{ "counts": { "adjacent": 9, "core": 6, "errors": 0, "negative": 74, "total": 89 }, "date": "2026-07-15", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-15T16:52:07Z", "items": [ { "age_days": 5, "arxiv_id": "2607.09217", "authors": [ "Matěj Kripner", "Milan Straka" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09217", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-07-10", "score": 16.9, "source": "arxiv-ai4math-core", "summary": "In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification. OpenProver integrates a Planner-Worker-Verifier architecture inspired by recent ATP agentic systems such as Aletheia. A Planner agent maintains a compact Whiteboard scratchpad and an unbounded Repository of intermediate findings, and decomposes mathematical work into parallel Workers. OpenProver is fully open-source, offers reproducible evaluation through automatic formal verification of generated proofs, and provides an interactive terminal interface for human-guided proof search. In interactive mode, OpenProver allows the human operator to monitor and steer the proof search process, motivated by the established human-AI synergy in interactive code generation. To showcase the potential for quantitative ablation experiments enabled by automatic formal verification, we evaluate OpenProver on ProofNet and compare it with a simple baseline. OpenProver is publicly available at https://github.com/kripner/OpenProver.", "title": "OpenProver: Agentic and Interactive Theorem Proving with Lean 4", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09217" }, { "age_days": 2, "arxiv_id": "2607.11258", "authors": [ "Burak S. Akbudak", "Zeynel A. Uluşan", "Can S. Erer", "Gözde Gül Şahin" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11258", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-13", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Tree search algorithms enable systematic exploration of the proof space in neural theorem proving. Existing LLM tree search libraries primarily target natural language reasoning and do not provide native integration with formal verifiers, while theorem proving systems often rely on task-specific search implementations. We introduce TreeThink, an open-source Python library for modular, fully asynchronous tree search in neural theorem proving. It integrates established tree search methods with vLLM-based inference pipelines and diverse node evaluation techniques, ranging from lightweight heuristics to neural evaluators. We support Lean~4, Rocq, and Isabelle/HOL alongside natural language. It connects directly to each language's Read-Eval-Print Loop (REPL) server for real-time verification and proof state extraction. We evaluate TreeThink on miniF2F and MATH500, demonstrating cross-language formal proof search, natural language reasoning support, and up to 6.3$\\times$ wall-clock speedup from asynchronous execution. Source code is released under the MIT license at https://github.com/GGLAB-KU/treethink , and the library is accessible as a downloadable package at https://pypi.org/project/treethink/ .", "title": "TreeThink: A Modular Tree Search Library for Mathematical Reasoning with LLMs", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11258" }, { "age_days": 2, "arxiv_id": "2607.11307", "authors": [ "Tian-Shuo Liu", "Shiyuan Zhang", "Zijie Geng", "Haoyu Liu", "Runjie Xu", "Pengyuan Wang", "Lei Yuan", "Yang Yu" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11307", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-07-13", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning. Unlike statement-level formalization, proof autoformalization is a long-horizon challenge requiring coordination of claims, contexts, and dependencies across many proof steps, yet has only recently come under focused study. Current approaches either rely on costly model training or apply excessive, unguided repair at inference time. To this end, we introduce ToMap, a multi-agent framework that structures proof autoformalization as a Decomposer-Formalizer-Prover pipeline with efficient test-time optimization guided by formal verification and semantic rubrics for proof quality. Rather than distributing test-time compute across all agents, we perform bottleneck analysis and identify the Decomposer as the critical bottleneck: the quality of its atomic, self-contained proof units directly determines whether downstream agents can successfully formalize and prove each step. ToMap therefore treats the Formalizer and Prover as downstream executors and efficiently focuses test-time compute on Decomposer refinement. This refinement follows a loop inspired by GEPA, evolving prompts over candidate decompositions and using formal verification progress together with semantic proof rubrics to define a Pareto frontier that guides the next decomposition update. Experiments on ProofFlowBench show that ToMap improves over the best previous method by 19.0% when evaluated by both syntactic correctness and semantic faithfulness, while requiring lower test-time cost. Scaling analysis shows that most gains emerge within a few iterations of decomposition evolution, guiding test-time budget selection.", "title": "Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11307" }, { "age_days": 5, "arxiv_id": "2607.09632", "authors": [ "Chengkai Zhu", "Ziao Tang", "Guocheng Zhen", "Yimeng Cao", "Yusheng Zhao", "Ranyiliu Chen", "Xuanqiang Zhao", "Lei Zhang", "Xin Wang" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09632", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error correction. Formalizing its coding theorems requires connecting finite-block protocols, analytic inequalities, and asymptotic limits within a unified machine-checked framework. Existing developments, however, lack a reusable operational layer that defines codes, error criteria, achievable rates, and capacities independently of their information-theoretic characterizations. In this work, we present LeanQIT, a Lean 4 library for finite-dimensional QIT. It provides composable, kernel-checked interfaces for quantum states and channels, source and channel codes, finite-block performance criteria, hypothesis testing, one-shot quantities, and asymptotic rate constructions. Using this infrastructure, we formalize Schumacher's quantum source-coding theorem, the Holevo--Schumacher--Westmoreland classical-capacity theorem, and the entanglement-assisted classical-capacity theorem together with its strong converse. By separating operational definitions from analytic characterizations and exposing reusable achievability, converse, and asymptotic components, Lean-QIT provides a machine-readable foundation for formal QIT and a compositional knowledge substrate for emerging AI-assisted formalization, automated proof search, and agentic reasoning in quantum information and computation.", "title": "Lean-QIT: Towards a Formal Infrastructure for Quantum Information Theory", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09632" }, { "age_days": 5, "arxiv_id": "2607.09072", "authors": [ "Seongmin Lee", "Yaoxuan Wu", "Miryung Kim" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09072", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "As the cost of code generation becomes cheaper with AI, the new bottleneck in software engineering has shifted to intent specification and validation. Overcoming this durability crisis of AI-driven coding requires more than traditional fuzzing: each candidate property must be proven correct over a model and shown to hold on the real implementation, making formal proof and systematic property-based testing (PBT) complementary. However, validating properties this way at scale requires solving two subproblems: verifying candidate properties and operationalizing PBT without AI hallucination. We hypothesize that recurring property patterns, cast as property templates--abstract, parameterized forms with holes--address both at once. This paper investigates recurring property patterns in Apache Spark. In data-intensive scalable computing systems, correctness properties arise from the principles of data partition, computation decomposition, and dataflow computation. For instance, aggregation decomposition relates a global function executed on the entire dataset to a local function followed by a recombiner. We design an agentic, dual-track validation framework that uses property templates to formally verify correctness in the Lean 4 theorem prover and instantiate PBT templates as executable PySpark tests. Our evaluation shows that property templates increase agentic proof engineering success by up to 2.6x (1.6x on average) and reduce proof hallucinations by 59%. Template-guided PBT synthesis reduces intent misalignments from 22 to 1 and cuts synthesis cost by up to 5.7x (3.8x on average). Template-guided synthesis further exceeds a state-of-the-art Spark fuzzer and approaches unguided LLM-based PBT on code coverage. Finally, comparing the two tracks is informative: when a proof succeeds yet a PBT finds a counterexample, the mismatch identifies a gap between the formal model and implementation.", "title": "Agentic Proof and Property-Based Testing via Property-Templates in Data-Intensive Computing", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09072" }, { "age_days": 6, "arxiv_id": "2607.08692", "authors": [ "Arthur F. Ramos", "Tulio Soria" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08692", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-09", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We present a metagame analysis of the competitive Pokemon Trading Card Game, machine-checked in Lean 4 over real tournament data. The headline game-theoretic results, including Nash equilibrium, replicator dynamics, and the matrix-level type-bridge computation, rely on native_decide, which trusts Lean's compiler rather than its kernel; the trust boundary is made explicit. The artifact spans approximately 31,900 lines, 87 files, and 2,627 theorems, of which roughly 200 directly verify empirical claims, with no sorry, admit, or custom axioms. Analyzing Trainer Hill data from January to February 2026 for events with at least 50 players, over 14 archetypes and their full pairwise matchup matrix, we prove a popularity paradox: the most played deck, Dragapult, with 15.5% metagame share, has only 46.7% expected win rate, while Grimmsnarl, with 5.1% share, achieves 52.7%. A machine-checked Nash equilibrium of the raw game assigns Dragapult 0% weight; exhaustive enumeration over all nonempty support subsets confirms a unique symmetric Nash equilibrium of the constant-sum symmetrization with seven-deck support. Against this equilibrium mix, Dragapult falls 40.4 permil below the game value. Single-step replicator dynamics indicate downward fitness pressure on Dragapult, upward pressure on Grimmsnarl, and strongest extinction pressure on Alakazam. A 10,000-iteration sensitivity analysis confirms qualitative stability, with core support decks appearing in more than 96% of resampled equilibria. The primary contribution is methodological: a reproducible case study showing how formal verification can turn qualitative metagame narratives into machine-checkable, re-runnable strategic science.", "title": "From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08692" }, { "age_days": 3, "arxiv_id": "2607.10654", "authors": [ "Mahadee Al Mobin", "Md. Shariful Islam" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "arxiv:2607.10654", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-12", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Let $S_n=\\{p\\in\\mathbb{P}:p<10^n\\}$, $N_n$ denote the total number of decimal digits occurring in the primes of $S_n$, $C_n(d)$ be the number of occurrences of a digit $d\\in\\{0,\\ldots,9\\}$ among those digits, and $P_n(d)$ be the probability of occurrence of a digit, $d$ among those digits. We prove that \\[ P_n(d)=\\frac{C_n(d)}{N_n} =\\frac{1}{10} +O\\!\\left(\\frac{\\log n}{n}\\right), \\qquad n\\to\\infty, \\] uniformly for every decimal digit $d$. The argument is entirely unconditional and combines the Prime Number Theorem, the Erdős--Turán discrepancy inequality, and classical Vaughan--Vinogradov estimates for exponential sums over primes. The principal step establishes quantitative equidistribution for interior digit positions, while the logarithmically many exceptional positions near the ends of the decimal expansion are shown to have asymptotically negligible influence after averaging over all digit positions and prime lengths. Consequently, the decimal digits occurring in primes, when pooled over all positions and all primes below $10^n$, become asymptotically equidistributed. We also clarify the precise scope of the theorem by distinguishing this averaged equidistribution result from the substantially stronger and presently unresolved questions concerning pointwise digit equidistribution, normality, and higher-order digit correlations in the sequence of prime numbers.", "title": "The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers", "updated": "2026-07-12", "url": "https://arxiv.org/abs/2607.10654" }, { "age_days": 6, "arxiv_id": "2607.08366", "authors": [ "José A. R. Fonollosa" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08366", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Fix n >= 2. A set A = {a_0 < a_1 < ... < a_{n-1}} of n residues in Z_N is \"valid mod N\" if the all-ones multiset is the only size-n multiset drawn from A whose sum is p := sum_i a_i (mod N). For the super-increasing set A = {2^k - 1 : 0 <= k <= n-1} we determine the least valid modulus exactly: N_min(n) = 2^n - 2^floor(log_2 n) for all n >= 2. Both directions of the proof are elementary, resting on a sharp minimal-digit-sum estimate for representations by binary coins, and the full theorem has been machine-checked in Lean 4/Mathlib for all n (https://github.com/jarfo/min-modulus). We conjecture that no size-n residue set admits a smaller valid modulus. This validity condition is exactly what makes the permanent of an n x n matrix equal to a single coefficient of a row-product polynomial modulo x^N - 1, extractable by a size-N discrete Fourier (or number-theoretic) transform; the theorem thus identifies the smallest transform, N ~ 2^n, for which this evaluation is exact. That application -- and the resulting common framework for the classical formulas of Ryser and Glynn and this transform -- is developed in a companion paper (arXiv:2607.09949).", "title": "Minimum modulus for the unique multiset-sum problem", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.08366" }, { "age_days": 6, "arxiv_id": "2607.09793", "authors": [ "Josué Alexander Ibarra" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.09793", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "An integer $n \\ge 1$ is cyclic if $\\gcd(n,\\varphi(n))=1$ (equivalently, if every group of order $n$ is cyclic), and Sophie Germain cyclic if both $n$ and $2n+1$ are cyclic. Let $C_σ(N)$ count the Sophie Germain cyclic integers in $[1,N]$. Cohen conjectured that $C_σ$ is subadditive, $C_σ(m+n) \\le C_σ(m)+C_σ(n)$ for all $1 \\le m \\le n$ (his Conjecture 66), having checked $m,n \\le 10^6$ without finding a counterexample. We give one: at $m=31$, $n=3928$, $C_σ(3959)=697 > 696 = C_σ(31)+C_σ(3928)$. The argument is short, and is verified by the Lean 4 kernel.", "title": "A counterexample to a subadditivity conjecture of Cohen for Sophie Germain cyclic numbers", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.09793" }, { "age_days": 1, "arxiv_id": "2607.12650", "authors": [ "Junyu Ren" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12650", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-14", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny. We present EG-VAR (Evidence-Grounded Verified Agentic Reasoning), a Lean 4-based tool-calling architecture in which the Lean kernel is the sole minter of Verified claims via tool-attestation axioms and declared source lifts. Every verified output structurally descends from an attested tool call (Thm. 3.1) and a kernel-checked chain of valid inference (Thm. 3.2); residual outputs are honest Abstain with a replayable audit trail. On a subcollection of TableBench numerical reasoning (n=120), EG-VAR attains 120/120 versus a 95% same-tool baseline; on counterfactual stress tests (5 domains x 2 models), EG-VAR stays 100% source-faithful while same-tool drops to 80-90% (no-tool 50-80%). With the LLM as deployment-time formalizer, residual semantic-formalization error is 3.3% on Sonnet and 1.7% on Opus. We position EG-VAR as a technical-governance interface for high-stakes empirical claims: a formal sidecar makes the target proposition, source scope, evidence boundary, proof obligation, and abstention condition auditable, eliminating unsupported Verified outputs today while turning formalization errors, lift and source-authority disputes, ambiguities, and abstentions into explicit audit targets. Over time, typed sidecars in datasets, APIs, public records, and AI-generated documents can amortize this formalization burden into reusable infrastructure.", "title": "Evidence-Grounded Verified Agentic Reasoning: A Path Toward Eliminating LLM Hallucination in Empirical Inference via Tool-Attested Kernel Proofs", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12650" }, { "age_days": 1, "arxiv_id": "2607.12981", "authors": [ "Mingrui Jing", "Lei Zhang", "Yusheng Zhao", "Hongshun Yao", "Xin Wang" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12981", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-14", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A central model in quantum machine learning is the quantum neural network (QNN), whose design requires balancing expressivity and trainability. Technically, expressivity is studied through circuit-function analysis, such as quantum signal processing, while trainability is analyzed using dynamical-Lie-algebra (DLA) methods. To support certified QNN design, we formalize these major components of QNN theory in a connected lean 4 development checked by a proof kernel, where every analytic input is either proved or exposed as a named hypothesis. On the expressivity side, we prove exact if-and-only-if characterizations of single-qubit QNNs, a resource-counted quantum phase processing theorem, and an overparameterization ceiling that bounds the quantum Fisher information rank by the DLA dimension. On the trainability side, we derive the direct-sum loss-variance law through a de-circularized second-moment interface. A parameterized Casimir-uniqueness engine discharges the required inputs for fully controllable, orthogonal, and matchgate circuit families, while single-qubit and product-Clifford ensembles close the two-design assumptions directly. A capstone theorem pairs the conditional variance law with exact loss reconstruction in DLA coordinates. The development record identifies eight corrections and clarifications that were not explicit in the informal arguments. We expect this work to provide a machine-checkable foundation for QNN theory and a step toward AI-assisted or automated design of quantum machine learning algorithms.", "title": "An Agentic Formalization for Certified Quantum Neural Network Design", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12981" }, { "age_days": 5, "arxiv_id": "2607.09383", "authors": [ "Yichen Xu", "Oliver Bračevac", "Cao Nguyen Pham", "Yaoyu Zhao", "Martin Odersky" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09383", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Substructural type systems give strong static control over aliasing. Examples include uniqueness, separation, and borrowing. How can such control be brought to established languages whose programming models rely on higher-order abstraction, unrestricted aliasing, and pervasive sharing? We study this problem in the context of Scala. We show how to retrofit these guarantees selectively instead of globally: ordinary code keeps Scala's usual aliasing discipline, while stronger guarantees can be enforced where they matter. Our starting point is Scala's capture checking, whose treatment of capabilities is inspired by the object-capability tradition: capabilities are ordinary values, and capture sets record, in a value's type, which capabilities the value may use. We develop System Capybara, which adds a selective alias-control layer to this mechanism. By tracking separation, consumption, freshness, and read-only access for capabilities, Capybara recovers key reasoning principles from substructural and ownership-based disciplines without global invariants. We give a type-preserving translation from the surface calculus Capybara to CoreCapybara, a core calculus extending System Capless, the earlier foundation for capture checking. The translation uses quantifiers for capture polymorphism and freshness, and constraint-indexed modal types for separation. We prove a semantic soundness result for the core calculus in Lean 4 and derive type safety, memory safety (no use-after-free or double-free), immutability of read-only computations, and data-race freedom for well-typed programs. Finally, we implement Scala 3's new separation checker, which brings higher-order separation reasoning about effects, capabilities, and resources to ordinary Scala, including fearless concurrency.", "title": "System Capybara: Tracking Capabilities for Separation and Freshness (Extended Version)", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09383" }, { "age_days": 5, "arxiv_id": "2607.09014", "authors": [ "Patrick White" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09014", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A proper sub-box of $A=\\{0,1,2\\}^d$ is a product $S_1\\times\\dots\\times S_d$ with each $\\varnothing\\neq S_i\\subsetneq\\{0,1,2\\}$. A double cover is a finite multiset of proper sub-boxes covering every point of $A$ exactly twice; write $f(d)$ for the minimum size of a double cover. Leader, Milicevic and Tan asked whether $f(d)\\ge 2^d$ for all $d$ (Question 4.1 of the PatternBoost paper of Charton-Ellenberg-Wagner-Williamson), analogous to the Alon-Bohman-Holzman-Kleitman partition bound $2^d$. No better than the trivial volume bound was previously known, for any $d\\ge 2$. We prove the first nontrivial lower bounds. A modular refinement of the parity argument gives $f(d)\\ge 2^{d+1}/(d+1)$; a slicing argument gives $f(4)\\ge 19$, $f(5)\\ge 33$, both above $2^d$, resolving the question for $d=4,5$ -- the first cases beyond the trivially known $d\\le 3$. A finer \"line rigidity\" argument yields $f(6)\\ge 60$, breaking the profile-statistic barrier (capped at $57$, shown here). This is formally verified in Lean 4: $f(6)\\ge 60$ is machine-checked on the three standard Mathlib axioms alone. On the upper-bound side, a dimension-lifting construction $f(r+3)\\le 6\\cdot 2^r+3f(r)$ gives $f(6)\\le 81$ (improving the known $82$) and $f(d)\\le(\\tfrac65+o(1))2^d$ asymptotically; a refinement improves the constant to $\\tfrac87$. This makes partial progress on PatternBoost's problem of reducing their constant $1.28$, and refutes the closed-form guess $f(d)=5\\cdot 2^{d-2}+1$ from $d=7$ on. Together, $60\\le f(6)\\le 81$. Finally we isolate the construction-side obstruction -- an \"S+c=2^j+1\" phenomenon, every skeleton sitting exactly one box past the partition bound -- and show it is of a piece with the Leader-Milicevic-Tan question itself.", "title": "New bounds for double covers of the discrete box {0,1,2}^d", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09014" }, { "age_days": 6, "arxiv_id": "2607.08656", "authors": [ "Jaume de Dios Pont", "Lukas Liehr", "Mitchell A. Taylor" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08656", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the Cantor measure with base $b$ does not admit a Fourier frame whenever $b > 1$ is an odd integer. In particular, this answers a question of Strichartz on the existence of a Fourier frame for the middle third Cantor measure. A formalization of our main result in Lean 4 is also provided.", "title": "Cantor measures with odd base do not admit Fourier frames", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08656" }, { "age_days": 6, "arxiv_id": "2607.08986", "authors": [ "Joseph K. Miller" ], "content_date": "2026-07-09", "freshness": "fresh", "id": "arxiv:2607.08986", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game. The objective is to turn a LaTeX document into Lean. The game is won when the development compiles, contains no sorry, and a machine check shows the target theorems rest on Lean's foundational axioms alone. Reuse is a second check, by a definition we introduce: whether the development yields a self-contained layer of general mathematics the wider library could absorb. The case study is a complete, axiom-clean formalization of well-posedness for the nonlinear Vlasov equation via Dobrushin's mean-field route -- existence, uniqueness, the stability estimate and mean-field limit, and a short-window superposition principle (weak solutions are Lagrangian). The human's role was to direct, not to write proofs: to scope the definitions, steer the decompositions, and triage the library's gaps; the AI agent executed. The formalization certifies the proof of each statement as written; whether the written statement is the intended theorem stays the mathematician's judgment. The optimal-transport machinery that fell out of the build (in particular, properties of the Wasserstein-1 metric and the Kantorovich-Rubinstein duality theorem) separates into a self-contained layer that compiles against Mathlib alone: about a sixth of the development (49 of 299 declarations), behind a 22-declaration interface with no reverse dependency. The headline theorems ran in about a week, the full development in about a month. We report the quantitative claims as observations of one game, not as general laws. The game's rules name no particular system, so the methodological framing is meant to outlast the tools of any one run.", "title": "A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game", "updated": "2026-07-09", "url": "https://arxiv.org/abs/2607.08986" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:47cd72d8fb20", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: use WHNF cache in `whnfMatcher` also at sub-default transparency (#14323)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/47cd72d8fb20c357f306c5b49648ce46e34c4dc6" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:39e35f1aa474", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: optimize `String.charactersIn` (#14395)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/39e35f1aa4742c74ae64b32378b6de4602df98ed" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:0c937a2c6a43", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: show correct tactic state in whitespace between tactics without incrementality (#14396)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/0c937a2c6a43d6ba215b92e0aa3dedef1e03f544" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:d3b9c577a4fd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make String.toList semireducible (#14294)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/d3b9c577a4fd93f7bf2bf0c315b6cd7347159e64" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:6e88accef8ec", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: store traces in memory for deeper inspection (`store_traces_as`) (#14386)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/6e88accef8ecb6248063f61b169dd030cc00a612" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:3c8321cc331a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: persist `logLintExt` data at `server` level (#14387)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/3c8321cc331a1af70281375ec369c8df82827864" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:47212d83e893", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: make tactic `set_option` incremental (#14397)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/47212d83e893b5e9039c0bff55ac6dc00ff39bcc" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:a4b639c5a1e5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: grind propagators that evaluate BitVec operations on literals (#14393)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/a4b639c5a1e545677b36b09a4770b7b559df805b" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:4ee6ea0f6818", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: prepare development cycle for v4.34.0 (#14399)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/4ee6ea0f6818d57670993f84130301a0bc7ccf56" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover/lean4:4dbad693dd54", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: fail if more than one changelog label is applied to a PR (#14382)", "updated": "2026-07-15", "url": "https://github.com/leanprover/lean4/commit/4dbad693dd5451f263d6211df00c0a7801ac1aa1" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:faad2e989a8f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf: speedup kernel typechecking of `PadicInt.coe_adicCompletionIntegersEquiv_symm_apply` (#41700)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/faad2e989a8f8d7350faddbd9bdbf2f8e7939e7f" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:50b6a3e8856f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: use `to_dual` for `HeytingAlgebra` (#33543)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/50b6a3e8856f7b91078153a43f1657cbfbd63c9f" }, { "age_days": 0, "authors": [ "Antoine Chambert-Loir" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6449c8f82f42", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Transvection/Generation): non-exceptional case in Dieudonné's theorem (#33392)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/6449c8f82f4244db24ac9ea81209f63af933f651" }, { "age_days": 0, "authors": [ "mitchell-horner" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5ef639762b76", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph): define the Zarankiewicz function (#34633)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/5ef639762b76eeeaca08f7e227234ab3ca278625" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a570e2ca7c82", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Monoidal): `copy` for functor properties (#41764)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/a570e2ca7c8265dc89d47a85cf629e4048e726f0" }, { "age_days": 0, "authors": [ "Re'em" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a687aebb4fb2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Divisibility/Basic): introduce right division (RightDvd) (#40843)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/a687aebb4fb2c46405a3fe301fdceeefb633d0c7" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6c26a11c1cae", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove redundant `decreasing_by` (#41760)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/6c26a11c1caeec10c0227f19a7c0386a6f11bc69" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:86a97b0db12a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove all unneeded `classical` (#41532)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/86a97b0db12a5a2928157f561cf5bcd1e6ed3b96" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:462dde945bf1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/IntegralClosure/Algebra/Basic): generalize `isIntegral_natCast` and `isIntegral_intCast` (#41746)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/462dde945bf18c2ae494fc5e012d24260e32a897" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:11d11a11a667", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(NumberTheory/NumberField/InfinitePlace/Basic): add abbrev of `LiesOver` for `InfinitePlace` (#41747)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/11d11a11a667a8fa8ea19d9456fe059f683e308f" }, { "age_days": 0, "authors": [ "Patrick Massot" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ed810a9b2a5d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LocalFrame): remove outdated sentence in module docstring (#41070)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/ed810a9b2a5def62c3bd2920b085e08bfb330577" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c5f3b983e4a3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Matrix/Defs): automated extraction from #41160 (#41770)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/c5f3b983e4a32cd64a5d604d7f3a943e888eab8e" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e0824fdc1cf9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(FieldTheory/KrullTopology): move lemmas to earlier file (#39759)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/e0824fdc1cf95ea19518210636c74510a36acb05" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:28313485bc62", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Finsupp): rename `mapDomain_notin_range` to `mapDomain_of_notMem_range` (#41766)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/28313485bc624fcd16dcb162dd2e2c3c813aa8fe" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-07-15", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:52e9692265c7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-15", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Presentable/Basic): remove bad instance (#41660)", "updated": "2026-07-15", "url": "https://github.com/leanprover-community/mathlib4/commit/52e9692265c7a6de5a39913fa8f847d4909309eb" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:db5c0cb8215b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: move initialization functions to `BaseIO` (#14372)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/db5c0cb8215bc75d9835d19106f89e3497ee6b97" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:fe3f1d33ea95", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: slightly faster `UInt8.toAsciiLower` (#14385)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/fe3f1d33ea95cc267c91039f293c0debbb7b05fe" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:d16f7143576d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `grind ring` approximation (#14390)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/d16f7143576d0d0a9770a944ae46602c0c142716" }, { "age_days": 1, "authors": [ "Paul Reichert" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:3c080a47dbbe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: trace postprocessors (#14352)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/3c080a47dbbe4b32ab01fd7ae332ad6bd30b4054" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:501e4e81986c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: extensible frame inference for vcgen via @[frameproc] (#14195)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/501e4e81986cf04b38987d8f2647da8a0e099760" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:356a7e56ccb1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add the `liaSteps` configuration option to `grind` (#14392)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/356a7e56ccb198470b0c4fef0a9019145af0b971" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:af2bbc36a021", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `String.Internal.ugetUTF8Byte` (#14388)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/af2bbc36a021d880db40ab65fd5a0eb6dc943515" }, { "age_days": 1, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:9b9ebcb1d8c9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/9b9ebcb1d8c95bd308b540ba1ae4390e9eb1141e" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:7847ce513637", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove `Ne.elim` (#14345)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/7847ce51363794755252279e6732240bd4f27ca8" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:0fc9303abbe1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: reduce namespace pollution (#14384)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/0fc9303abbe173e190807be13a59f17b04a285b5" }, { "age_days": 1, "authors": [ "Garmelon" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover/lean4:3506c490b437", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: get lakeprof upload url from env var (#14355)", "updated": "2026-07-14", "url": "https://github.com/leanprover/lean4/commit/3506c490b437970e1cd13160b4fc08fb4f3811b7" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:aae61ae084c2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Order/JordanHolder): remove `Iso` from `JordanHolderLattice` (#41445)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/aae61ae084c21995ee248964a81e3750ad0db2db" }, { "age_days": 1, "authors": [ "Sebastien Gouezel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5134085bde65", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: weaken assumptions to construct vector measures (#41153)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/5134085bde65e2a257d3556c7038cb2bbee2f380" }, { "age_days": 1, "authors": [ "Sebastien Gouezel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c866e9d5f66f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: the product of bounded variation functions has bounded variation (#41195)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/c866e9d5f66fe471af7d6e8ba8e8d5704a577a6b" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:383070160f86", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/NumberField/Completion/Ramification): add `InfinitePlace.mult_mul_finrank` (#41600)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/383070160f86da967c9c899ca1bdf97f2938d618" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2d8c533bd0a0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Dimension/Localization): `Module.rank` is preserved by `IsFractionRing` (#41698)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/2d8c533bd0a0515caa32f18c0ab4485bd6229378" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4a73a604a632", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Dimension/Finite): add `rank_eq_zero_of_not_faithfulSMul` (#41697)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/4a73a604a632a0ccbfede27ec82c817aca9b043d" }, { "age_days": 1, "authors": [ "Yi.Yuan" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:daa89cd356fa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra): characterize triangularizable semisimple endomorphisms (#41590)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/daa89cd356faf84149d57396da106505635af41a" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:249c48c2c2b5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FieldTheory/IntermediateField/Adjoin/Defs): prove `adjoin F (adjoin K S) = adjoin F S` (#41416)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/249c48c2c2b5d7ebf8e765c30ce13b680e99cf04" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f98b1aa39a57", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Fintype/Order): generalize index type to `Sort*` (#41714)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/f98b1aa39a570b402eef93d709b461924e2d6da1" }, { "age_days": 1, "authors": [ "Thomas R. Murrills" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:85b471ce5a26", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: replace `haveI`/`letI` with `have`/`let` in tactics when the goal is a prop (#41708)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/85b471ce5a26910a597e61505014715aed7cde1e" }, { "age_days": 1, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:39568fbb654e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: replace (d)simp +instances with (d)simp whenever possible (#40650)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/39568fbb654ee838444c610979c312acc1b40caf" }, { "age_days": 1, "authors": [ "Sebastien Gouezel" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:827142c3f60c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: fix non-reducible diamond in C^* algebras (#40431)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/827142c3f60cc75c16f6acd229c2aa2d502bd19e" }, { "age_days": 1, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:783ccda4ee52", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Topology/Algebra/Module/FiniteDimension): automated extraction from #39100 (#41738)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/783ccda4ee524f13cc5636237be0a1942bc04824" }, { "age_days": 1, "authors": [ "Monica Omar" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:056733e1c314", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Dimension/Torsion/Finite): a torsion module has rank zero (#41739)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/056733e1c3149a8b9a4c85e4cb0f52db473df942" }, { "age_days": 1, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ee04c5cbaa01", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Module/Submodule/EqLocus): automated extraction from #39100 (#41726)", "updated": "2026-07-14", "url": "https://github.com/leanprover-community/mathlib4/commit/ee04c5cbaa01ea37630885a08e667025542957ce" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:2a2a479e9da2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: borrow annotation on `Syntax.structEq` (#14375)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/2a2a479e9da2f2297b820cddb85724f19fb99771" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:46cf2b9ead5d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: boostrapping issue in `grind` (#14379)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/46cf2b9ead5df46fbb91e45cf58e5764717767d5" }, { "age_days": 2, "authors": [ "Paul Reichert" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:0d2a4847435e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: clarify warning for semireducible definitions of class type (#14196)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/0d2a4847435ef95e2aa2eba0a7783ab945e44b76" }, { "age_days": 2, "authors": [ "Paul Reichert" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:3dde0217374c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: re-enable `grind_bitvec2.lean`, revert \"chore: disable grind_bitvec2 benchmark (#14377)\" (#14380)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/3dde0217374c32e3be0eb42338105dd3d821177d" }, { "age_days": 2, "authors": [ "Paul Reichert" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "github:leanprover/lean4:8bcd02e578d7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: disable grind_bitvec2 benchmark (#14377)", "updated": "2026-07-13", "url": "https://github.com/leanprover/lean4/commit/8bcd02e578d7479fa0eb52e64015b54873619da7" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:5c749092faf4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: normalization of bitvector literals in `grind` (#14371)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/5c749092faf4c9c121eaa5ac5071ac93b37fb7e8" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:1d69dd53445e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: bitvec simproc bug (#14370)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/1d69dd53445ef8e60c7ec9728b44383ebb76b5bf" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "github:leanprover/lean4:7f3f2fd48c70", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: 0 divides constraint in `grind` (#14373)", "updated": "2026-07-12", "url": "https://github.com/leanprover/lean4/commit/7f3f2fd48c70226d9dd15b0f9125c5d8262893e4" }, { "age_days": 1, "arxiv_id": "2607.12873", "authors": [ "Evan Chen", "Ken Ono", "Michal Mogielnicki" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12873", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-14", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Amdeberhan, Shareshian, and Stanley recently proved that a function $\\varphi$ arising in the theory of partition Eisenstein series counts the alternating permutations of $\\{1,\\dots,2n\\}$ with a given `record' partition, and they asked whether there is a similar theory for record compositions, suggesting a role for noncommutative symmetric functions. Here we solve their open problem by showing that the number of alternating permutations of $\\{1,\\dots,2n\\}$ with record composition $(α_1,\\dots,α_\\ell)$ is \\[ \\prod_{j=1}^{\\ell}\\binom{2s_j-1}{2α_j-1}E_{2α_j-1}, \\] where $s_j=α_1+\\dots+α_j$, $E_k$ is an Euler number, and the record composition of $w=a_1a_2\\dots a_{2n}$ (so $a_1>a_2\\dotsb$) lists the factor lengths obtained by cutting $a_1a_3\\dots a_{2n-1}$ before each left-to-right maximum other than the first. These numbers are the coefficients of a natural lift of the degree-$n$ sprout symmetric function with seed $\\sec(\\sqrt{t}\\,)$ to noncommutative symmetric functions, expanded in products of noncommutative power sums of the first kind. An analogous refinement holds for every sprout sequence whose seed is given by the exponential formula. AxiomProver autonomously produced and verified the results in this paper in Lean.", "title": "Record compositions of alternating permutations and noncommutative symmetric functions", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12873" }, { "age_days": 1, "arxiv_id": "2607.12226", "authors": [ "Jam Kabeer Ali Khan", "Petros Markopoulos", "Nico Lehmann", "Ranjit Jhala" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12226", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-14", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "SMT-based program verifiers are hamstrung by two problems: expressiveness, because predictable verification restricts to the boundaries of SMT decidability, and trust, because the solver is a large, unverified artifact whose soundness bugs may quietly compromise every tool built on it. We present FLEX, a foundational Constrained Horn Clause (CHC) solver implemented in LEAN, that reduces the trusted base to the kernel alone, and allows using LEAN's entire proof ecosystem to verify low-level systems code, via three contributions. First, FLEX encodes CHCs as plain LEAN propositions where the Horn variables are existentially bound predicates, and shows how to implement CHC solvers as tactics (meta-programs) that compute kernel checkable proofs of the CHC propositions. Second, we show how to implement two verified CHC generators in LEAN: a Floyd-Hoare style generator for an imperative language, and a refinement-type-based generator for a functional calculus, which can be composed with the solving tactics to yield the first end-to-end foundational CHC-based verifiers. Finally, we show how FLEX allows us to leapfrog the expressiveness limitations of SMT by unleashing LEAN's entire ecosystem of proof machinery to prove arbitrary functional correctness properties of various low-level Rust libraries using the FLUX refinement type checker, and demonstrate the viability of FLEX as a trustworthy CHC backend, by showing it automatically discharges 95.7% of the CHCs from FLUX's benchmark suite.", "title": "Foundational Constraint Solving for Expressive Refinement Typing", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12226" }, { "age_days": 2, "arxiv_id": "2607.11648", "authors": [ "Ralf Stephan" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11648", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Write $(3/2)^n = m_n + \\eps_n$ with $m_n$ the nearest integer and $\\eps_n\\in[-\\tfrac12,\\tfrac12)$, and let $T=(t_n)$, $t_n=2m_{n+1}-3m_n$, be the resulting \\emph{steering word}: the step-by-step record of the map $x\\mapsto\\tfrac32 x$ on the orbit of $1$, coded by nearest-integer rounding. Using results by Corvaja--Zannier and Nair--Kumar--Rout we prove that the subword complexity $\\pT(k)$ of $T$ is superlinear, $\\pT(k)/k\\to\\infty$. The argument is completely formalized in Lean-4, depending only on the Subspace Theorem.", "title": "Superlinear complexity of the $(3/2)^n$ steering word", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.11648" }, { "age_days": 2, "arxiv_id": "2607.12221", "authors": [ "Grace Barkhuff", "Ian Pruitt", "William Gregory Johnson", "Rodrigo Borela", "Ben Rydal Shapiro", "Anu G. Bourgeois" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.12221", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Industry is leaning into generative artificial intelligence (GenAI), and higher education is under pressure to prepare graduates for a GenAI-augmented workforce. Yet, there is still no clear structure for defining AI readiness across disciplines, programs, courses, and assignments. Current approaches often rely on broad institutional policies or individual course-level decisions, which can also create mixed messages for students, fragmented expectations across programs, and limited visibility for university leaders. In this paper, we argue that higher education needs a more coherent way to connect institutional priorities to curriculum-level action. We propose Program-Level AI Learning Outcomes (PLAI-LOs) as a framework for defining what students graduating from a program should know and be able to do with, without, and about GenAI in a given discipline. The PLAI-LOs framework complements existing program-level learning outcomes and supports alignment across institutional priorities, program-level AI learning outcomes, course-level learning outcomes, and assignment-level objectives. We illustrate the framework with examples from computing and music and show how PLAI-LOs can be implemented through artifact-level GenAI policies, helping programs decide where GenAI should be taught and used, and when students should be expected to work without GenAI. We offer PLAI-LOs as a concrete, measurable, and adaptable path for moving higher education from scattered GenAI rules toward a strategy with clear, learning-centered alignment.", "title": "From Chaos to Clarity: A Framework for Program-Level AI Learning Outcomes", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.12221" }, { "age_days": 2, "arxiv_id": "2607.11376", "authors": [ "Jeffrey Kuan" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11376", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The type D ASEP is an asymmetric two--species interacting particle system on $\\Z$, in which two separately conserved species hop, bind into a composite ``bound pair'', and split. The model, along with its reversible measures and orthogonal polynomial duality, was constructed using the representation theory of $U_q(\\so_{2n})$. The reversible measures and orthogonal polynomial duality are each a product of two copies of the single-species ASEP reversible measures and orthogonal polynomial duality. In this paper, we study the long-time asymptotics of the type D ASEP. In the fixed--$q$ regime, using an exact current--decoupling identity, we prove that the asymptotic hydrodynamic limit and Tracy--Widom fluctuations decouple, as predicted from the duality. In the weak--asymmetry (Edwards--Wilkinson) regime, when $q=1-c/N^2$, we prove that the two density fluctuation fields \\underline{decouple}: each converges to a linear stochastic heat equation, with no cross--coupling in either the drift or the noise, the limiting noises having vanishing cross--correlation. More surprisingly, we then prove that the two limiting normal random variables are \\underline{correlated} with a seemingly new correlation function. The correlation is exactly equal to $(1-e^{-4c})/(4c)$, with the positive parts of the normal random variables having correlations expressed by the Bessel--Struve function. This paper, with the exception of the abstract and introduction, was written entirely by Claude Opus 4.8 and Fable 5. The proofs were then formalized in Lean, using Aristotle by Harmonic AI. The human author of this paper verified the proofs manually.", "title": "Correlated and uncorrelated long--time asymptotics of type D ASEP", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11376" }, { "age_days": 2, "arxiv_id": "2607.11471", "authors": [ "Dmitry Nikolaev" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11471", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A lot of research attention has been devoted to checking whether large language models (LLMs) are politically biased. This work has largely focused on high-level ideological dimensions, such as left--right or progressive--conservative, and it has been shown that while LLMs are predominantly left and progressive leaning, largely mimicking the biases in the training data, they can be to some extent steered to change their preferences in post-training. In this short note, we check if LLMs have robust stances with regard to major substantive societal issues, on which members of the same ideological camp are often in disagreement, summarised in a novel dataset \\textsc{HardChoices}. We show that, faced with this line of questioning, LLMs, both large and small, surprisingly rarely declare neutrality, are often incoherent, and demonstrate a remarkable degree of agreement on issues where they do take stances.", "title": "Are LLMs ready for HardChoices?", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11471" }, { "age_days": 3, "arxiv_id": "2607.10621", "authors": [ "Zheng Pei", "Mingwei Liu", "Zhenxi Chen", "Zihao Wang", "Yanlin Wang" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "arxiv:2607.10621", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-12", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Front-end development accumulates change after change at the repository level, weaving complex cross-file dependencies that current LLM coding agents tuned for single-shot tasks cannot reliably track across multiple iterations, leading to functional regressions and code that resists maintenance. We argue the missing piece is design knowledge: architectural principles, module responsibilities, and structural constraints that developers lean on to keep code readable, maintainable, and evolvable as a system scales. To operationalize this, we propose WebDesignIter, a framework built around a persistent knowledge graph (WebAppArchKG) that fuses repository structure with design knowledge and keeps both in sync across development cycles. WebDesignIter works in two stages: design-informed planning pulls historical context and architectural overviews from WebAppArchKG to produce an implementation plan with corresponding test scripts, and design-aware generation executes that plan through targeted diff-based patches, validated by sandbox execution and automatic syntax repair. On Web-Bench, WebDesignIter delivers an average Pass@2 gain of 9.55 percentage points across nine foundation models over existing baselines. More importantly, WebDesignIter outperforms every general-purpose coding agent Claude Code, OpenHands, SWE-Agent, Codex CLI on every model configuration, posting the highest Pass@1 and Pass@2 while consuming 2530 fewer input tokens. Ablation singles out design knowledge as the most impactful component: stripping it drops Pass@1 by 11.40 percentage points, a degradation far larger than removing code-graph retrieval, patch-based generation, or sandbox verification, confirming that design knowledge provides a fundamentally more efficient and reliable path to repository-level code generation.", "title": "WebDesignIter: Co-Evolving Design Knowledge for Repository-Level Front-End Code Generation", "updated": "2026-07-12", "url": "https://arxiv.org/abs/2607.10621" }, { "age_days": 4, "arxiv_id": "2607.10314", "authors": [ "Martin Berger", "Amir Naseredini" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "arxiv:2607.10314", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Rowhammer is a hardware vulnerability in dynamic random-access memory (DRAM) in which repeated accesses to aggressor rows can induce bit-flips in victim rows. This phenomenon violates a core assumption of conventional programming language semantics: reading or writing one memory location does not modify others. Despite the security importance of this phenomenon, there is no formal framework connecting Rowhammer faults with program behaviour. We present a probabilistic small-step operational semantics for an idealised imperative language subject to Rowhammer-style faults. The semantics abstracts from DRAM internals and semiconductor physics. A general probabilistic fault model parameterises the semantics, representing Rowhammer-style faults by assigning probabilities to bit-flips during read or write operations. The resulting distributions are propagated through programs using the standard monadic structure of probabilistic computation. As a case study, we formalise a well-known defence that places program variables sufficiently far apart in physical memory that an access to one variable cannot disturb another. We prove a distribution-independent semantic collapse theorem: for every finite execution, including prefixes of terminating and non-terminating executions, the protected projection of the probabilistic Rowhammer semantics is the Dirac distribution of the corresponding Rowhammer-free execution. We develop an observation-parametric account of secure information flow. Non-interference is expressed as a hyperproperty comparing the distributions of low observations from low-equivalent initial memories. Consequently, physical separation preserves non-interference for every admissible fault model, while every Rowhammer non-interference violation reflects a violation already present in the Rowhammer-free semantics. The development is fully mechanised in Lean using mathlib.", "title": "Mechanised operational semantics of Rowhammer", "updated": "2026-07-11", "url": "https://arxiv.org/abs/2607.10314" }, { "age_days": 4, "arxiv_id": "2607.10170", "authors": [ "Saharsh", "Vedhas Talnikar", "Pushpak Jagtap" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "arxiv:2607.10170", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Communication graph rigidity is a fundamental requirement in many multi robot formation control approaches. However, ensuring and maintaining a rigid communication topology becomes challenging in practice due to limited sensing ranges and dynamic operating conditions. This paper provides a method for achieving an inter robot collision free, rigid time varying communication graph, where communication links are established or broken according to limited sensing ranges, without assuming an initial rigid graph. In addition, the proposed approach guarantees the realization of a rigid graph for heterogeneous nonlinear multi robot systems. A computationally lean, distributed quadratic optimization-based controller is developed for a leader follower architecture, acquiring rigidity based on hierarchical second-order consensus among robots. Follower agents do not require global absolute positions of any agent, including their own. The proposed method is validated through both simulations and hardware experiments in a motion-capture environment, demonstrating reliable performance under the limited sensing capabilities of individual robots.", "title": "From Non-Rigid to Rigid: Safe Acquisition of Rigid Communication Graphs under Limited Sensing", "updated": "2026-07-11", "url": "https://arxiv.org/abs/2607.10170" }, { "age_days": 4, "arxiv_id": "2607.10216", "authors": [ "Garett Cunningham", "Daniel Zach", "Stefan Friedl" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "arxiv:2607.10216", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The theory of simplicial complexes is a cornerstone of topology, offering a sophisticated tool for computing invariants. We present a formalization of abstract simplicial complexes and stellar subdivisions in the Lean proof assistant. We adopt a purely combinatorial framework in order to provide a cohesive foundation for studying the theory of stellar subdivisions as seen in many contexts of combinatorial topology. In particular, we provide formalizations of morphisms between abstract simplicial complexes; several crucial constructions and operations on complexes, such as links and joins; and perform a comprehensive study of how stellar subdivisions interact with these operations. We state and prove a number of identities commonly used in the study of triangulated manifolds, such as deriving equivalences between links in an abstract simplicial complex $K$ and in a stellar subdivision $σ_s K$, including results with no references in the standard literature. To our knowledge, this is the first formalization of stellar subdivisions in any proof assistant.", "title": "Formalizing Abstract Simplicial Complexes & Stellar Subdivisions in Lean", "updated": "2026-07-11", "url": "https://arxiv.org/abs/2607.10216" }, { "age_days": 4, "arxiv_id": "2607.10444", "authors": [ "Michal Widera" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "arxiv:2607.10444", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A data management system can be separated in typical data processing systems. Unfortunately, relational data management systems are not efficient enough to handle the on-line signal processing task in a monitoring system. The main current in research into database management system model for the needs of monitoring systems is connected with a data stream model. However, these systems are non-deterministic. This paper presents the developed methods of data stream processing for signal processing tasks in medical database management systems, as well as the developed theorems of data sequences (stream) algebra with formal proofs. A direct link between some introduced operators and Beatty and Fraenkel theorems has been proved", "title": "Deterministic method of data sequence processing", "updated": "2026-07-11", "url": "https://arxiv.org/abs/2607.10444" }, { "age_days": 4, "arxiv_id": "2607.10084", "authors": [ "Maseeh Ghodsi" ], "content_date": "2026-07-11", "freshness": "fresh", "id": "arxiv:2607.10084", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Chan and Pak introduced the relative linear extension ratio $ρ(P,x)=e(P)/e(P-x)$, where $e(P)$ is the number of linear extensions of a finite poset $P$, and let $ν(c,d)$ be the least number of elements of a poset that realizes $ρ(P,x)=d/c$. They proved that $ν(c,d)\\le d/c+O(\\log d\\log\\log d)$ for $d\\ge 3c$, and asked whether the hypothesis $d\\ge 3c$ can be relaxed to $d\\ge(1+\\varepsilon)c$ or removed. We prove the fixed-gap form of this question: for every fixed $\\varepsilon>0$, $ν(c,d)\\le \\frac{d}{c}+O_{\\varepsilon}(\\log d\\log\\log d)$ whenever $d\\ge(1+\\varepsilon)c$, and the implied constant is absolute once $d\\ge 2c$. The new ingredient is a one-element overlap construction: if $x$ is minimal in $P$ and $y$ is minimal in $Q$, then there is a poset $R$ with $|R|=|P|+|Q|-1$ and an element $z$ such that $ρ(R,z)=ρ(P,x)+ρ(Q,y)-1$. Together with the continued-fraction construction of Chan and Pak and Rukavishnikova's tail bound for sums of partial quotients, this removes the factor $3$ in their range. We also show that the fixed-gap hypothesis is essentially optimal for this construction. In the range $1 < d/c < 2$, with $h=d-c$, the size bound the construction can certify is at least $\\lfloor c/h\\rfloor$, so the method reaches the stated error term only when $h$ is at least of order $c/(\\log c\\log\\log c)$. The remaining obstruction to removing the hypothesis is a short-interval problem for sums of partial quotients, which we describe. The deductive part of the argument has been checked with the Lean proof assistant.", "title": "An Overlap Construction for Relative Linear Extension Ratios", "updated": "2026-07-11", "url": "https://arxiv.org/abs/2607.10084" }, { "age_days": 5, "arxiv_id": "2607.09990", "authors": [ "Ashwin Bhattathiripad", "Vipin P Veetil" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09990", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Economic power in international trade is the capacity of one country to impose loss on another by withdrawing from a trading relationship. This paper measures it. A model of the short run represents each trade restriction as a pattern of barred entries in the world matrix of input shares and maps it into a vector of losses by country and sector. The asymmetry between the two countries' losses under the same severance is the measure of power: a gap in substitution, since a buyer's dependence turns on how easily it finds another source and a seller's on how easily it finds another market. When a relationship is barred, buyers lean on alternative suppliers and barred suppliers on alternative buyers already present in the benchmark network, under the ceiling that no producer exceeds its pre-shock scale. The reallocation is a RAS balancing of the disrupted matrix that lets \\emph{both sides} adjust together. Across 9,480 counterfactual severances on the 2022 world input--output network, mutual trade dependence is anything but mutual. The average bilateral asymmetry is 0.6 on a scale that runs from balance at zero to complete lopsidedness at one. The United States holds the favorable side in all its relationships, China in all but one. The same tilt runs far down the hierarchy: a severance with Russia would cost Belarus more than a tenth of its economic activity, but Russia only half of one percent. The asymmetry bears only a weak relation to bilateral trade imbalance but closely tracks whether a country sits at the core or the periphery. Power is a property of network position, not deficits.", "title": "Political Power in International Trade", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09990" }, { "age_days": 5, "arxiv_id": "2607.09582", "authors": [ "Okezzi Ukorigho", "Opeoluwa Owoyele" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09582", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.", "title": "Entropy-Constrained Machine Learning with Residual Data Augmentation for Modeling Chemical Kinetics", "updated": "2026-07-10", "url": "https://arxiv.org/abs/2607.09582" }, { "age_days": 5, "arxiv_id": "2607.09564", "authors": [ "Andrew Slattery", "Jonathan Sterling" ], "content_date": "2026-07-10", "freshness": "fresh", "id": "arxiv:2607.09564", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Surface syntax in proof assistants like Rocq, Lean, Agda, and Idris is highly implicit, lacking many details that are needed for user-written code to denote precisely defined mathematical objects. Elaboration is an algorithm that accounts for these details by translating surface syntax to an explicit enough core syntax. The reliability and predictability of elaboration relies on several critical properties of the core type system, including decidability of judgemental equality and the injectivity of type constructors; these dependencies are witnessed in a concrete system by explicit calls to conversion checking and weak-head reduction subroutines. We introduce a dependently typed monadic domain specific language for the executable specification of correct-by-construction elaboration algorithms that is abstracted from any particular representation of normal forms or algorithm for conversion checking. In particular, we represent a bidirectionally typed surface language for Martin-Löf type theory by shallow embedding in this DSL so that the translation of surface terms into core terms amounts to elementary equational calculation. This translation is correct by construction in the sense that it cannot produce ill-typed terms, and is automatically stable under judgemental equality of core terms and even under substitution; from the latter property, we obtain a new denotational interpretation of the suspension of elaboration problems. Finally, a concrete elaboration algorithm is extracted by algebraic means from a presheaf model of the DSL built out of the bi-initial natural model of Martin-Löf type theory.", "title": "Bidirectional Elaborators à la Carte", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.09564" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }