{ "counts": { "adjacent": 11, "core": 4, "errors": 0, "negative": 75, "total": 90 }, "date": "2026-10-08", "errors": [], "fresh_content_days": 21, "generated_at": "2026-10-08T20:46:27Z", "items": [ { "age_days": 2, "arxiv_id": "2610.08246", "authors": [ "André G. Pereira", "Augusto B. Corrêa", "Felipe Meneguzzi", "Jendrik Seipp" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08246", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-10-06", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Frontier large language models (LLMs) can generate heuristic functions that guide search to achieve state-of-the-art performance in satisficing planning, where any plan is acceptable. However, these heuristics are not guaranteed to be admissible and can lead to suboptimal plans. We introduce LeanPlan, the first planning system that finds optimal plans with LLM-generated heuristics whose admissibility is machine-checked. Given a domain description and training tasks, an agentic loop uses planner feedback to iteratively improve a reusable domain-specific heuristic, its admissibility proof and the required domain assumptions. LeanPlan implements the heuristic, its proof and an efficient planner with machine-checked grounding and search in Lean 4. We evaluate LeanPlan on ten domains from the International Planning Competition and three new domains, using test tasks with up to 57 times as many objects as the training tasks. With GPT-5.6 Sol in the agentic loop, we successfully generate heuristics and admissibility proofs for all these domains. With the resulting heuristics, LeanPlan usually expands fewer states than the state-of-the-art Scorpion planner and solves more tasks overall.", "title": "LeanPlan: Optimal Planning with LLM-Generated Heuristics and Admissibility Proofs", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08246" }, { "age_days": 2, "arxiv_id": "2610.08329", "authors": [ "Zhiyuan Zhang", "Axel Delaval", "Leheng Chen", "Jinxuan Chen", "Jie Xu", "Yuxuan Liao", "Jiedong Jiang", "Chunlei Liu", "Bin Dong" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08329", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents", "seed_author:Bin Dong", "seed_author:Jiedong Jiang" ], "published": "2026-10-06", "score": 7.3, "source": "arxiv-ai4math-core", "summary": "We present an AI-assisted Lean 4 formalization of the Poincaré conjecture. The project began with limited reusable formal infrastructure for the geometric analysis behind the proof. To organize this work, we combined a proof blueprint prepared by mathematicians with explicit milestone statements. These milestones enabled parallel agent work and gave mathematicians clear points to locate blockers and provide effective mathematical guidance. Our analysis identifies the human interventions and organizational choices behind this workflow. The project provides a starting point toward reusable infrastructure for future formalization projects; such infrastructure, once developed, could eventually reduce the cost of verifying mathematical results in geometric analysis.", "title": "An AI-Assisted Formalization of the Poincaré Conjecture", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08329" }, { "age_days": 2, "arxiv_id": "2610.07943", "authors": [ "Wei Li", "Kevin Vallier", "Tong Zhang" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.07943", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-06", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "For a finite forest $F$ let $i_k(F)$ be the number of independent sets of $F$ with $k$ vertices. Zhang and Li proved that the sequence $i_0(F),i_1(F),\\dots,i_{α(F)}(F)$ is unimodal for every finite forest $F$, which answers Erdős Problem 993. We give a second proof. It starts from their decomposition relative to a fixed independent set and from the bounds of Zhang and Li and of Fang, Lu, Nevo, Yao and Zheng that confine a valley of the sequence to an explicit window of ranks. For a forest with at least $25$ vertices, one moment argument excludes a valley at every rank of the window: at the activity where the hard-core mean equals the rank, the size of a random independent set is a mixture of binomial laws over an independent set of maximum weight, a valley is a moment inequality for this mixture, and it is excluded by duality given three bounds that hold for every forest, on the variance of the number of free vertices and on its Laplace transforms, and on the variance ratio. The variance bound is proved by hand up to finitely many interval checks and the other two bounds are verified by computer on finite interval-arithmetic coverings; on the resulting parameter domain a valley is excluded by exact tests on finitely many rational boxes while the mean number of free vertices is below an explicit starting mean between $19$ and $50$, and above it by one inequality, with explicit constants, for the fibers of a weighted valley kernel, proved by hand up to a finite list of explicit checks and averaged over the mixture. Forests with at most $24$ vertices are treated by exact counting, by hand except for exact rational evaluations of two explicit formulas at $43$ parameter triples. No forest is enumerated. A formal proof of the theorem in Lean 4 accompanies the paper.", "title": "Unimodality of Forest Independence Polynomials", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.07943" }, { "age_days": 2, "arxiv_id": "2610.08900", "authors": [ "Sihao Liu", "Ligeng Zhu", "Zijian Zhang", "Dongyun Zou", "Zhengyang Zhang", "Changye Li", "Song Bian", "Song Han", "Tony Nowatzki" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08900", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-10-06", "score": 6.3, "source": "arxiv-ai4math-core", "summary": "Agentic coding makes code generation cheap, but reliable completion remains difficult: the agent that writes the code is a weak judge of whether it is done. We present Humanize, a multi-agent orchestration workflow for agentic coding built around judgement engineering: explicit, mechanically enforced decisions at the boundaries between planning, implementation, review, and learning. A human approves a plan contract, a builder agent implements it in rounds, and a reviewer agent from another vendor decides completion; deterministic hooks, not a model, route work between these roles and enforce 72 mechanical gates. Viewed as a Markov chain over repository states, alternating builder and reviewer samples jointly from two models, so a defect survives only if both miss it. We study Humanize through its deployment, 118 public postmortems of real loops, and its applications. Over 68 versions in 108 days, it gathered 1,468 GitHub stars. Applications include a 567-file gem5 build-system migration under upstream review; Kernel Design Agents, which extend the loop with a kernel knowledge base and profiling feedback and placed in the top three of all three Full-Agent tracks of the MLSys 2026 FlashInfer contest; and, through Humanize Olympiad Agents (HOA), full scores in IOI 2026, IMO 2026, IPhO 2026, and IBO 2024, 418.5/437 in IChO 2026 (gold-medal). Humanize also achieves 672/672 on PutnamBench and ranks first (251/303) on Lean-Eval's leaderboard even competiting with professional mathematicians. The postmortems show that independent review catches unsupported builder claims, but stopping remains a key weakness. In reports that separate rounds by phase, two thirds of rounds occurred after implementation was accepted. This evidence is observational, not a controlled comparison of workflows.", "title": "Humanize: Judgement Engineering for Agentic Coding", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08900" }, { "age_days": 2, "arxiv_id": "2610.08980", "authors": [ "Wenqi Zhu", "Ping Nie" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08980", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-10-06", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Toeplitz matrices are among the simplest structured models of translation invariance, arising naturally in convolution, stationary covariance models, and discretizations of translation-invariant operators. For a pair of real matrices, the Böttcher--Wenzel form (BW form) is a nonnegative quartic measuring the gap in the corresponding commutator inequality. László conjectured that, when both matrices are Toeplitz, this quartic is a sum of squares for every matrix order. We show that the conjecture is false. More precisely, we identify an explicit family of corner-supported Toeplitz pairs, retaining only the outermost diagonals on the two sides, for which the associated BW form is not a sum of squares at all sufficiently large orders. The proof reduces the complete family of Gram representations to a finite complex test: its Gram-invariant part develops a strictly negative limiting direction, while the remaining Gram-dependent contribution vanishes. We also give an explicit sufficient threshold for the matrix order. The negative result is complemented by two positive regimes. If either Toeplitz factor is symmetric or skew-symmetric, then the corresponding BW form is SoS for every order, with the other factor allowed to be an arbitrary real Toeplitz matrix. For unrestricted Toeplitz pairs, we further prove SoS representability for every $2\\le N\\le50$, with formal Lean 4 verification through order 20.", "title": "Sum of Squares and Non Sum of Squares Regimes for the Toeplitz Bottcher Wenzel Form", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08980" }, { "age_days": 1, "arxiv_id": "2610.09681", "authors": [ "Shuangjie Yao", "Nikolaus Holzer", "Mark Paul Santolucito", "Baishakhi Ray", "Suman Jana", "Dongdong She" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.09681", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Program verification establishes software correctness through machine-checkable proofs constructed in theorem provers. It's a guarantee especially valuable for code generated by large language models (LLMs), which is fluent but carries no assurance of correctness. Almost all existing provers, however, pursue pass rates alone at whatever sampling or search budget it takes, and overlook the success-vs-cost frontier; yet real software often carries hundreds of interdependent proof obligations, so what matters at scale is not whether one theorem can be proved, but how many can be proved economically. We introduce CoCo-Prover, which formalizes cost-efficient program proving as metalevel decision-making under cost, grounded on two-level proof graphs: an AND/OR proof hypergraph within each declaration is joined to a lemma-dependency graph across declarations; and at each step, it answers two questions: which open goals to select, and which actions to purchase on these goals. Selection stays symbolic as a topological pass over the proof graphs. Action choice is agent orchestration via metalevel decision-making: an agentic router treats every bounded specialist invocation as a separately priced, best-effort computation, matching heterogeneous specialist agents together with configurations, under evolved routing rules as evidence accumulates. On five program verification benchmarks in Lean 4 including function-level CLEVER, VERINA, and AlgoVeri, and repository-level NTP4VC and Vero, we show that CoCo-Prover achieves a better success-vs-cost frontier than baselines including frontier coding agents and state-of-the-art LLM-based provers: it achieves the best solve rate on every benchmark and up to 100% on two benchmarks. It also reduces cost by up to 30.9% compared to the strongest baseline with the strongest LLM in our evaluation.", "title": "Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.09681" }, { "age_days": 2, "arxiv_id": "2610.09005", "authors": [ "Brett Saiki", "Bill Zorn", "Cynthia Richey", "Zachary Tatlock" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.09005", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Number libraries, which implement number formats and their arithmetic in software, are used to simulate hardware, making hardware behavior reproducible and thus verifiable and easier to design. However, modern machine learning accelerators are difficult to simulate, as they increasingly use specialized number formats that existing number libraries do not support. It is costly to extend these libraries using traditional methods: each combination of operation, format, and rounding mode typically requires a bespoke implementation. An easier way is to double round---compute at higher precision, then re-round---so that one high-precision kernel serves many formats, but double rounding is only known to be correct in select cases. We give a precise, efficiently checkable characterization of when double rounding is correct across many formats and rounding modes. Our result rests on a novel abstract number format that unifies fixed- and floating-point representations, reducing the correctness of double rounding to format containment: whether every value of one format is representable in another. We mechanized these results in Lean 4. In addition, we introduce a format inference algorithm that, given a sequence of operations, bounds each expression by a number format guaranteed to contain its result. We apply these insights in two ways. First, we present MPFX, a correctly-rounded, multi-precision number library that exploits correct double rounding to efficiently simulate many number formats. MPFX's correctly-rounded operations are up to 11x (mean: 6.05x) faster than MPFR's, and competitive with SoftFloat's---between 0.46x and 1.63x as fast (mean: 0.94x)---at the same precision. Second, in a case study, we implement a software simulation of a hardware specification using both SoftFloat and MPFX's primitives; the MPFX version is up to 13.5x faster.", "title": "When Double Rounding is Correct", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.09005" }, { "age_days": 2, "arxiv_id": "2610.09159", "authors": [ "Param Biyani", "Krishnamurthy Dvijotham" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.09159", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "As autonomous coding agents get increasingly deployed, the risk that accidental or adversarially injected misspecifications in tasks lead to dangerous agent behavior is critical to address. Prior work has shown that agents given such tasks rarely flag the conflict and instead cheat, editing tests or hard-coding expected outputs, and the actions taken to cheat can cause real damage, such as deleting a security defense to make a corrupted test pass. It remains unclear whether such conflicts can be established with independently verifiable evidence before the agent acts. We present SpecGuard, which detects and formally certifies these conflicts between task intent and tests. Given only the task description and codebase, SpecGuard autoformalizes the intended behaviour into a Lean 4 specification. The tests are formalized independently, and the Lean kernel checks whether any implementation could satisfy both formalizations, producing a machine-checked certificate when none can. On conflicted SWE-bench tasks, SpecGuard detects up to 72.8% of conflicts and formally certifies up to 51.1%, with a nearly five-fold lower conflict miss rate than model-based judgment. SpecGuard provides a pre-execution safety check that identifies reward-hacking opportunities through formal certification of task-level conflicts, before any agent behavior is observed. Our code is available at https://github.com/prmbiy/specguard.", "title": "SpecGuard: Proving a Task Is Broken Before the Agent Cheats", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.09159" }, { "age_days": 2, "arxiv_id": "2610.08965", "authors": [ "Kristian Muri Knausgård" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08965", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Let N(T) count the nontrivial zeros of the Riemann zeta function up to height T with multiplicity, N_d(T) the distinct ones, and N_0^s(T) those that are simple and on the critical line. We prove liminf N_d(T)/N(T) >= 1645064/1960733 = 0.83900...; earlier work proves 0.83699..., and a report we have not verified claims 0.83805.... Hence more than 67.80% are simple. Also liminf N_0^s(T)/N(T) >= 0.67353...; earlier work proves 0.67250..., and reports we have not verified claim 0.673492. Two estimates of Lamzouri are improved: at least 88.93% of the zeros are simple or on the critical line, and the proportions of simple zeros and of zeros on the line average at least 83.67%. By the unconditional form of Montgomery's pair-correlation theorem the energy, a sum of a test function over pairs of zeros, is known asymptotically. A zero of multiplicity d contributes d^2 to it and nearby zeros contribute too, so a lower bound for such pairs leaves less energy for multiple zeros. The proof has three steps. First, for zeros at least a fixed fraction of the mean spacing apart, a large sieve inequality lets their pairs be used in full, with multiplicities. Second, their contribution is bounded below by a computer-assisted inequality for seven or eight consecutive zeros which distinguishes simple and double zeros. Its correction terms telescope, as increments of a storage function. Third, the test function is chosen to make this contribution large, at the cost of more energy. We also prove upper limits for what such inequalities can give with the two main test functions. The lower bounds and these limits are proved in Lean 4, analytic inputs included. The proofs use three axioms beyond those of Mathlib, one per inequality. Each records that a search program returned true; Lean's kernel does not check the run itself. This work is an experiment in AI-assisted mathematical research.", "title": "More than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical line", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08965" }, { "age_days": 1, "arxiv_id": "2610.10049", "authors": [ "Obada Kraishan" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10049", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-10-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Reasoning models allocate extra computation at inference time and present their answers as the product of deliberate thought. If this deliberation works the way dual-process accounts of human cognition suggest, longer thinking should weaken the classic decision biases that fast, intuitive judgment produces. Using 30 vignettes covering six biases (anchoring, framing, loss aversion, escalation of commitment, availability, confirmation) from an established benchmark, we run a dose-response study across four model families, pairing each reasoning model with a matched non-reasoning sibling and requesting thinking ceilings of 0, 1,024, 4,096, and 8,192 tokens, for 12,350 API calls. Because a requested ceiling is not the same as realized deliberation, we use the reasoning tokens each call consumed as the dose. First, reasoning models are not less biased than their siblings; the point estimate leans the other way in every family, but the item-level pooled contrast is not reliable (Delta = +0.031, t(29) = 1.45, p = .157). Second, bias magnitude does not reliably fall as realized deliberation grows: no slope is significantly negative, and where anything moves it is the signed score drifting further from the human direction. Third, anchoring is the only bias in the human direction (d = 1.89). Four of the other five lean the opposite way in all seven models; with five items per bias, that reversal is reliable for framing and directional for escalation of commitment, confirmation, and loss aversion, while availability is absent. A one-line instruction to restate the anchor before answering lowered anchoring on all five anchoring items, which no amount of additional thinking did, although the effect does not reach significance (p = .057). The results argue against treating test-time reasoning as a rationality guarantee and for auditing deployed models bias by bias.", "title": "The Long Road to the Same Answer: Cognitive Bias Under Escalating Reasoning Budgets in Large Language Models", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10049" }, { "age_days": 1, "arxiv_id": "2610.09367", "authors": [ "Xindan Zhang", "Baochun Li", "Zongpeng Li" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.09367", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-10-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Network coding lets the nodes of a network combine messages rather than merely forward them. In undirected networks, where the two directions of an edge share its capacity, Li and Li conjectured in 2004 that coding offers no advantage over fractional routing; the conjecture has been confirmed for many special classes but never settled in general. In this paper, we disprove it by constructing a finite connected simple undirected network with unit shared edge capacities, maximum degree three, and distinct leaf terminals, on which a binary linear block code achieves a common rate strictly above the maximum fractional routing rate. The construction turns a short completion-time code into a reversible circuit whose registers all carry independent messages, and a temporal metric on its wires yields the strict routing bound. The underlying integer-coefficient construction works over every finite field and every nontrivial finite abelian group; for deterministic fixed-schedule codes the common-rate supremum is one and the closure of the rate region is the unit cube. Amplifying the gap with a degree-preserving tensor construction and an even subdivision gives, for every $0<β<1$, an unbounded family of connected, simple, subcubic, bipartite networks with girth at least $n^β$ on which coding approaches rate one while routing is bounded by $K_β/(\\log n)^c$, with one positive exponent $c$ independent of $β$. The finite counterexample and the family theorem are formalized in Lean.", "title": "Network Coding Can Beat Routing in Undirected Multiple-Unicast Networks", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.09367" }, { "age_days": 1, "arxiv_id": "2610.10243", "authors": [ "David Kurniadi Angdinata", "Kenny Lau", "Ken Ono", "Ashvin Swaminathan", "Sameera Vemulapalli" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10243", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-10-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "For elliptic curves $E/\\mathbb{Q}$ in short Weierstrass form \\[ E=E(a_4,a_6): y^2=x^3+a_4x+a_6, \\] we derive a multivariable Euler product generating function which encodes the Tamagawa product $Tam(E)=\\prod_p c_p(E)$. Using this generating function, we compute limiting distributions, exact covariances, and moment and tail bounds for four important statistics on the Tamagawa number; for example we show that more than half of all curves in this height ordering have trivial Tamagawa product, about $42.2\\%$ have exactly one prime with nontrivial local Tamagawa number, and only about $6.8\\%$ have exactly two such primes. The product is obtained by specializing an Euler product indexed by local reduction data that we derive from Tate's algorithm. The results in this paper were autoformalized in Lean by AxiomProver.", "title": "Local Factors in the BSD Conjecture: A Unified Statistical View", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10243" }, { "age_days": 1, "arxiv_id": "2610.09401", "authors": [ "Xiaopeng Yuan", "Suijin Wang", "Yanli Wang", "Haibo Jin", "Peng Kuang", "Jerry Wang", "Lijun Yu", "Haohan Wang" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.09401", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-10-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "LLM-based formal provers can retrieve relevant lemmas and prior proofs, but relevance alone does not say whether a mathematical method can be used on the current theorem. A method has prerequisites, a target, an intended action, and obligations that its use leaves to prove. Methods that look equally related to a theorem may therefore differ substantially in whether they offer a plausible next step. We formulate this as an applicability-aware method-selection problem and introduce self-advertisement: before candidates are ranked, a model generates a problem-specific proposal for each one, stating what part of the goal it targets, what action it would take, and what conditions that action requires. We organize 82 reusable methods from Putnam 2000-2014 as Method Contracts, which pair applicability descriptions with Mathlib anchors, a checked example or scaffold, and expected proof obligations. A single batched call elicits proposals across the library; vague or unsupported proposals are demoted, yielding a ranked shortlist accompanied by inspectable claims about each candidate's use. We analyze when similarity-based representations cannot distinguish methods with different applicability, how errors in applicability estimates affect shortlist quality, and what a checked scaffold guarantees under its stated assumptions. Against lexical, embedding, and embedding-plus-LLM reranking baselines, self-advertisement achieves 95.0% hit@5 on Putnam 2015-2025, compared with 84.2% for the strongest reranker. On IMO ProofBench, it achieves 91.7% compared with 88.3%. These results indicate improved coverage of annotated methods in the retrieved shortlists, particularly on Putnam.", "title": "Let the Library Speak: Self-Advertised Method Selection for Formal Proving", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.09401" }, { "age_days": 2, "arxiv_id": "2610.08319", "authors": [ "Hanchao Zhou", "Jialei Li" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08319", "kind": "paper", "label": "adjacent", "matched_signals": [ "tool_use_agents" ], "published": "2026-10-06", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "In proof assistants such as Lean, a generated proof must pass machine compilation checks, so evaluation needs no human scoring. Direct generation fails on multi-step numeric propositions: a proof is valid only if every content integer is correct, so the pass rate is bounded by the k-th power of the per-integer accuracy. Controlled corruption across 2,617 reference proofs confirms this power law. SCOPE (State-Conditioned Operator Planning and Execution) enforces the natural division of labor: the model plans over an operator vocabulary, a symbolic engine executes the numerics, and a compiler renders the proof. On a 218-problem suite it certifies 191/218 (87.6%) with a 135M backbone; the 7B DeepSeek-Prover-V1.5-RL certifies 18/218 at 27.5 times the tokens and 37.5 times the wall-clock, and DeepSeek-Prover-V2-7B certifies zero on a bidirectional dual suite. Multi-step thinking costs 6.12 discrete decision actions per problem and produces no natural-language thinking text. Replacing the lagged engine state in the decision frame with the current one lifts the pass rate from 117/218 to 191/218, while up-weighting the chain-end loss hurts. On the public Lean-Workbook library, 2,132 of 3,536 gradeable admissible problems certify (60.29%) with zero regression on the main suite. All readings come from a version-frozen review with independent rechecks and reverse verification. Restricting free generation and keeping decision-time information visible is a more direct route than enlarging the model.", "title": "SCOPE: Certified Theorem Proving with a Language Model as the Policy Planner", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08319" }, { "age_days": 2, "arxiv_id": "2610.07905", "authors": [ "Gábor P. Nagy", "Douglas S. McNeil", "Attila Vajda" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.07905", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-10-06", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let $K$ be a finite field of characteristic two with $|K| = 2^{n}$, let $\\gcd(k,n) = 1$, let $d_{k} = 4^{k} - 2^{k} + 1$ be the Kasami exponent, and let $Δ_{k} = \\{(b+1)^{d_{k}} + b^{d_{k}} + 1 : b \\in K\\}$ be the image of the normalised derivative of the Kasami monomial in the direction $1$. We show that, for all distinct nonzero $v_{1},v_{2} \\in K$, \\[ \\bigl|\\{(x,y,z) \\in Δ_{k}^{3} : v_{1}x + v_{2}y + (v_{1}+v_{2})z = 0\\}\\bigr| = 2^{2n-3}. \\] This establishes the cyclic-additive difference-set condition introduced by Carlet and later posed for the Kasami functions at NSUCRYPTO~2019. Starting from the known half-size property of the derivative image, we express the Fourier correction as twisted root counts and prove their required nonnegativity by an incidence argument on the Fermat cubic. An exact average over the slopes then forces equality pointwise. The argument covers every admissible pair $(n,k)$ and has been formalised and machine-checked in Lean~4 with Mathlib.", "title": "Carlet's cyclic-additive conjecture for the Kasami monomials", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.07905" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:c00732e7e732", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: size IR `importedEntries` only for extensions with IR entries (#15538)", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/c00732e7e732af49ea3958aedde4ed8e9cc89408" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:7afad6f034b1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: initialize only what `leanir` imports (#15566)", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/7afad6f034b179b6e827a8f9b2f24340387b720a" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:64942e142f2c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make equation lemma statements independent of the caller's options (#15499)", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/64942e142f2cbd3576ad89c3df41f8b6ccee91d9" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:0bb12a87a834", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: assorted `compiler.postponeCompile` fixes (#15565)", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/0bb12a87a8347e45560bc4b4f21c9abd83bbca0a" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:e55bff4c603b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/e55bff4c603b9e6faff347e46ccc463dbc26ee38" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover/lean4:94e4953a0c0a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update release scripts (#15564)", "updated": "2026-10-08", "url": "https://github.com/leanprover/lean4/commit/94e4953a0c0ac2dbf727abf40620e68a147c8f30" }, { "age_days": 0, "authors": [ "Xavier Roblot" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6be3d352cec3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(RingTheory/FractionalIdeal): make spanSingleton a monoid with zero homomorphism (#44475)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/6be3d352cec3ceabd28bf85266d28646e02f1975" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:257ed010f3d3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Translate): improve translation heuristic (#44266)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/257ed010f3d30d9f9b6ad7c97bf59a28bf64fbe1" }, { "age_days": 0, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cb08acac3857", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: zero-dimensional spaces (#40901)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/cb08acac385772a235cfa5bea8a52ae96f1e7130" }, { "age_days": 0, "authors": [ "Luigi Massacci" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:968097f29589", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: the delta distribution is induced by the dirac measure (#41884)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/968097f29589fc5d77b41a6eac235a9a8977696d" }, { "age_days": 0, "authors": [ "Yi.Yuan" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:76dc6b8c79e7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology): add `IsClosed.nhdsSet_inter_eq` (#44587)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/76dc6b8c79e734bceb577d3450b79c90985d89fe" }, { "age_days": 0, "authors": [ "stalex444" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:19b96f57da08", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/IntegralClosure): integer powers of integral elements are integral (#41871)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/19b96f57da082d81a8fe7ca247e0bd36970449fd" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:62bf13aabd0d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory,FieldTheory): add instances for `adjoin` (#42154)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/62bf13aabd0db1bf4cbe2a6ec087c6f7a677f448" }, { "age_days": 0, "authors": [ "Nailin Guan" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d1a28f4132a1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra): base change of exterior algebra (#44604)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/d1a28f4132a183f8dc05f46156e603fd326858e7" }, { "age_days": 0, "authors": [ "JadAbouHawili" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a6de5db92301", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/Connectivity): change IsEdgeReachable and IsEdgeConnected to accept ENat instead of Nat (#43346)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/a6de5db92301f15e310e4ac8b9129a3d7e7dbe15" }, { "age_days": 0, "authors": [ "Blake Farman" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a6c28d046d56", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/ObjectProperty): closure properties of orthogonals and S. E. Dickson's theorem (#44226)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/a6c28d046d566e64ccccfd03d0af65b142251f23" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a2c69e8e2c7b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Cache): treat nightly-testing as a fork (#44388)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/a2c69e8e2c7bc519380b9a5d8a966a69aa8fbe6b" }, { "age_days": 0, "authors": [ "Paul Cadman" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:79edc735c197", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Polynomial/CoeffList): construct a polynomial from its list of coefficients (#44430)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/79edc735c1979a4f9d61962f5826834d07fcc889" }, { "age_days": 0, "authors": [ "Gian Sanjaya" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:59cf8085d54d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/CharP/Two): weaken theorem hypothesis (#42346)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/59cf8085d54d23fe4224eaa3a23eae2c7fac61bf" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:553dc93e7dd8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: fix and add docstrings in RingTheory/Invariant/Galois (#41570)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/553dc93e7dd82c8c1455779db94688d872661d0a" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:49fd9dee36e7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci: build Archive, Counterexamples and Wanted in one lake build (#44650)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/49fd9dee36e7bbf345fe7981d2de6aeeb591f75b" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:62562f457786", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci(cache): run ci_dev.yml uploads under a reviewed environment (#44648)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/62562f457786f39a2b54de872b5fd308c30ecfda" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:146bf3892bac", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci(cache): make R2 the primary cache upload; stop uploading developer cache to Azure (#44640)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/146bf3892bac61fa32d50296804e15405e1d7f11" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9304843e73da", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: weaken hypotheses of Algebra.IsUnramifiedIn.ramificationIdx_eq_one (#41578)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/9304843e73daf93d99fa89cfc4112b0a2fb435bb" }, { "age_days": 0, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4a3cff2c9216", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: split `Topology.SmallInductiveDimension` (#44617)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/4a3cff2c9216262b3e173547a543e524f5d6be6e" }, { "age_days": 0, "authors": [ "David Kurniadi Angdinata" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1d9647a73012", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `fromOpcyles_δ` to `fromOpcycles_δ` (#44519)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/1d9647a730128730a27c3801fe37b095e3d3ed10" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:47d0979a70aa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: import Batteries.Tactic.Alias in Mathlib.Init already (#44621)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/47d0979a70aae276f1ffcbb7e975b87981137409" }, { "age_days": 0, "authors": [ "Jireh Loreaux" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6395a231aede", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: correct instances for normed rings on subrings (#44082)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/6395a231aede91690520a4816a08caad7cf771ca" }, { "age_days": 0, "authors": [ "Yi.Yuan" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5347805dd5a2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Combinatorics/Additive/Corner): use explicit Fin embeddings and kill TODOs (#44453)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/5347805dd5a2c0d9a28f393be8a8a80c531d1bb9" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1b3c41969602", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-08", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/Shapes/BinaryProducts): use `to_dual` (#43571)", "updated": "2026-10-08", "url": "https://github.com/leanprover-community/mathlib4/commit/1b3c41969602424bd2f04b3d4f731734e5b00cde" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:153e01180e59", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: implement `String.toList` in Lean (#15533)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/153e01180e59305df575e24b803cf7416a251bcf" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:3bd0c26d4730", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: store imported module names in the environment header (#15543)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/3bd0c26d4730fb2ece12d54c600ffa97099a77d3" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:0cea69c5d0c1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: read reducibility status of theorems without waiting for their proofs (#15534)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/0cea69c5d0c17d6d7eb81e6d3da7bed4c61953c0" }, { "age_days": 1, "authors": [ "Carlo Hamalainen" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:e7f3d517cd66", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use the RFC 9110 `GMT` date format for the HTTP `Date` header (#15469)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/e7f3d517cd664fdd533f90d785d1a4e50263c8c6" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:7e9f797401dd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: race condition in IR interpreter debug code (#15539)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/7e9f797401ddd7110f57e3f16b95cdf3414f6767" }, { "age_days": 1, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover/lean4:59bd5aaaccba", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make timers and signals safe against re-entrant continuations and lost signals - #15191 (#15523)", "updated": "2026-10-07", "url": "https://github.com/leanprover/lean4/commit/59bd5aaaccbab3a866b4d35a7fdbc0e1acfe36d3" }, { "age_days": 1, "authors": [ "Zhi Kai Pong" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:78429a9da112", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(scripts/dag_traversal.py): kill timed-out builds on Windows (#44403)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/78429a9da11204808ac62a267ec9f1a250c9389a" }, { "age_days": 1, "authors": [ "Weiyi Wang" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ba05a60aae0b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed): embedding of PiLp along indices (#44340)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/ba05a60aae0b14f987e66038f13eed6669c166cb" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:021ce68bf125", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(Tactic): prefer ` over ' and use .ofConstName (#44322)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/021ce68bf125a049beee22b3fc7664d78728e21d" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9e6b3aac99b6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: silence module system warning in a few mathlib-adjacent execut… (#44307)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/9e6b3aac99b624d10c84653ab9c5357283b9b3b8" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2d39771fb0c8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/Shapes/Equalizers): use `to_dual` (#44215)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/2d39771fb0c87211301a0b2c1db681382099485e" }, { "age_days": 1, "authors": [ "Yan" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:221512f0526a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Distributive/Monoidal): scope ∂R notation and fix docstrings (#44602)", "updated": "2026-10-07", "url": "https://github.com/leanprover-community/mathlib4/commit/221512f0526ae80bb3ef870100d6e960317bb110" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:2369f26faa87", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: index `Lean.Order.iSup` and `iInf` over `Sort` (#15517)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/2369f26faa873e34e281057dbac329a57a356b2d" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:6f79a3e117e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: share server extension entries with the main table outside the server (#15512)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/6f79a3e117e4cffc425d7514df3ae9b512a37ea3" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:3dc0360c4af4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: return a pointer into the ir cache (#15520)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/3dc0360c4af4ea919b5fa3db7953f74fa58b5c4d" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:4d609dfd22eb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: make high arity closures pass their arguments linearly if possible (#15131)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/4d609dfd22eb77e453b021967d52135e7ce98fb8" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:e51e86f86062", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: split an `∃` or `⨆` over a proposition on the RHS of a `vcgen` entailment (#15515)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/e51e86f86062a43671adba761d0eab985f40e7b8" }, { "age_days": 2, "authors": [ "Richard Beauchamp" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:0f6e0e910a2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: fetch partial facets under their resolved keys (#15474)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/0f6e0e910a2b4aaa46735c2b0dc992ef789df3a1" }, { "age_days": 2, "authors": [ "Carlo Hamalainen" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:1bc0c1c2da8e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: generate the HTTP `Date` header without the timezone database (#15443)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/1bc0c1c2da8e3f7e2432bb3807ead509119b5246" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:4656f09f8444", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: expose `Lean.Arrow` so `sym` proofs type-check in modules (#15526)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/4656f09f8444431c7ea91a2abe5860957b90483a" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:03eeb6f90f5b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `grind` runs upward propagation from the `toProcess` queue (#15506)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/03eeb6f90f5bc225bbbb01ad670efcd3810fe3e0" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:cd842b6db936", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `grind` hints whose holes are all proofs (#15524)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/cd842b6db936b2c5e7e254f011a57eb96fd7cf3b" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:3e3b5b1ea35c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `Sym.Arith.classify?` on carriers in `Sort u` (#15503)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/3e3b5b1ea35c0087a40c19c0886f04d0c104ae6e" }, { "age_days": 2, "authors": [ "Garmelon" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:f93a70a92b41", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: stop poking mathlib4 nightly-testing (#15519)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/f93a70a92b4175850711417231cc5c13a0e461a9" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:80fbe9c02f82", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: disable all async tests in asan CI (#15513)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/80fbe9c02f826f7e2ad0d69fa492585be9fdfe75" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "github:leanprover/lean4:c6591180eb4c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: `private`/`public` modifier syntax on `variable` (#15518)", "updated": "2026-10-06", "url": "https://github.com/leanprover/lean4/commit/c6591180eb4c3ea5a39f1bcb3b35558bc4d50634" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "github:leanprover/lean4:7537fb9348bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: make variable access in IR interpreter branch free (#15493)", "updated": "2026-10-05", "url": "https://github.com/leanprover/lean4/commit/7537fb9348bfd6ab0787bb636b576baeb9ed2e7b" }, { "age_days": 3, "authors": [ "David Thrane Christiansen" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "github:leanprover/lean4:eff552d00c4a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: stop consuming newlines for role and inline code recovery (#15495)", "updated": "2026-10-05", "url": "https://github.com/leanprover/lean4/commit/eff552d00c4a6f2f92fd3106f6b1817e21ff34d5" }, { "age_days": 3, "authors": [ "Wojciech Nawrocki" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "github:leanprover/lean4:c1ac28d61e54", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: register syntax kinds (#15500)", "updated": "2026-10-05", "url": "https://github.com/leanprover/lean4/commit/c1ac28d61e549de4ec1cc1d619007a2ee0e833f6" }, { "age_days": 3, "authors": [ "Wojciech Nawrocki" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "github:leanprover/lean4:967598cb69e1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: HTML-like syntax (#15002)", "updated": "2026-10-05", "url": "https://github.com/leanprover/lean4/commit/967598cb69e1a4d46ae393c17cba144da06729f6" }, { "age_days": 1, "arxiv_id": "2610.09258", "authors": [ "Arjun Pemmasani" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.09258", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We observe a ball bouncing down a Galton board with any number of directions. At each peg it either keeps its direction with some fixed probability or randomly turns to one of the other directions. Its bin measures how often it went each way, a point of a simplex. When the ball rarely turns, the most likely bins are the corners, which only a ball that never turns can reach. We ask when the best bin of each face of the simplex becomes as likely as a corner. To first order every face catches up at the same moment. We break this tie at second order, with an explicit constant for each face. Hence on a long board, as the expected number of turns grows to any fixed multiple of the length's logarithm, the most likely bin jumps once, from the corners straight to the center. A nonuniform start or a weak external field changes the constants, potentially allowing an intermediate face to win.", "title": "Vertex crossings in a symmetric Markov multinomial model", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.09258" }, { "age_days": 1, "arxiv_id": "2610.10397", "authors": [ "Angelina Blahodatna", "Lauren Detmold", "Daniel Glasscock", "Anh N. Le" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10397", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The regionally proximal and equicontinuous structure relations are fundamental relations in topological dynamics that capture the equicontinuous behavior in a topological dynamical system and its factors. For minimal actions of abelian groups, these relations are known to be equivalence relations and are known to coincide. In this paper, we generalize these facts to semigroup actions: for minimal actions of commutative semigroups, the regionally proximal and equicontinuous structure relations are equivalence relations and the two coincide. We also develop the machinery of natural extensions for commutative semigroup actions that act by surjections, concluding that the maximal equicontinuous factor of a minimal action of a commutative semigroup is the same as the maximal equicontinuous factor of the group action into which it embeds. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.", "title": "The regionally proximal relation for commutative semigroup actions", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10397" }, { "age_days": 1, "arxiv_id": "2610.10416", "authors": [ "Angelina Blahodatna", "Lauren Detmold", "Daniel Glasscock", "Anh N. Le" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10416", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In this paper, we strengthen the connection between the combinatorics of difference sets and the dynamics of group rotations. Our main result shows that sets which have non-empty intersection with all difference subsets of a commutative semigroup possess local Bohr structure. This generalizes results of Bergelson, Furstenberg, and Weiss and Host and Kra from the integers to arbitrary commutative semigroups. We accomplish this by A) utilizing a recent result showing that the regionally proximal relation is an equivalence relation for minimal actions of commutative semigroups and by B) describing a new, DeMorgan-type algebra on Furstenberg families that allows for efficient manipulation and computation. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.", "title": "The local dynamical structure of $Δ^*$ sets via a new Furstenberg family algebra", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10416" }, { "age_days": 1, "arxiv_id": "2610.10162", "authors": [ "Ahmed Bou-Rabee", "Yuval Peres" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10162", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A centrally excited random walk on ${\\mathbb Z}^d$ moves like simple random walk, except that its first step from each site has a drift of fixed size toward the origin. Kozma (2007) conjectured that after $n$ steps the visited set approximates a ball with radius of order $n^{ 1/(d+1)}$. We prove this in every dimension $d\\geq2$ and show that the rescaled numbers of visits converge uniformly to a cone, which is the potential generated by the drift on a ball. The same argument shows that a drift opposite to a subgradient of a norm produces the ball of that norm. In the plane, the outer and inner radii of the visited set differ by at most $ n^{1/6}$ times a power of $\\log n$, and the exponent $1/6$ cannot be lowered.", "title": "Kozma's centrally excited walk converges to a Euclidean ball", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10162" }, { "age_days": 1, "arxiv_id": "2610.09733", "authors": [ "Seunghan Kim", "Minyeong Choe", "Hyunil Kim", "Haehyun Cho" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.09733", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Multilingual LLMs answer the same multi-hop reasoning question across languages, but we lack a mechanistic account of whether they share an internal circuit. We identify Bridge Routing Heads (BRH) in two large multilingual LLMs through a three-stage pipeline. The resulting language-specific head sets exhibit near-complete mutual exclusivity across the five languages, with a mean Jaccard similarity of only 0.017 for Llama 3.1 70B and 0.057 for Qwen 2.5 72B, revealing language-idiosyncratic circuits. Ablating general BRH increases two-hop Negative Log-Likelihood (NLL) by 39-89x the random-head baseline, providing direct causal evidence of their role. Amplifying these heads in a failing target-language pass rescues up to 51.7% of cross-lingual failures, with no training. The two models share this dual-circuit pattern but allocate heads differently: Llama concentrates chaining in a large general pool, while Qwen leans on larger language-specific pools. Together these results show that activation-level intervention alone can recover correct answers from cross-lingual reasoning failures.", "title": "Bridge Routing Heads: Where Multilingual Multi-hop Reasoning Lives in LLMs", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.09733" }, { "age_days": 1, "arxiv_id": "2610.10248", "authors": [ "Minbo Gao", "Tianshi Yu", "Lihong Zhi" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10248", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We construct an explicit binary linear system game that separates \\(C_{qa}\\), the closure of the set of finite dimensional quantum correlations, from \\(C_{qc}\\), the set of commuting operator correlations. The game admits a perfect commuting operator strategy, while every correlation in \\(C_{qa}\\) has a success probability strictly less than 1. This provides a concrete counterexample to Tsirelson's problem in its approximation form. The defining system has \\(1{,}417{,}152\\) equations in \\(1{,}889{,}684\\) variables, with exactly three nonzero coefficients per equation and a single nonzero entry on the right hand side. We also compute the classical value exactly. The complete system is specified in Lean~4, and the separation and exact classical value are formalized using Mathlib.", "title": "An Explicit Counterexample to Tsirelson's Problem via a Linear System Game", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10248" }, { "age_days": 2, "arxiv_id": "2610.08144", "authors": [ "Alexander Bastounis", "Fabian Circelli", "Anders C. Hansen" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08144", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI $= \\infty$). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI $= 1$). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include OpenAI's announced Navier-Stokes proof. In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations.", "title": "Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08144" }, { "age_days": 2, "arxiv_id": "2610.08723", "authors": [ "Erfan Amidi", "Ali Asadian", "Ali Hamed Moosavian" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08723", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove that unknown pure fermionic states prepared from disjoint-branch fixed-particle-number blocks can be reconstructed after general quadratic evolution, including pair creation and annihilation. For a fixed particle cap per block, adaptive or nonadaptive single-copy Gaussian measurements yield classical input and circuit descriptions with prescribed fidelity and confidence, using polynomial resources in system size and inverse infidelity. The adaptive procedure has the sharper copy guarantee. Connected quartic correlations and a covariance-compatible commutant identify the hidden blocks; local states are recovered from fresh measurements or a predetermined bounded-degree moment table. Stable branch recovery gives valid preparation descriptions. Neither particle-number conservation nor block homogeneity is required; no lower bound on branch weights or covariance gaps is assumed. A certified variant returns a passive preparation whenever one exists within the promised family, without advance membership information. On the full Gaussian orbit of paired magic states, quartic measurements alone suffice, with an explicit bound converting observable error into state error.", "title": "Efficient Learning of Structured Fermionic States under General Quadratic Evolution", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08723" }, { "age_days": 2, "arxiv_id": "2610.07605", "authors": [ "Jinseong Kim", "Hyunchang Lee", "Keeman Lee", "Assaad R. Masri" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.07605", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In this study, the lean extinction behaviors of CH4 and a 16% cracked ammonia surrogate fuel, CR16, in counterflow premixed flames were compared. Experiments were conducted along with one-dimensional simulations using OPPDIF; the GRI-Mech 3.0 and UCSD mechanisms were applied to CH4 and CR16, respectively. CR16 exhibited higher extinction strain rates and resilience to strain-induced blow-out (RSIB) than those of CH4 under lean conditions. At Phi = 0.66, although both flames had the same extinction strain rate, CR16 showed a higher RSIB because of its longer flame time. Near its extinction, CR16 sustained H2 consumption, radical reactions, and heat release through the interflame region toward the stagnation plane. Hydrogen oxidation coupled with nitrogen-related pathways, including NH2 + NO and HNO reactions, supported this behavior. These results clarify the chemical basis for the superior extinction resistance of economically favorable low-cracking-ratio ammonia fuel.", "title": "Characteristics of extinction behavior of ammonia partial cracking simulated fuels in counterflow premixed flames under lean condition", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.07605" }, { "age_days": 2, "arxiv_id": "2610.08988", "authors": [ "Vincent Liew" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.08988", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "SAT solvers are empirically known to perform poorly when reasoning about multiplication. Yet for over a decade we have lacked a theoretical explanation for this phenomenon. CDCL SAT solvers implicitly search for resolution proofs, and no lower bound on proof size has ruled out the existence of short proofs that solvers simply fail to find. We give the first lower bound of this kind by showing that general resolution proofs of the associativity of $n$-bit multiplication require size $2^{Ω((n/\\log n)^{1/4})}$. This lower bound holds for a broad class of multiplier encodings based on partial product summation, including the standard array and Wallace-tree multipliers used to bit-blast multiplication in SMT solvers. This result resolves an open problem of Beame and Liew. The proof constructs a reduction from a perfect-matching principle on bounded-degree bipartite expander graphs to multiplier associativity. Itsykson, Slabodkin, and Sokolov proved that this principle is hard for resolution. The lower bound for multiplier associativity follows. The same reduction, when combined with Håstad's recent lower bound for the perfect-matching principle of the odd grid, yields an exponential lower bound for multiplier associativity in the stronger bounded-depth Frege proof systems.", "title": "Associativity of Multiplication Is Hard for Resolution", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.08988" }, { "age_days": 2, "arxiv_id": "2610.09206", "authors": [ "Hazar Yueksel" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.09206", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Loss-difference conditional mutual information (ld-CMI) uses the smallest of the standard observations in the supersample hierarchy of generalization bounds: it measures what a learner's loss differences reveal about which candidate of each pair it was trained on. Accuracy is known to force information into the model; data processing does not carry such lower bounds to losses. We show, by bounding three moments of the loss differences, that accuracy also forces ld-CMI. For linear predictors with a smooth convex loss of nonzero slope at zero, such as the logistic loss, plus a regularizer whose curvature and growth are both of power $r\\ge2$, on product distributions over a scaled sign cube in dimension at least linear in $n$, every proper learner with expected excess risk at most $\\varepsilon$ on these distributions at the optimal sample size $n\\asymp\\varepsilon^{-2+2/r}$ has worst-case ld-CMI of order $n$ bits, and $Θ(n/(1+(τ/\\varepsilon)^2))$ bits under Gaussian noise of standard deviation $τ$ on the loss differences. The same holds without a regularizer, at $n\\asymp\\varepsilon^{-2}$. Consequently, range-scaled ld-CMI bounds cannot vanish on these distributions, although every proper learner's generalization gap is $O(n^{-1/2})$. We also show that model-level information does not determine noisy loss-difference information, and that the growth, slope and dimension conditions are needed, the last up to a logarithm.", "title": "An Accuracy--Information Tradeoff for Loss-Difference Conditional Mutual Information", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.09206" }, { "age_days": 2, "arxiv_id": "2610.09093", "authors": [ "Nathaniel Craig" ], "content_date": "2026-10-06", "freshness": "fresh", "id": "arxiv:2610.09093", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.", "title": "A gauge-invariant measure for lattice chiral fermions", "updated": "2026-10-06", "url": "https://arxiv.org/abs/2610.09093" }, { "age_days": 3, "arxiv_id": "2610.06742", "authors": [ "Patrick Hayden", "Alexander Maloney", "Jinzhao Wang", "Yuxiang Yang" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "arxiv:2610.06742", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We study a variant of Schumacher compression. The task asks for the minimal memory cost for compressing many copies of a density matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive eigenvalues, we obtain the cost through its additive constant. Achievability uses a generalization of Werner's cloning map to $\\mathrm{GL}(d,\\mathbb C)$ irreducible representations, with finite trace-distance bounds controlled by highest-weight differences and row gaps. The matching converse follows from a quantitative form of Koashi--Imoto incompressibility for irreducible group orbits under a spectral-gap assumption. We also identify the relation between this quantum minimum description length and universal lossless coding overhead, and its connection to free entropy is explained in a companion letter. We provide a Lean certificate for our proofs.", "title": "Quantum minimum description of density matrices", "updated": "2026-10-05", "url": "https://arxiv.org/abs/2610.06742" }, { "age_days": 3, "arxiv_id": "2610.06674", "authors": [ "Srija Chakraborty" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "arxiv:2610.06674", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Nighttime lights from NASA's Black Marble product suite capture thermal and light emission signals from anomalous events including fires, volcanic eruptions, and gas flaring. Existing detection approaches rely primarily on thermal bands, limiting sensitivity to weaker signals. We propose a novel machine learning framework that jointly models Black Marble M-band and Day/Night Band (DNB) signals to derive a generalized, spatio-temporally robust ensemble of anomaly detectors. The framework iteratively builds detectors that scale across regions, seasons, anomaly classes, and extends over land and ocean. Detection sets at varying confidence levels are derived based on relevant bands and detector agreement. The approach improves true detection rate while reducing spurious detections and results demonstrate strong generalizability with applications in natural hazard monitoring and energy extraction.", "title": "Detecting Nighttime Anomalies from NASA Black Marble Using a Generalized Spatio-Temporally Robust Framework of Machine Leaning Ensembles", "updated": "2026-10-05", "url": "https://arxiv.org/abs/2610.06674" }, { "age_days": 3, "arxiv_id": "2610.07292", "authors": [ "Jyotishka Ray Choudhury", "Kabir Aladin Verchand", "Richard J. Samworth", "Ashwin Pananjady" ], "content_date": "2026-10-05", "freshness": "fresh", "id": "arxiv:2610.07292", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Missing covariates are frequently encountered in supervised learning problems, and classical methods for estimation using such data use carefully chosen imputation schemes for missing data, or likelihood approximations that lead to nonconvex $M$-estimation problems. These methods and their relatives are suitable for scenarios in which the covariate distribution is known, and more broadly, have enjoyed tremendous success in linear models. But even in basic nonlinear problems such as logistic regression in moderate dimensions, such methods can experience drastic failure modes when the covariate distribution is unknown. Motivated by the need for reliable alternatives, we consider the problem of parameter estimation in logistic regression with missing covariates. Crucially, we operate in the assumption-lean setting where the covariate distribution is unknown (but bounded). We design a stochastic approximation method that is based on $Z$-estimation with a novel monotone operator, and establish that our algorithm is computationally efficient and achieves provable signal recovery at parametric rates under the hypothesis that covariates are missing completely at random. Our theory sharply characterizes the $\\ell_2^2$ risk of the estimator in terms of the missingness profile, accommodating heterogeneous observation probabilities. Importantly, it shows that our method always outperforms the de facto ``complete-case'' estimator that ignores observations with any missing data. Even in the setting with homogeneous missingness (in which each covariate is observed independently with probability $q$), our bounds exhibit intricate and nonstandard dependence on $q$ that can yield significant improvements over using only complete cases. We complement our upper bounds with new information-theoretic lower bounds that show that this intricate dependence on $q$ is fundamental in a minimax sense.", "title": "Assumption-lean logistic regression with missing covariates", "updated": "2026-10-05", "url": "https://arxiv.org/abs/2610.07292" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }