{ "counts": { "adjacent": 17, "core": 10, "errors": 0, "negative": 70, "total": 97 }, "date": "2026-07-02", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-02T17:12:02Z", "items": [ { "age_days": 5, "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": 3, "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": 2, "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": "2026-06-30", "url": "https://arxiv.org/abs/2606.31134" }, { "age_days": 2, "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": 5, "arxiv_id": "2606.28710", "authors": [ "Darrell Lewis-Sandy" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "arxiv:2606.28710", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-06-27", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We ask under what conditions an agent with a harm-minimizing policy can displace an approval-seeking (RLHF) agent in a competitive market, and when that policy is sufficient to prevent community harm. We use evolutionary game theory (finite-population Moran-Fermi pairwise comparison) to formalize this subject to assumptions of wisher hindsight, peer testimony, a monotone harm ledger, sufficient information density of community feedback, and a finite, depleting resource pool, in a negative-sum environment. We show that adoption is favored when the prior distributions on how readily wishers attune to community sentiment are monotone, exhibit endpoint inversion, and have a centro-symmetric pairing property, and demonstrate this with several long-tailed priors (Hill, Pareto, Lomax, Frechet). Where it is favored, a critical adoption level separates communities that drift back to the approval-seeking agent from those for which the audited agent fixes; above that level fixation is the overwhelmingly likely outcome. We derive when fixation is attainable as a bound on the effective (informational) size N_c of the community, which must be small enough to allow fixation before depletion. We present these as Theorems 5.4 and 5.5; the algebraic and finite-grid backbone is machine-checked in Lean 4, with the barrier-crossing asymptotics retained as explicit hypotheses. We show that a self-audited agent with a community ledger is not, in general, sufficient to prevent community harm. Sufficiency depends both upon the alignment of the agent's audit with community values and the timeframe over which harm is evaluated. Regardless of alignment, once adoption reaches dominance, the state is absorbing. The same policy that reduced harm under alignment becomes a trap, welfare-negative under misalignment and, even under alignment, one that locks in harm deferred past the adoption horizon.", "title": "The Two Genie Game: Adoption and Welfare in Audit-Grounded AI Governance", "updated": "2026-06-27", "url": "https://arxiv.org/abs/2606.28710" }, { "age_days": 6, "arxiv_id": "2606.28013", "authors": [ "Chengxiao Dai", "Zhaokun Yan", "Zhanhui Lin" ], "content_date": "2026-06-26", "freshness": "fresh", "id": "arxiv:2606.28013", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "verifier_guided_reasoning" ], "published": "2026-06-26", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Headline type-correctness (TC\\%) of LLM autoformalization has climbed from $\\sim$53\\% to $\\sim$76\\% in two years, yet this scalar conceals which errors each method resolves. We propose a signal-coverage matrix that crosses the Lean elaborator (pass/fail) with a semantic-equivalence judgment (equivalent/not), sorting every output into one of four cells: true success (TS), type-only (TO), semantic-only (SO), or both fail (BF). On ProofNet\\# and MiniF2F-test with DeepSeek V4-Pro across Vanilla, Lean-Retry, Sample-Filter, and Stratified Autoformalization (SAF): (1) the +34 to +36 TS gain across the three elab-feedback methods is $\\sim$64\\% type-stratum recovery, with SO flat on net (87.5\\% of original semantic errors rescued, 8 newly created). (2) The TO-to-TS rate is 23/61 for each method (Wilson 95\\% CI [26.6\\%, 50.3\\%]), and this stratum-level recovery rate predicts $Δ$TS on held-out methods to within 2/186 and renders $Δ$TC linear in the Vanilla elab-fail rate across six (model, dataset) cells ($R^2=0.96$). (3) The two judges disagree by 26 to 37 pp on elab-feedback outputs (vs. 7 pp on Vanilla), with 30 to 56\\% of symbolic-judge false negatives traceable to elaborator-forced rewrites. The persistent residual reduces to two gold-formalization errors. TC\\% gains should be credited by which cell moved, not by the scalar alone.", "title": "The Signal-Coverage Matrix: Stratifying Type and Semantic Errors in Statement Autoformalization", "updated": "2026-06-26", "url": "https://arxiv.org/abs/2606.28013" }, { "age_days": 2, "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": 6, "arxiv_id": "2606.27926", "authors": [ "Can Li", "Ting Zhang", "Junbo Zhao", "Hua Huang" ], "content_date": "2026-06-26", "freshness": "fresh", "id": "arxiv:2606.27926", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization", "reasoning_rl_distillation" ], "published": "2026-06-26", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor. However, current frameworks suffer from severe bottlenecks in two core stages: autoformalization, which treats multimodal translation as a static task decoupled from downstream solver compatibility, and theorem prediction, where solvers frequently hit a deductive impasse due to fixed rule libraries. To address these, we propose SD-GPS, a solver-driven framework that treats the symbolic solver as an execution oracle throughout both formalization and deduction. First, Solver-Driven Autoformalization unifies supervised formal-language adaptation and solvability-guided reinforcement learning into a single module built on QwenVL3-2B, making executability the central training signal. Second, Verified Theorem Proposing introduces an impasse-aware agent that proposes local auxiliary lemmas from current proof states, ensuring soundness by filtering all proposals through symbolic verification. Empirical evaluations on Geometry3K and PGPS9K demonstrate that SD-GPS consistently outperforms existing MLLM, neural, and neuro-symbolic methods across standard completion, multiple-choice, and cross-modal reference regimes, proving that closing the loop between multimodal perception and symbolic execution significantly improves geometric reasoning, offering profound insights into how neural agents can be grounded by formal systems to achieve verifiable problem-solving capabilities.", "title": "Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing", "updated": "2026-06-26", "url": "https://arxiv.org/abs/2606.27926" }, { "age_days": 1, "arxiv_id": "2607.01223", "authors": [ "Ben Slivinski", "Michael Saldivar" ], "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": "2026-07-01", "url": "https://arxiv.org/abs/2607.01223" }, { "age_days": 1, "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": 2, "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": 3, "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": 3, "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": 4, "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": 4, "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": 5, "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": "2606.28572", "authors": [ "Rodrigo Mendoza-Smith" ], "content_date": "2026-06-26", "freshness": "fresh", "id": "arxiv:2606.28572", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-06-26", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one. We use Lean 4's kernel-level tracking of axiom dependence to show that the axiom of choice has a measurable geometric correlate in proof space that obeys a one-parameter mixture law and has operational consequences for neural theorem provers. To do this, we partition $471{,}260$ declarations of Mathlib by transitive dependence on the axiom of choice and represent a filtered population of $42{,}355$ traced theorems by their sequences of tactic invocations. We use the constructive proofs in this dataset to train a self-supervised proof encoder and show that when using it to measure classical proofs, three complementary measurements (anomaly score, reconstruction loss, and density-superlevel containment) exhibit a common decline with the proof's distance from the axiom in the dependency graph, from sharp separation at the shallow boundary (AUC $0.847$ at distance $2$) to indistinguishability at distance~$9{+}$. Robustness controls show that the signature survives length, file, author, and topic controls, and replicates under full-source encoders trained on normalised proof source. Operationally, we show that on an evaluation sample of $251$ Mathlib theorems, Lean's \\texttt{aesop} tactic solves constructive theorems at $13\\times$ the rate of classical ones, and a neural-guided hybrid using the ReProver tactic generator compresses the gap to $5\\times$. The geometric anomaly score predicts \\texttt{aesop} failure beyond proof length, providing an operational link between the geometric signature and prover performance.", "title": "Geometric Measurements of the Axiom of Choice in Neural Proof Embeddings", "updated": "2026-06-26", "url": "https://arxiv.org/abs/2606.28572" }, { "age_days": 7, "arxiv_id": "2606.26525", "authors": [ "Yuming Feng", "Frederick Pu", "One An", "Osbert Bastani", "Li Zhang", "Jiani Huang", "Xujie Si", "Ziyang Li" ], "content_date": "2026-06-25", "freshness": "fresh", "id": "arxiv:2606.26525", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-06-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Auto-formalization is critical for scalable formal verification, but existing progress largely focuses on isolated statements, while theory-scale auto-formalization, which coherently translates hundreds of interdependent definitions, lemmas, and theorems, remains open due to challenges in consistency, faithfulness, scalability, and correctness. In this paper, we introduce LCS-Bench, a stand-alone, theory-scale benchmark based on Logics for Computer Science. LCS-Bench is built through a novel semi-automated agentic pipeline that leverages concept graphs, formal signature planning, issue tracking, sorry-filling with counter-example search, complemented by faithfulness review from human experts. The resulting artifact covers 327 textbook items, over 4,076 Lean declarations, and more than 85K lines of Lean code. The dataset supports broad evaluation through a data engine that automatically derives five tracks of evaluation benchmarks, measuring different aspects of auto-formalization and theorem-proving capabilities. We also introduce a novel evaluation protocol featuring definitional equivalence checkers, enabling more fine-grained and faithful assessment. Through extensive evaluation on 14 models, we demonstrate that (1) LCS-Bench is of high quality, consistent, and faithful; (2) the benchmark is challenging, with state-of-the-art models achieving only 20.1% on auto-formalization tasks; and (3) our analysis reveals key findings regarding theory-scale auto-formalization and suggests promising directions for future work.", "title": "Theory-Scale Auto-Formalization of Logics for Computer Science", "updated": "2026-06-25", "url": "https://arxiv.org/abs/2606.26525" }, { "age_days": 7, "arxiv_id": "2606.27041", "authors": [ "Andrei-Alexandru Oltean", "Bogdan Macovei", "Ioana Leuştean" ], "content_date": "2026-06-25", "freshness": "fresh", "id": "arxiv:2606.27041", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-06-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We present a Lean formalization of a general hybrid modal logic with many-sorted signatures and polyadic modal operators. The system borrows ideas from both algebraic specification and dynamic logics, and is designed to serve as a uniform axiomatic foundation for specifying and verifying programming languages and security protocols. We expose a DSL for users to define languages and protocols as many-sorted signatures, specify the relevant domain-specific axioms, and reason about program executions or protocol runs. We provide a machine-checked proof of its soundness theorem and showcase the framework's versatility through several applications: an imperative programming language for code verification, the BAN logic for security protocols, and the modal system S5. We have designed our formalization to be intrinsically sorted, that is, well-sorted formulas in the base language are well-typed terms in Lean. Thanks to intrinsic sorting, all domain specific applications can be easily embedded in our framework via the DSL, at no additional syntactic overhead required for the user to prove. All code presented in this paper is openly accessible in the following repository: https://github.com/alexoltean61/msphml-lean", "title": "Formalizing a Many-Sorted Hybrid Polyadic Modal Logic in Lean", "updated": "2026-06-25", "url": "https://arxiv.org/abs/2606.27041" }, { "age_days": 7, "arxiv_id": "2606.26649", "authors": [ "Adam Mondl", "Matthew Maisel", "John H. Brock" ], "content_date": "2026-06-25", "freshness": "fresh", "id": "arxiv:2606.26649", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-06-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Agent safety in high-stakes domains requires formal policy enforcement, but most existing approaches either rely on probabilistic guardrails (fine-tuned classifiers, prompt-based steering) that offer no formal guarantees, or on hand-coded symbolic enforcement that does not scale to the breadth of real policy specifications. We present an autoformalization pipeline that translates agent prompts, MCP tool descriptions, and natural language policy documents into formally verified policies using an LLM-based generator-critic loop. The resulting policies are written in the Cedar Policy Language. On the MedAgentBench benchmark, our autoformalized policies cover substantially more of the source natural-language specification than the hand-coded symbolic enforcement in prior work.", "title": "Autoformalization of Agent Instructions into Policy-as-Code", "updated": "2026-06-25", "url": "https://arxiv.org/abs/2606.26649" }, { "age_days": 1, "authors": [ "Aditya Menon" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6eacf8db4e1a", "kind": "github_update", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-01", "repo": "leanprover-community/mathlib4", "score": 2.2, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: IMO 2000 Q2 (#40286)", "updated": "2026-07-01", "url": "https://github.com/leanprover-community/mathlib4/commit/6eacf8db4e1a524ea1a2c3784d5c3d5948f03650" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:1391dbb67e3e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: structure handling in bv_decide (#14241)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/1391dbb67e3e837241306c1ab50e3d17f20cdcf2" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:ce85346e2724", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: work around non-linearity in ElimDead (#14245)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/ce85346e2724c6839a5c83bc1ac83a2ea4265342" }, { "age_days": 0, "authors": [ "Mac Malone" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:e281ba87c2c9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: correct exe perms on restore (#14240)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/e281ba87c2c967b1662ee28bd201046956d0494a" }, { "age_days": 0, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:8ca1cb8d43fe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: correctly add Verso docstrings to coinductive predicates (#14247)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/8ca1cb8d43fe07a0f222adb9e304a80f65477b06" }, { "age_days": 0, "authors": [ "Julien Cretin" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:989fca42c6a8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix typo in Quot (#14244)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/989fca42c6a86569eed541a446c5960d304ae522" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:fbe3221389f1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/fbe3221389f1ec056f5ee901be958ef09b52b151" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:2df8f51e63c2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: shorten pole (#14242)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/2df8f51e63c25d329432e1c0bf1d4cd91a363157" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover/lean4:5e846677a9b0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: annotate some types (#14250)", "updated": "2026-07-02", "url": "https://github.com/leanprover/lean4/commit/5e846677a9b0988309cceb504dd066a577419906" }, { "age_days": 0, "authors": [ "Sabrina Jewson" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:52846449a4fa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Order/OrdContinuous): redefine left and right order continuity to not require preserving ⊥/⊤ (#37682)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/52846449a4fa62c105e3af4a11b4c375b23c1645" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c19037a81001", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Translate): fix universe reorder inference (#40493)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/c19037a8100134c62a19bc5dbaffb633c4b9f3b4" }, { "age_days": 0, "authors": [ "Rémy Degenne" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:af4123a60c15", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: lemmas about operations on EReal (#41246)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/af4123a60c150d588ffbc6228a83c27ef133fe0d" }, { "age_days": 0, "authors": [ "Yongxi (Aaron) Lin" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:40b45a066a39", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: generalize some lemmas by using conditional Jensen (#36888)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/40b45a066a39ea5a58a2acf3cf85bf513fc0e241" }, { "age_days": 0, "authors": [ "teorth" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4f548c102d53", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Order/IntermediateValue): images of intervals under monotone continuous functions (#41130)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/4f548c102d53c65f8b60e5811a9f54a72fcaeaec" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:af2f0a4b1dac", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(SetTheory/Cardinal/Finite): add a NeZero instance for Nat.card (#41274)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/af2f0a4b1dacaae7569a82641960b7f833bc3a69" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:36d9c9f45567", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(GRewrite): strict rewriting (#38868)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/36d9c9f455679093c901bcab147fbe8bc1c1ec2c" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:52b549a28077", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/List/Chain): generalize `WellFounded.asymmetric₃` to chains (#36922)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/52b549a28077070173094a1ee121f6326cb555e2" }, { "age_days": 0, "authors": [ "mitchell-horner" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b9df47b72b28", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph): prove the minimal-degree version of the Erdős-Stone theorem (#28685)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/b9df47b72b287802f6d40cf7588dada976bc657d" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:765274a7959a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Limits): definition of weighted limits (#41163)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/765274a7959afcd210149efc10b904d71bc2edcc" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:db73cf1a4b64", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Module/LinearMap/FiniteRange): iff version of isQuasiInverse_subtype_projectionOnto (#41272)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/db73cf1a4b64b689cd8fa77fcfef2c895028588a" }, { "age_days": 0, "authors": [ "Artie Khovanov" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5fe4bfd593b8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(LinearAlgebra/FreeModule/StrongRankCondition): clarify context of `commRing_strongRankCondition` (#38347)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/5fe4bfd593b85d063af1dff2ede334da193e7d71" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a22faf7b71a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(CategoryTheory/Preadditive/LeftExact): fix stale declaration names in module docstring (#41270)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/a22faf7b71a717c172640d940a5be690949d2f85" }, { "age_days": 0, "authors": [ "Rémy Degenne" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:05742115c13f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: generalize `instPosPart` to SubNegMonoid (#41247)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/05742115c13f3a461ea7b6f07afa80f99dfb1531" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:48489ec86e76", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add an empty line after module headers (#39428)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/48489ec86e768e6d248d33fa9ea9b05c97e32b17" }, { "age_days": 0, "authors": [ "Suzuka Yu" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8f5331973a3e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RepresentationTheory/Character): golf some results in FDRep (#41278)", "updated": "2026-07-02", "url": 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"published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Dimension/Free): fix docstring (#41257)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/564ff5af9b5f3b50769a51c10def6bbdcf9c9471" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:42b23e7cd99f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(GroupTheory/*): remove more `NeZero (Nat.card G)` (#41287)", "updated": "2026-07-02", "url": 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"2026-07-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/WeakLimits): fix weak pullbacks theorem name and docstrings (#41266)", "updated": "2026-07-02", "url": "https://github.com/leanprover-community/mathlib4/commit/42e335ab819aaa0c2283686ec0a7bbd9bccedc9f" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover/lean4:3196914162dd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: `USize`/`ISize` handling in `bv_decide` (#14227)", "updated": "2026-07-01", "url": "https://github.com/leanprover/lean4/commit/3196914162ddc4436574021838d2953decaf69cd" }, { "age_days": 1, "authors": [ "Joachim Breitner" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover/lean4:85e60ac6d27b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: push a fresh InfoTree context for term-level `open ... in` and `set_option ... in` (#14234)", "updated": "2026-07-01", "url": "https://github.com/leanprover/lean4/commit/85e60ac6d27bd44a415bf3cb42fb1cbeb6d9da63" }, { "age_days": 1, "authors": [ "Joachim Breitner" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover/lean4:4907d41bedb1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: automatic `try?` suggestions for empty `by`, unsolved goals, and `sorry` (#13830)", "updated": "2026-07-01", "url": "https://github.com/leanprover/lean4/commit/4907d41bedb1ef2ed1d064d6ba21114f409a9b2f" }, { "age_days": 1, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover/lean4:89d728b53ccf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: remove circularity from #eval docstring (#14223)", "updated": "2026-07-01", "url": "https://github.com/leanprover/lean4/commit/89d728b53ccfda77971b5381649d2bbe9eae2039" }, { "age_days": 1, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-07-01", "freshness": "fresh", "id": "github:leanprover/lean4:3d064f2732c3", "kind": "github_update", "label": 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[], "published": "2026-06-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: ci: fix adaptation PR CI (#14229)", "updated": "2026-06-30", "url": "https://github.com/leanprover/lean4/commit/a08dc72dd43698ba5488a00ab03831d11a749c38" }, { "age_days": 3, "authors": [ "Joachim Breitner" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "github:leanprover/lean4:bf755648d817", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `impossible` to not `cleanup` the goal (#14205)", "updated": "2026-06-29", "url": "https://github.com/leanprover/lean4/commit/bf755648d817af332909637a9ab0573dadef542f" }, { "age_days": 3, "authors": [ "Kim Morrison" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "github:leanprover/lean4:c81da0935910", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add idxOf/getElem round-trip lemmas (#14210)", "updated": "2026-06-29", "url": "https://github.com/leanprover/lean4/commit/c81da0935910c096fdbc74250932227b68a3c7a6" }, { "age_days": 3, "authors": [ "Kim Morrison" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "github:leanprover/lean4:82730f7031ad", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add finRange nodup and monotonicity lemmas (#14209)", "updated": "2026-06-29", "url": "https://github.com/leanprover/lean4/commit/82730f7031adf75850f8cd5f6d59a75e50d93748" }, { "age_days": 3, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "github:leanprover/lean4:82ba8e2c5197", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: revert #14193 (#14214)", "updated": "2026-06-29", "url": "https://github.com/leanprover/lean4/commit/82ba8e2c51972053aceedc04d0fe00e4bdf5d615" }, { "age_days": 3, "authors": [ "Bhavik Mehta" ], "content_date": "2026-06-29", "freshness": "fresh", "id": "github:leanprover/lean4:1a13e4fd5ea0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: make `Nat.ne_of_gt` protected (#14216)", "updated": "2026-06-29", "url": "https://github.com/leanprover/lean4/commit/1a13e4fd5ea095723eea6b7473e42c61d8e463fb" }, { "age_days": 4, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-06-28", "freshness": "fresh", "id": "github:leanprover/lean4:de5b7f235a71", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: used parsed docstring format regardless of local setting (#14200)", "updated": "2026-06-28", "url": "https://github.com/leanprover/lean4/commit/de5b7f235a71d301bffbb2dbe607ec36dd58cce7" }, { "age_days": 5, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "github:leanprover/lean4:45e668d09492", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: parameter references in Verso docstrings (#14198)", "updated": "2026-06-27", "url": "https://github.com/leanprover/lean4/commit/45e668d09492b90939bd072e3cd1769e9f71893c" }, { "age_days": 5, "authors": [ "Garmelon" ], "content_date": "2026-06-27", "freshness": "fresh", "id": "github:leanprover/lean4:6b941e7a112c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: ci: follow downstream action rename (#14199)", "updated": "2026-06-27", "url": "https://github.com/leanprover/lean4/commit/6b941e7a112c6548732a30f51e4f887f4db9039f" }, { "age_days": 6, "authors": [ "Henrik Böving" ], "content_date": "2026-06-26", "freshness": "fresh", "id": "github:leanprover/lean4:84b251f7390c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-06-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: less aggressive {List,Array}.count e-matching (#14177)", "updated": "2026-06-26", "url": "https://github.com/leanprover/lean4/commit/84b251f7390c20a0a00a221050ab4a6e6c46a191" }, { "age_days": 1, "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": 3, "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": 3, "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": 3, "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": "2026-06-29", "url": "https://arxiv.org/abs/2606.30450" }, { "age_days": 3, "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": 4, "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": 5, "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": 6, "arxiv_id": "2606.28043", "authors": [ "Samuele Meschini", "Matteo Moscheni" ], "content_date": "2026-06-26", "freshness": "fresh", "id": "arxiv:2606.28043", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-06-26", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "This work identifies an inconsistency between plasma operating scenarios and tritium fuel cycle (TFC) requirements, calling for a re-examination of the traditional reactor-led design approach. The key point is simple: in current TFC architectures, fuel puffing must contain tritium. Moscheni et al. (2026 Nucl. Fusion 66 026008) investigated fuel puffing rates in detached operation. Expanding that database, puffing is shown to exceed core fuelling by about an order of magnitude, from present-day tokamaks to next-step stellarators. Though not unknown in the plasma community, TFC models instead assumed core fuelling to dominate. The implications are severe. In recent TFC architectures, direct internal recycling (DIR) is intended to minimise tritium inventory, but assumes near-50:50 D:T composition. This assumption may become self-defeating: a substantial fraction of the puffed fuel must be tritium. Tritium inventory, doubling time, required breeding ratio, and pump sizing therefore become critical once puffing is properly accounted for. Mitigation is assessed by extending the models of Meschini et al. (2023 Nucl. Fusion 63 126005). For a notional plant, realistic TFC requirements can be met with D-rich, T-lean puffing, at the cost of about 10% lower fusion power. Alternatively, for near-50:50 D:T puffing, reduced fuel puffing with stronger impurity seeding can maintain detachment while alleviating TFC constraints, albeit with higher core contamination. Combined use of these strategies enables scenarios that minimise tritium inventory and throughput while balancing competing requirements. Ultimately, these results place renewed emphasis on the TFC as a central element of reactor design. A viable fusion reactor requires joint optimisation of core plasma, edge plasma, and TFC, implying unavoidable trade-offs across all three.", "title": "On the Relationship Between Plasma and Tritium Fuel Cycle Through Matter Injection and Particle Exhaust", "updated": "2026-06-26", "url": "https://arxiv.org/abs/2606.28043" }, { "age_days": 7, "arxiv_id": "2606.27045", "authors": [ "Hartwig Grabowski" ], "content_date": "2026-06-25", "freshness": "fresh", "id": "arxiv:2606.27045", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-06-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "AI coding agents dramatically accelerate implementation speed but introduce two structural failure modes that existing spec-driven approaches do not fully solve: (1) context explosion -- the agent must reason over an entire repository at once, degrading output quality as the context window fills; and (2) silent spec-code drift -- code evolves, the specification does not, and the divergence becomes invisible until it is costly to repair. We present the Spec Growth Engine, a lightweight framework that addresses both failure modes through a machine-readable spec graph whose nodes carry explicit contract/design separation, a Spine context assembler that scopes agent context to an ownership path, a vertical-slice growth protocol that enforces hardest-first ordering, and a drift gate that makes spec-code divergence a blocking merge condition. The design synthesises well-established software engineering principles (Parnas information hiding, C4, ADRs, Walking Skeleton, Reflexion Models, Fitness Functions) into a lean, code-coupled, machine-enforced whole -- without the overhead of heavy-weight frameworks such as RUP or MDA.", "title": "The Spec Growth Engine: Spec-Anchored, Code-Coupled, Drift-Enforced Architecture for AI-Assisted Software Development", "updated": "2026-06-25", "url": "https://arxiv.org/abs/2606.27045" }, { "age_days": 4, "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": 513, "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": 24, "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": 195, "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": 1101, "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": 163, "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" }