalizing the irrational factor $\\sqrt{2}$ in the Euler--Maclaurin expansion; we complement this proof with a heuristic derivation via Gosper's bihomographic continued-fraction algorithm that exposes the underlying mechanism. All claimed results have been formalized in LEAN with the aid of Aristotle.",
      "title": "Anomalous Partial Quotients in the Continued Fraction of $\\sqrt{ζ(3)-S_N}$",
      "updated": "2026-07-05",
      "url": "https://arxiv.org/abs/2607.04077"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.00563",
      "authors": [
        "Yuan Si",
        "Jialu Zhang"
      ],
      "content_date": "2026-07-01",
      "freshness": "fresh",
      "id": "arxiv:2607.00563",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Block-based end-user languages such as Scratch run tens of millions of programs. Existing tools establish behavior preservation through program analysis and testing without a checked guarantee. We turn optimization into certificate-carrying source-to-source rewriting. An untrusted optimizer proposes a rewrite; a trusted, fail-closed checker accepts it only after recomputing every side condition that the rewrite's behavior preservation depends on under an explicit observation lens. The checker is the sole authority: given a correct checker and a small, explicitly stated set of model-to-VM assumptions, an optimizer bug cannot mint an unsound acceptance. The observation lens is a parameter, and the central soundness argument is a cooperative-frame refinement theorem: a write overwritten before any thread observes it, within a window in which no thread yields, can be removed. We mechanize this theorem in Lean and show that one parametric statement covers two concrete rewrite families instantiated to variable state and renderer state. We build a checker for six rewrite families and evaluate it on 300 real Scratch projects. The checker accepts a behavior-preserving rewrite on 94.3% of projects (283 of 300); certification costs under one tenth of a second per project; and a cross-family adversarial campaign of 4,278 perturbed rewrites produces zero false accepts. An audit found eight false accepts the per-family test suites missed; each is now rejected. An ablation that strips the semantic side conditions, leaving analysis and testing alone, ships rewrites the virtual machine confirms change behavior; the full checker rejects every one. The result shows how to provide behavior-preservation guarantees for a concurrent, event-driven, end-user language. The checker recomputes every required condition instead of trusting optimizer claims, keeping the trusted base small.",
      "title": "Certificate-Carrying Transformation of Event-Driven Block Programs",
      "updated": "2026-07-01",
      "url": "https://arxiv.org/abs/2607.00563"
    },
    {
      "age_days": 9,
      "arxiv_id": "2606.30868",
      "authors": [
        "Congzhou M Sha"
      ],
      "content_date": "2026-06-29",
      "freshness": "fresh",
      "id": "arxiv:2606.30868",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-06-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The difference in gauge between two observers of the same physical system can be thought of as a group element acting on their common vector representations. Recovering that group element from a finite, noisy list of paired observations may be of use in both theory and experiment. The Kabsch and Horn algorithms efficiently align point clouds in $\\mathbb R^3$, reconciling rotated frames of reference in Galilean relativity (i.e. $SO(3)$). In a previous work, we proposed an alternative Lie algebra method which extends to the Lorentz group $SO(3,1)_+$, and putatively to all Lie groups. In this work, we report the explicit formulae for applying the Lie algebra method to the classical matrix Lie groups (general linear $GL(n)$, special linear $SL(n)$, special orthogonal $SO(n)$, unitary $U(n)$, indefinite special orthogonal $SO(p,q)$, symplectic $Sp(n)$, spin $Spin(n)$, special Euclidean $SE(n)$) over both the real and complex fields. The four steps (pseudoinverse, matrix logarithm, projection onto the Lie algebra, matrix exponential) are exact in the noiseless case. The only group-dependent step is the projection, which we show produces the unique least squares-optimal element of the Lie algebra whenever its image lies in $\\mathfrak g$ and its residual is orthogonal to $\\mathfrak g$. Additionally, the Lie algebra method is optimal only to leading order for noisy data, so we refine it with a Newton-style correction. This correction matches the Lie algebra method in the noiseless case and direct least squares optimization in the noisy case, with performance between that of the Lie algebra method without correction and naive least squares optimization. The projections, their optimality, and the identity underlying the correction are formally proven in Lean~4.31.0 (with Mathlib 4.31.0), and numerical experiments are benchmarked in Julia.",
      "title": "Vector alignment in matrix Lie groups",
      "updated": "2026-06-29",
      "url": "https://arxiv.org/abs/2606.30868"
    },
    {
      "age_days": 9,
      "arxiv_id": "2606.30801",
      "authors": [
        "Alessandro Morosini",
        "Sarah H. Cen",
        "Andrew Ilyas",
        "Hedi Driss",
        "Aleksander Mądry",
        "Chara Podimata"
      ],
      "content_date": "2026-06-29",
      "freshness": "fresh",
      "id": "arxiv:2606.30801",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-06-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Personalization algorithms determine what content users encounter on online platforms. Auditing these systems is difficult because independent auditors have only black-box access to the algorithms, while personalization depends on users' attributes, behavior, and evolving interaction histories. Existing auditing methods face a tradeoff: studies with real users capture realistic behavior but are costly and hard to control, whereas sock-puppet audits scale more easily but often rely on scripted behavior that limits realism. Beyond this, both approaches struggle to decouple user attributes from user behavior, limiting our ability to causally understand personalization. To address this gap, we introduce a framework for black-box audits of personalization algorithms using generative AI agents as behavioral engines for synthetic accounts. Each agent is instantiated with a fixed persona, grounded in demographic and political survey data, and interacts with a platform's content by reasoning about it and choosing actions. Because behavior is fixed within each persona while platform-visible signals such as age, gender, or location can be experimentally perturbed, our design enables counterfactual auditing of how platforms respond to user attributes. As a case study, we deploy 1,120 agents on X shortly after the 2024 U.S. election, spanning 14 personas and three counterfactual conditions, collecting over 200,000 content exposures. We find that X's algorithmic feed amplifies toxic, polarizing, political, and right-leaning content relative to the chronological feed, with amplification varying sharply by user ideology. Counterfactual analyses show that demographic signals affect content delivery in persona-dependent ways: pooled effects are largely null, while subgroup-level effects vary in direction and magnitude. Our work establishes GenAI-based agents as a new tool for algorithmic auditing.",
      "title": "Using AI Agents to Automate Black-Box Audits of Personalization Algorithms at Scale",
      "updated": "2026-06-29",
      "url": "https://arxiv.org/abs/2606.30801"
    },
    {
      "age_days": 9,
      "arxiv_id": "2606.30450",
      "authors": [
        "Jinliang Xu",
        "Liping Ma"
      ],
      "content_date": "2026-06-29",
      "freshness": "fresh",
      "id": "arxiv:2606.30450",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-06-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "This paper presents the Metabolic Multi-Agent Optimizer (MMAO) as an adaptive metaheuristic built around endogenous resource circulation. The central premise is that search intensity, exploration--exploitation balance, and lifecycle turnover should be induced by a shared metabolic controller rather than by separately attached schedules. We formulate MMAO through bounded private energy, a communal budget, normalized reward, continuous role adaptation, and resource-financed branching and pruning. The method is then instantiated in both continuous and discrete domains and evaluated on a matched small-scale suite including Sphere, Rastrigin, a synthetic Euclidean TSP, and two TSPLIB instances. The results show a consistent pattern: the same metabolic loop remains workable across domains, the discrete realization remains relatively stable under a compact design, and continuous refinement quality is the main cost of keeping the method lean. Taken together, these findings position MMAO as a coherent framework for adaptive heuristic design rather than a loose collection of operators.",
      "title": "Minimal MMAO: A Resource-Closed-Loop Framework for Adaptive Metaheuristic Search",
      "updated": "2026-07-04",
      "url": "https://arxiv.org/abs/2606.30450"
    },
    {
      "age_days": 519,
      "arxiv_id": "2403.13310",
      "authors": [
        "Guoxiong Gao",
        "Jiedong Jiang",
        "Haocheng Ju",
        "Bin Dong",
        "Zihan Qin"
      ],
      "content_date": "2025-02-04",
      "freshness": "background",
      "id": "manual:semantic-scholar-mathlib4-search",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "mathlib_retrieval",
        "seed_author:Guoxiong Gao",
        "seed_author:Haocheng Ju",
        "seed_author:Jiedong Jiang"
      ],
      "observed_date": "2026-06-20",
      "published": "2025-02-04",
      "score": 9.5,
      "source": "semantic-scholar-library",
      "source_app": "semantic_scholar",
      "summary": "Semantic Scholar library seed for mathlib retrieval and premise search. This is infrastructure-level signal for theorem-proving agents.",
      "title": "A Semantic Search Engine for Mathlib4",
      "updated": "",
      "url": "http://arxiv.org/abs/2403.13310"
    },
    {
      "age_days": null,
      "arxiv_id": "",
      "authors": [],
      "content_date": "",
      "freshness": "background",
      "id": "manual:scholar-inbox-distilling-lean-feedback",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "observed_date": "2026-06-20",
      "published": "",
      "score": 9.0,
      "source": "scholar-inbox-manual",
      "source_app": "scholar_inbox",
      "summary": "Scholar Inbox positive seed for verifier-guided learning from Lean feedback. Useful for proof repair loops and training signal design.",
      "title": "Distilling LLM Feedback for Lean Theorem Proving",
      "updated": "",
      "url": "https://www.semanticscholar.org/search?q=Distilling%20LLM%20Feedback%20for%20Lean%20Theorem%20Proving"
    },
    {
      "age_days": 30,
      "arxiv_id": "",
      "authors": [
        "Jui-Hui Chung"
      ],
      "content_date": "2026-06-08",
      "freshness": "background",
      "id": "manual:x-juihuichung-goedel-architect",
      "kind": "post",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "seed_author:Jui-Hui Chung"
      ],
      "observed_date": "2026-06-20",
      "published": "2026-06-08",
      "score": 7.2,
      "source": "x-manual",
      "source_app": "x",
      "summary": "X post surfaced during tuning about Goedel-Architect, a Lean 4 formal theorem proving agent built around blueprint generation and refinement.",
      "title": "Jui-Hui Chung: Goedel-Architect launch thread",
      "updated": "",
      "url": "https://x.com/juihuichung/status/2064023094197707161"
    },
    {
      "age_days": 201,
      "arxiv_id": "2512.17260",
      "authors": [
        "Huajian Xin",
        "Zhicheng Jiang",
        "Allan Jie",
        "Xiaoran Jin",
        "Xing Jin"
      ],
      "content_date": "2025-12-19",
      "freshness": "background",
      "id": "manual:semantic-scholar-seed-prover-1-5",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "seed_author:Allan Jie",
        "seed_author:Huajian Xin",
        "seed_author:Zhicheng Jiang"
      ],
      "observed_date": "2026-06-20",
      "published": "2025-12-19",
      "score": 6.5,
      "source": "semantic-scholar-library",
      "source_app": "semantic_scholar",
      "summary": "Semantic Scholar folder seed for experience-driven formal theorem proving. Watch for methods that turn failed proof attempts into useful training data.",
      "title": "Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience",
      "updated": "",
      "url": "http://arxiv.org/abs/2512.17260"
    },
    {
      "age_days": 1107,
      "arxiv_id": "2306.15626",
      "authors": [
        "Kaiyu Yang",
        "Aidan M. Swope",
        "Alex Gu",
        "Rohan Chalamala",
        "Peiyang Song",
        "Shuyuan Yu",
        "Saad Godil",
        "Ryan Prenger",
        "Anima Anandkumar"
      ],
      "content_date": "2023-06-27",
      "freshness": "background",
      "id": "manual:scholar-inbox-leandojo",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents",
        "seed_author:Kaiyu Yang"
      ],
      "observed_date": "2026-06-20",
      "published": "2023-06-27",
      "score": 4.7,
      "source": "scholar-inbox-manual",
      "source_app": "scholar_inbox",
      "summary": "Scholar Inbox surfaced this as a core retrieval-augmented Lean theorem proving baseline. It is relevant to premise retrieval, proof search, and agent evaluation.",
      "title": "LeanDojo: Theorem Proving with Retrieval-Augmented Language Models",
      "updated": "",
      "url": "https://arxiv.org/abs/2306.15626"
    },
    {
      "age_days": 169,
      "arxiv_id": "2601.14027",
      "authors": [
        "Junqi Liu",
        "Marco Dos Santos",
        "Zekai Zhu",
        "Jiawei Liu",
        "Ran Wang",
        "Jia Li",
        "Wenda Li"
      ],
      "content_date": "2026-01-20",
      "freshness": "background",
      "id": "manual:semantic-scholar-numina-lean-agent",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "seed_author:Junqi Liu",
        "seed_author:Marco Dos Santos",
        "seed_author:Zekai Zhu"
      ],
      "observed_date": "2026-06-20",
      "published": "2026-01-20",
      "score": 3.5,
      "source": "semantic-scholar-library",
      "source_app": "semantic_scholar",
      "summary": "Semantic Scholar folder seed for agentic formal mathematics. Relevant to open Lean proof-agent workflows and reusable evaluation setups.",
      "title": "Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics",
      "updated": "",
      "url": "http://arxiv.org/abs/2601.14027"
    },
    {
      "age_days": null,
      "arxiv_id": "",
      "authors": [],
      "content_date": "",
      "freshness": "background",
      "id": "manual:scholar-inbox-lean-copilot",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "observed_date": "2026-06-20",
      "published": "",
      "score": 0.0,
      "source": "scholar-inbox-manual",
      "source_app": "scholar_inbox",
      "summary": "Scholar Inbox positive seed for Lean-facing proof assistance. Keep visible as a practical bridge between LLM tooling and interactive theorem proving.",
      "title": "Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean",
      "updated": "",
      "url": "https://www.semanticscholar.org/search?q=Lean%20Copilot%3A%20Large%20Language%20Models%20as%20Copilots%20for%20Theorem%20Proving%20in%20Lean"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}