{ "counts": { "adjacent": 16, "core": 11, "errors": 0, "negative": 69, "total": 96 }, "date": "2026-07-07", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-07T17:33:51Z", "items": [ { "age_days": 10, "arxiv_id": "2606.28841", "authors": [ "Santhana Srinivasan R", "Maithilee Patawar" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "arxiv:2606.28841", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-06-27", "score": 13.7, "source": "arxiv-ai4math-core", "summary": "Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify. Interactive theorem provers such as Lean 4 address this by accepting only kernel-checked proofs; however, their reach is bounded by the formalized knowledge available. While Mathlib, a repository of formalized Lean 4 theorems that covers diverse mathematical areas, certain specialized areas remain underrepresented; notably, the domain of Combinatorics on Words (CoW). CoW studies sequences, exploring their properties such as periodicity, borders, conjugacy, and morphisms. As a result, specialized provers, trained on Mathlib-centered data, lack the lemmas to operate in CoW. We present two contributions. First, we introduce a Lean 4 formalization of CoW containing eight modules and \\textbf{93} declarations of core definitions and foundational lemmas. Second, we present LAMP, a multi-agent framework that synthesizes kernel-verified Lean 4 proofs by providing explicit, structured domain knowledge at inference time through an ontology, rather than by fine-tuning a prover. LAMP coordinates a Planner, Builder, and Verifier with Model Context Protocol based access to a domain-specific CoW ontology. In a suite of 90 CoW theorems that span all eight modules and three difficulty levels, LAMP synthesizes verified proofs for 96.7% of theorems, substantially exceeding both an unscaffolded baseline and existing specialized provers. An ablation shows that removing LAMP's tool-grounded architecture or its Planner/Builder separation each cost roughly 12 percentage points, even with the backbone model held fixed.", "title": "LAMP: Lean-based Agentic framework with MCP and Proof Repair", "updated": "2026-06-27", "url": "https://arxiv.org/abs/2606.28841" }, { "age_days": 8, "arxiv_id": "2606.29687", "authors": [ "Uri Kol", "Maor Ben-Shahar", "Kfir Sulimany", "Dirk Englund" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "arxiv:2606.29687", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents", "mathlib_retrieval", "verifier_guided_reasoning" ], "published": "2026-06-29", "score": 10.9, "source": "arxiv-ai4math-core", "summary": "We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p+2)$ exactly. We found the proof using a large language model, Claude Fable 5, and verified its correctness end-to-end by the Lean 4 proof assistant. Our methodology includes several ingredients: building on a substantial Lean library of quantum information, we formalized the QAOA components and the known parts of the problem, and reduced the conjecture to a single open mathematical statement. The model was then handed the library and our agentic toolkit, and tasked with closing that gap by constructing a proof in Lean. The resulting process is a feedback loop between the model's natural-language reasoning and Lean's mechanical verification, which converged to a machine-verified proof. Human verification is required only for the structural scaffolding - that the formal statement faithfully encodes the intended claim - while the proof itself is supplied by the model and certified mechanically by Lean. The proof is nevertheless striking - the model uncovered a hidden dynamical symmetry of the problem and exploited it, borrowing tools and machinery from an adjacent field to turn a hard existence problem into an explicit construction. This work paves the way for resolving open conjectures in quantum information science and beyond.", "title": "A Machine-Verified Proof of a Quantum-Optimization Conjecture", "updated": "2026-06-29", "url": "https://arxiv.org/abs/2606.29687" }, { "age_days": 7, "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": 1, "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": 2, "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": 3, "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": 7, "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": 7, "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": 2, "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": 4, "arxiv_id": "2607.03406", "authors": [ "Simon Jeanteur", "Lorenzo Veronese", "Magdalena Soltiro", "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": "2026-07-03", "url": "https://arxiv.org/abs/2607.03406" }, { "age_days": 5, "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": 6, "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": 6, "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": 6, "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": 7, "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": 8, "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": 8, "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": 9, "arxiv_id": "2606.29493", "authors": [ "Pawan Sasanka Ammanamanchi", "Siddharth Bhat", "Stella Biderman" ], "content_date": "2026-06-28", "freshness": "fresh", "id": "arxiv:2606.29493", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-06-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof. However, the kernel only checks that a proof establishes a \\emph{formal} statement; it does not verify that the statement faithfully encodes the intended informal problem, nor that evaluation harnesses are robust to trivial or adversarial solutions. We audit five widely used Lean theorem-proving benchmarks and their forks, using corpus-scale static checkers to surface 4,833 findings, including 398 mechanically certified issues such as counterexamples, vacuous theorems, and unsound axioms. We also document semantic defects such as missing hypotheses, problem simplification, incomplete or incorrect translations, and Lean-specific specification hazards. Beyond dataset construction, we survey evaluation-time failure modes and show, on corrected subsets, that defects can both inflate and deflate reported prover scores. We propose a fault taxonomy, a suite of automated checkers and recall-oriented semantic audit prompts, and release standards to guide the creation of formal math datasets and to make evaluation more reproducible and trustworthy. Our checkers, audit prompts, and corrected dataset snapshots are available at https://github.com/Shashi456/atp-checkers.", "title": "Faults in Our Formal Benchmarking: Dataset Defects and Evaluation Failures in Lean Theorem Proving", "updated": "2026-06-28", "url": "https://arxiv.org/abs/2606.29493" }, { "age_days": 9, "arxiv_id": "2606.29361", "authors": [ "Ricky Cipollini" ], "content_date": "2026-06-28", "freshness": "fresh", "id": "arxiv:2606.29361", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-06-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Let $f_3(N)$ be the least integer such that every set $A\\subseteq\\{1,\\ldots,N\\}$ of size at least $f_3(N)$ contains distinct elements $a,b,c\\in A$ such that $a+b\\in A$, $a+c\\in A$, and $b+c\\in A$. We prove that $f_3(N)\\le 5N/8+O(1)$. Together with the standard construction $[N/8,N/4]\\cup[N/2,N]$, this gives $f_3(N)=5N/8+O(1)$, resolving Erdős Problem 865. The proof is self-contained. An earlier conditional version of the reduction has also been formalized in Lean 4/Mathlib with no sorries and no added axioms.", "title": "A sharp 5/8 bound for an Erdős-Sós pairwise-sums problem", "updated": "2026-06-28", "url": "https://arxiv.org/abs/2606.29361" }, { "age_days": 10, "arxiv_id": "2606.28990", "authors": [ "Raphael Coelho" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "arxiv:2606.28990", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-06-27", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The Fundamental Theorem of Asset Pricing states that a market is free of arbitrage exactly when it admits an equivalent martingale measure. We formalize it in Lean 4 over Mathlib in three settings: a finite-state market over a finite horizon (Harrison-Pliska), a one-period market on an arbitrary probability space with a single scalar return (Follmer-Schied), and a one-period market with finitely many assets. The finite case is the geometry of a separating hyperplane; the scalar one-period case is an elementary change of measure. In the $d$-asset case the equivalent martingale measure is constructed explicitly, as the minimiser of the smooth convex potential $\\mathbb{E}[\\log(1+e^{\\langleθ,Y\\rangle})]$: absence of arbitrage is precisely coercivity of the potential, its first-order condition is the martingale property, and the minimiser's logistic weight is the density of the measure. The construction uses no Hahn-Banach theorem, no $L^0$-closedness argument, no measurable selection, and no non-redundancy hypothesis. To our knowledge this is the first machine-checked Fundamental Theorem of Asset Pricing in any proof assistant. The boundary is explicit: the general multi-period Dalang-Morton-Willinger theorem lies outside the development. Every theorem is sorry-free, each headline result's axioms are pinned to Mathlib's classical defaults by a build-enforced gate, and the whole is reproducible from a pinned toolchain.", "title": "The Fundamental Theorem of Asset Pricing, Formalized in Lean 4", "updated": "2026-06-27", "url": "https://arxiv.org/abs/2606.28990" }, { "age_days": 6, "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 Graf" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:1422c82ab7f5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: use plain shareCommon before kernel check in vcgen benchmarks (#14304)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/1422c82ab7f5d9124c6dbcf1bbe00b545ad6cb39" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:5afb6ff0c15b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: `shareCommon` at `SymM` (#14314)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/5afb6ff0c15b520e5d826e404c3f40e0bd5436ad" }, { "age_days": 0, "authors": [ "Robin Arnez" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:b23fa6ca2231", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: statement of `eqRec_heq_iff` (#13484)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/b23fa6ca2231ba35138d6bdbb5c107cffa5246ef" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:1855cc928ef0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: refine `return` in dependent `do`-`match` branches (#14297)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/1855cc928ef0cf4631c93697af569f0ce4c8fad8" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:5be27a0a1b71", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: maintain `SymM` term invariants at `shareCommon` (#14299)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/5be27a0a1b7140e4ae09dfdd8a155979bfebcadf" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:85e209a57ba9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: bound kernel recursion by `maxRecDepth` (#13956)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/85e209a57ba989ee9694ab3e72ddd29cace65154" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:433382580d31", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove dead `@[export]` attributes (#14306)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/433382580d312b43d7232531d67072df04b0e005" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:80be7b312023", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove custom small allocator (#14149)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/80be7b312023d7c0a6376e33c50aeca1c483e4db" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:63e728c94c90", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: reduce namespace pollution (#14307)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/63e728c94c909e828ff3aa8d78bb9dc8f9a580e6" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:3fce916472bd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move `ImportCompletion` into `Lean.Lsp` (#14305)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/3fce916472bdd01a447af95e4ea620695608f4b5" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:ad13d7e100e3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move `ExceptT` lemmas out of internal module (#14302)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/ad13d7e100e3133e64c45cbbf045c5b754d5d09a" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:dacee08d9a95", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: make builtin simproc helpers private (#14303)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/dacee08d9a95d1c32f97e68aa5ab1ec51543bb1b" }, { "age_days": 0, "authors": [ "Eric Wieser" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:9ebb35b4af62", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: delete unused C++ code (#14203)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/9ebb35b4af62ecec5ca54e100b796c897dfd0995" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:881b551d0516", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "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)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/881b551d05169e0865214a07884a9c3fe0bfda2f" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:15d8a31f8e19", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: bump msys2/setup-msys2 from 2.31.1 to 2.32.0 (#14238)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/15d8a31f8e199f1461d8d665aef0cb075a6594f4" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:90801d32800c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: bump actions/upload-artifact from 5 to 7 (#12752)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/90801d32800ca2ec1c898567a883fd8f8da6c90d" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:0628b1b43556", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: bump actions/download-artifact from 7 to 8 (#12751)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/0628b1b43556d43173bf9800f9e8d8efad5e8af0" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover/lean4:615f75806231", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: bump actions/cache from 5 to 6 (#14237)", "updated": "2026-07-07", "url": "https://github.com/leanprover/lean4/commit/615f758062319f8b5ff89e714b75d0be285acc4b" }, { "age_days": 0, "authors": [ "Attila Gáspár" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:72e1caf8d87b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Tactic/FunProp): resolve names to be unfolded (#41370)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/72e1caf8d87ba867b6cb87742c71832a9a298eee" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:19e592bcf5ad", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Combinatorics/SimpleGraph/Paths): typos in two deprecations from #38531 (#41311)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/19e592bcf5ad7e683e9d6e326b39c61e483190ed" }, { "age_days": 0, "authors": [ "Hagb (Junyu Guo 郭俊余)" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b5dc78b96f3e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Order/WellQuasiOrder): `WellQuasiOrdered` if onto homomorphous from a `WellQuasiOrdered` relation (#39787)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/b5dc78b96f3e39ad8f07179b42085920ef8e9add" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a92c9866e503", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Order/SuccPred): `succ a ≤ b ↔ a < b` when `b` is not maximal (#41371)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/a92c9866e503f6f721307ff001939461cfba9ccd" }, { "age_days": 0, "authors": [ "David Kurniadi Angdinata" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2e09891a520f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/EllipticDivisibilitySequence): add elliptic nets (#25989)", "updated": "2026-07-07", "url": 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"2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/SymplecticGroup): symplectic matrices have determinant 1 (#40352)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/ce0dcaa4265956ae72abd2dfa77214d838ddce24" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6f604786851f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/ENat/Basic): coe versions of `m + 1 ≤ n ↔ m < n` (#41372)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/6f604786851f312da512a988fd54eee4ca35dcf9" }, { "age_days": 0, "authors": [ "Whysoserioushah" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f0630767e52e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/EpiMono): add cube lemma (#41046)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/f0630767e52e1d946d29404a58982ed74d6f04c5" }, { "age_days": 0, "authors": [ "Evgenia Karunus" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5c206a857e64", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/RCLike/Basic): add norm_I (#41359)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/5c206a857e6422127e45b8823dd256e1b69918da" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4e566ca02d9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/MonoidAlgebra): more general `algHom_ext` (#41412)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/f4e566ca02d995d16c590cdfe4dc051cc80f4624" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cfa16a74cd62", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove redundant `open Classical in` (#41387)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/cfa16a74cd62a6608814a340f9ae2651d16f9828" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:80b457d52734", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: properly deprecate the `linter.style.commandStart` option (#41408)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/80b457d52734bab76b8b75adfc69c6e7ed4120f0" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d8d7c66091ed", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: prefer `open scoped Classical` over `open Classical` (#41414)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/d8d7c66091ed5798d562a2ad011746e013b190be" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:308db4b77766", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: localise use of the `backward.privateInPublic` option more (#41410)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/308db4b77766a1bf5aab4d678307978add6ab39a" }, { "age_days": 0, "authors": [ "Monica Omar" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9854f6dd2143", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/AffineSpace/AffineSubspace/Defs): unsimp `coe_affineSpan` (#41404)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/9854f6dd2143d4aeed97d33ac493531b6e1720f9" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4acc68084bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(GroupTheory/FreeGroup/Basic): automated extraction from #38114 (#41441)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/f4acc68084bf13dc6845a15176feab667477113b" }, { "age_days": 0, "authors": [ "Hagb (Junyu Guo 郭俊余)" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a77377db42d3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Finsupp/MonomialOrder): rename fields of `MonomialOrder` to match naming conventions (#39494)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/a77377db42d36c734ebc20721fbe6e0150498757" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-07-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:70f9aed325d8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/Types): change imports to avoid generating elementwise lemmas twice (#41425)", "updated": "2026-07-07", "url": "https://github.com/leanprover-community/mathlib4/commit/70f9aed325d8940844ad0e3246dc487f51bcb52a" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:f7cb0170acca", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: make `int_toBitVec` SymM compatible (#14290)", "updated": "2026-07-06", "url": 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leanprover/lean4.", "title": "leanprover/lean4: fix: restore go-to-definition on `mut` variables after a `for` loop (#14296)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/a54f7e9c7ec212c629363121c0f977d07a8c4eff" }, { "age_days": 1, "authors": [ "Paul Reichert" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:cc9a8de78c40", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: enable backward.isDefEq.respectTransparency.types by default (#13895)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/cc9a8de78c40c1a37726a511b656db0738ea0abf" }, { "age_days": 1, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:1db9c0d341d2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/1db9c0d341d25b01c00f43bab8c36beefda350b5" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:4cc11dd11419", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: unapply bootstrapping workarounds", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/4cc11dd11419aa851c3a4f2842792b26dbeaf126" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:b6e969df3243", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move `Nat.elimOffset` to internal namespace (#14292)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/b6e969df32431b8a6f5cb4c2c2b291676ad2211e" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:6247f052b47e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move `MessageType` to `Lean.Lsp` namespace (#14257)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/6247f052b47e5f69ffd63a716cccb808b7dd33ae" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:9b4f4656262c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move `Injective.leftInverse` out of `grind` module (#14293)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/9b4f4656262cbe5a6baa915e74df2d042f8b75ac" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover/lean4:8dc54c4f9f3d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: avoid namespace pollution while retaining dot notation (#14291)", "updated": "2026-07-06", "url": "https://github.com/leanprover/lean4/commit/8dc54c4f9f3d13eaebdf4eee05dd2e2b90e69cb8" }, { "age_days": 1, "authors": [ "Kevin Buzzard" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:db5c6a66675c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix: remove [IsMinimal R W] from HasSplitMultiplicativeReduction (#41391)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/db5c6a66675c39afae31ba65850058b68b37909f" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], 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leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: lemmas about equality of `EqvGen` (#40792)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/cef1e7de8e91a5dc9e89e484964f0735d048e3b4" }, { "age_days": 1, "authors": [ "Sebastien Gouezel" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d4fe71752a9f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: lemma `enorm_toReal` (#41386)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/d4fe71752a9fd59672d816143c9c97eae45dc9dc" }, { "age_days": 1, "authors": [ "Nailin Guan" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7bad0c47f922", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Polynomial): ideal span by monic polynomial (#41156)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/7bad0c47f9226828e409e03a208340404af88111" }, { "age_days": 1, "authors": [ "Justus Springer" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:12b4b4adf73c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory): add `Away.liftAlgHom` (#41321)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/12b4b4adf73c3bf0917409bb4b9dd4c8b96f4e8f" }, { "age_days": 1, "authors": [ "Jack McCarthy" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:85ce110e6bbb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Manifold): C^n smoothness of the inverse of a bundle trivialization (#41280)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/85ce110e6bbb05f3e9e60f6cd3c0e58cdb90c1b1" }, { "age_days": 1, "authors": [ "Weiyi Wang" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ec622b3712e3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(SetTheory): qualify `Cardinal.IsInaccessible.univ` in the doc (#41390)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/ec622b3712e306780ce97a7c057494e2dcb8a46d" }, { "age_days": 1, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a3b50ce4ec76", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove unused `linter.deprecated` exceptions (#41398)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/a3b50ce4ec76a7409b42c8fea5801d2f0b2a5d03" }, { "age_days": 1, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:eb56e53fe593", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove (all) redundant `backward.privateInPublic.warn` exceptions (#41382)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/eb56e53fe59380b78617e2a94dc4d0a479d8b9d4" }, { "age_days": 1, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:62aaa5c959a8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/ComposableArrows/Basic): localize use of the `backward.privateInPublic` option (#41407)", "updated": "2026-07-06", "url": "https://github.com/leanprover-community/mathlib4/commit/62aaa5c959a8c5cf491a22073ce59e97f7de5595" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-03", "freshness": "fresh", "id": "github:leanprover/lean4:e7929b93b433", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: apply bootstrapping workarounds", "updated": "2026-07-03", "url": "https://github.com/leanprover/lean4/commit/e7929b93b433a1b8bddbbf8749daf6edb14ebf89" }, { "age_days": 2, "arxiv_id": "2607.04077", "authors": [ "David Victor Feldman" ], "content_date": "2026-07-05", "freshness": "fresh", "id": "arxiv:2607.04077", "kind": "paper", "label": "negative", "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": 6, "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": 8, "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": 8, "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": 8, "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": 8, "arxiv_id": "2606.30419", "authors": [ "Kahbod Aeini", "Wojciech Golab" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "arxiv:2606.30419", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-06-29", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Einstein's theory of relativity correctly predicted that time is relative, and subject to both kinematic and gravitational dilation. Therefore, executions of distributed systems cannot always be modeled as sequences of events totally ordered according to wall clock time. To address this fundamental problem, Gilbert and Golab formulated a generalization of Herlihy and Wing's linearizability property for shared objects, which they called \\emph{relativistic linearizability}, and introduced a collection of theoretical tools to facilitate rigorous analysis. While they conjectured that several widely-studied classically linearizable algorithms are also relativistically linearizable, their work stopped short of presenting formal proofs of correctness, as pointed out recently by Jayanti. In this paper, we explain how Gilbert and Golab's techniques can be used to establish relativistic linearizability for a replicated state machine, as well as variations of the widely studied read/write register construction of Attiya, Bar-Noy and Dolev (ABD). Our results establish a stronger form of relativistic linearizability than Jayanti's central theorem for these asynchronous algorithms.", "title": "Analyzing Linearizability in Relativistic Distributed Systems", "updated": "2026-06-29", "url": "https://arxiv.org/abs/2606.30419" }, { "age_days": 9, "arxiv_id": "2606.29146", "authors": [ "Debatri Chattopadhyay" ], "content_date": "2026-06-28", "freshness": "fresh", "id": "arxiv:2606.29146", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-06-28", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We present a hierarchical Bayesian analysis of the joint mass, spin, and orbital properties of $\\sim 50$ Galactic binary radio pulsars with measured neutron star masses, classified by binary type into pulsar-white dwarf (PSR-WD) and double neutron star (DNS) systems. We find moderate evidence for an anti-correlation between neutron star mass and spin period in the pooled recycled population (correlation coefficient $ρ= -0.26$, with $96\\%$ of the posterior probability at $ρ<0$; the $90\\%$ credible interval excludes zero), robust to the treatment of candidate DNSs and to a radio-detectability selection correction. Although consistent with accretion-driven recycling, the correlation cannot statistically distinguish an accretion origin from a moment of inertia-driven spin-up mechanism, because the neutron star moment of inertia is nearly linear in mass over the observed range. The DNS systems alone instead lean to the positive side expected from the moment-of-inertia mechanism ($ρ=+0.13$), though with only ten systems this is not statistically conclusive. Mass shows no significant correlation with orbital period or inclination, and only a weak one with eccentricity. As a secondary result, neutron stars with helium white dwarf companions are marginally more massive than those with carbon-oxygen/oxygen-neon white dwarf companions ($Δ\\simeq 0.06\\,M_\\odot$), consistent with more extensive accretion in the helium white dwarf channel. We confirm, in a hierarchical framework, the previously reported correlation between companion mass and orbital eccentricity in double neutron stars ($ρ=+0.82$). We interpret these results within a two-channel picture -- accretion-grown PSR-WD versus birth-mass-dominated DNS.", "title": "Neutron Star Mass across Binary Pulsar Subpopulations: Mass-Spin Correlation, Mass Distributions, and Moment of Inertia Effects", "updated": "2026-06-28", "url": "https://arxiv.org/abs/2606.29146" }, { "age_days": 10, "arxiv_id": "2606.28989", "authors": [ "Shiva Chidambaram", "Timo Keller" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "arxiv:2606.28989", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-06-27", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Let $A$ be an abelian variety of dimension $g$ over a finite field $\\mathbf{F}_q$. We show that if $q$ is sufficiently large relative to $g$, the $g$ point counts $\\#A(\\mathbf{F}_{q^i})$ for $1 \\leq i \\leq g$ determine the zeta function of $A$, equivalently the characteristic polynomial of its Frobenius endomorphism, and hence the isogeny class of $A$. This count is best possible for $g=2$ and $g=4$, but not in general: for $g=3$ two point counts already determine the zeta function, whereas a single count never does. The proof combines the functional equation of the $L$-polynomial with Newton's identities and an inductive error analysis that controls the power sums of the inverse Frobenius eigenvalues with enough precision to recover them, as integers, by rounding.", "title": "Point counts of abelian varieties over finite fields determining their zeta function", "updated": "2026-06-27", "url": "https://arxiv.org/abs/2606.28989" }, { "age_days": 9, "arxiv_id": "2606.29400", "authors": [ "Giulio Federico", "Giuseppe Amato", "Claudio Gennaro", "Fabio Carrara", "Marco Di Benedetto" ], "content_date": "2026-06-28", "freshness": "fresh", "id": "arxiv:2606.29400", "kind": "paper", "label": "negative", "matched_signals": [ "negative:vision_world_models" ], "published": "2026-06-28", "score": -2.5, "source": "arxiv-ai4math-core", "summary": "In computer graphics, visual content is continuously warped, zoomed and resampled. This occurs when engines upscale frames, users zoom into 3D scenes, or foveated VR applies varying scaling. Handling these transformations requires Arbitrary-Scale Super-Resolution (ASR). Traditional models, designed for fixed scales, typically predict at a lower integer scale (e.g., x4) and rely on sub-optimal interpolation for continuous resolutions, compromising quality. Furthermore, most methods process pixels uniformly. Since fine details are sparse, this creates overhead; efficiency dictates concentrating resources only where structural complexity demands it. While implicit models and Gaussian Splatting (GS) enable continuous representation, GS is advantageous due to adaptive densification. However, transitioning GS into a feed-forward model for ASR is non-trivial. Standard GS optimization needs high-resolution gradients to drive primitive growth, which are unavailable during inference. Thus, the network must autonomously predict GS densification from low-resolution inputs. To solve this, we propose QuADA-GS. After encoding inputs into a latent space, a Neural Routing Architecture evaluates local complexity to distribute a global budget, assigning specific upsampling factors to features to avoid redundant processing. Features are dynamically densified based on these factors, forming an irregular topology decoded into 2D Gaussian primitives. To coordinate features before decoding, we introduce Hierarchical Pointer Convolution. This non-grid operator achieves O(1) neighbor lookup complexity, facilitating efficient spatial communication and bypassing dense bottlenecks. Experiments show QuADA-GS achieves state-of-the-art ASR performance, maintaining low latency and a lean memory footprint.", "title": "Learning to Adaptively Allocate Gaussians for Arbitrary-Scale Image Super-Resolution", "updated": "2026-06-28", "url": "https://arxiv.org/abs/2606.29400" }, { "age_days": 518, "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": 29, "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": 200, "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": 1106, "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": 168, "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" }