{ "counts": { "adjacent": 10, "core": 5, "errors": 0, "negative": 75, "total": 90 }, "date": "2026-10-12", "errors": [], "fresh_content_days": 21, "generated_at": "2026-10-12T22:33:24Z", "items": [ { "age_days": 4, "arxiv_id": "2610.11605", "authors": [ "Matěj Kripner", "Milan Straka" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.11605", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-10-08", "score": 12.5, "source": "arxiv-ai4math-core", "summary": "We introduce NanoProof, to our knowledge the first factorized execution-guided theorem prover in Lean 4 whose training data, extraction tooling, training pipeline, and weights are all released, making it end-to-end reproducible using open-source resources. To this end, we build and release a dataset of structured proof trees, as well as a tool for programmatic interaction and data extraction within the Lean 4 formal verifier. To support sustainable research, we focus on compute efficiency to facilitate accessible training and evaluation. NanoProof achieves 50.8% pass@16 on MiniF2F-Test, exceeding the two closest systems of its class, HyperTree Proof Search and ABEL, at roughly 90x and 7x less compute, and using more than four orders of magnitude less compute than AlphaProof. Stronger open-weight provers exist, but they are fine-tuned from large pretrained language models and release neither training data nor pipeline; NanoProof shows that the factorized execution-guided class of provers can be rebuilt from scratch with modest resources.", "title": "NanoProof: Open and Efficient Automated Theorem Proving in Lean 4", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.11605" }, { "age_days": 3, "arxiv_id": "2610.13632", "authors": [ "Zhengyang Zhang", "Jing Xiong", "Hongzhou Lin", "Juihui Chung", "Zijian Zhang", "Song Han", "Sihao Liu", "Ligeng Zhu" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13632", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "seed_author:Hongzhou Lin", "verifier_guided_reasoning" ], "published": "2026-10-09", "score": 10.5, "source": "arxiv-ai4math-core", "summary": "Large language model (LLM) agents are rapidly improving on long-horizon scientific and olympiad tasks. Recent systems have produced a Lean-formalized resolution of the Navier--Stokes problem and autonomous solutions to four open questions in the Erdős Conjectures database. Yet neither system releases both its underlying model and complete inference stack. More broadly, a single agent session remains brittle on difficult problems: early errors can propagate, missing domain knowledge can stall progress, and apparent success can mask a misinterpretation or weakening of the original task. We introduce HOA (Humanize Olympiads Agent), an open, flow-level framework that coordinates multiple agent sessions through three complementary feedback channels. First, an independent reviewer evaluates each candidate and provides actionable feedback. Second, a structured wiki supplies task-specific knowledge that may be missing or unreliable in model pretraining. Third, a verifier checks generated Lean proofs against trusted challenge statements. With GPT-5.6 Sol, HOA achieves perfect scores on the IMO, IPhO, and IOI 2026, near-full marks on the IChO 2026 problem set, and solves all 672 problems (100%) on PutnamBench. On the Lean-Eval leaderboard, HOA ranks first, solving 251 of 304 problems (82.6%). We further evaluate HOA with open models. Using Kimi-K3, HOA achieves full scores on the IMO, IPhO, and IOI, and a gold-level score of 97.1% on the IChO. These results closely match the closed-source GPT-5.6 Sol + /Goal baseline on the IMO and IPhO, while exceeding it on the IChO and IOI, demonstrating that systematic feedback can help bridge substantial differences in base-model capability.", "title": "Humanize Olympiad Agents: A Multi-Session Workflow for Olympiad Problem Solving with Solve, Review, Wiki, Verify", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13632" }, { "age_days": 4, "arxiv_id": "2610.12211", "authors": [ "Hazar Yueksel" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12211", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-10-08", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications. The usual remedy is to solve related source tasks, either all first, as a curriculum does, or interleaved with verification. We price this remedy in information and in calls. With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification. It lower-bounds the expected number of binary source calls, which designed sources meet within $1+\\log_25$ calls for unique answers and within a logarithmic term in general, where no additive constant suffices. With an exact verifier and fixed sources, moving every call before the first verification preserves all hard caps on calls, although interleaving can save unboundedly many expected calls; under a noisy verifier, source-first protocols can lose unbounded factors in information and in error. For linear banks over $\\mathbb{F}_2$, optimal accuracy has a closed form, and after a polynomial-time reduction the budget profile is computable in time $2^{O(h^2)}\\operatorname{poly}(J,k+h)$ for $J$ sources and nuisance dimension $h$. In these banks, for zero error under a hard cap, the calls beyond the rounded-up information price are exactly those spent on nuisance. Every numbered result apart from two clauses about the planner is machine-checked in Lean 4, assuming two published results. Used as a ruler, the frontier shows a small transformer using all delivered bits at latent dimension $5$ and none at $11$ within fixed training budgets; in a test with predictions recorded before training, low XOR degree of the target bits did not suffice for their use.", "title": "Verification with Transfer: Exact Information Frontiers and Their Price in Calls", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12211" }, { "age_days": 4, "arxiv_id": "2610.11862", "authors": [ "Nihal Jain", "Shuangjie Yao", "Begum Cicekdag", "Zhuo Zhang", "Suman Jana" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.11862", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-08", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Mathematicians value proofs for more than correctness: among correct proofs, simplicity, purity and the computational cost of finding them vary widely. Yet LLM-powered theorem provers largely search for any correct proof, and improve its quality only after it is found. We propose LEVER, a proof search algorithm that makes the objective over correct proofs programmable and optimizes it during search. LEVER scores partial proofs over an AND/OR proof graph, combining realized objective values with predictions for open subgoals, so the objective guides search before a proof is complete. The same mechanism optimizes computational cost, proof length, topical impurity, and even their weighted combinations, while the Lean kernel enforces correctness. On PutnamBench in Lean 4, under matched budgets, LEVER costs 34% less than a strong single-conversation agent while raising the solve rate from 80% to 96%. On reducing topical impurity, i.e., how far a proof strays from its theorem's subject, it improves over post-hoc refactoring (42% reduction against 33%) at two-thirds of the cost and more reliably; on proof length, the metric refactoring is built for, it approaches refactoring. Varying the objective's weights traces a quality-cost trade-off curve, so the user can choose how much a better proof is worth. Overall, LEVER is a performant, cost-efficient and tunable proof search algorithm for navigating the space of correct proofs.", "title": "LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.11862" }, { "age_days": 4, "arxiv_id": "2610.12218", "authors": [ "Chaoyang Qin", "Xiaoming Sun" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12218", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-10-08", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "The second part of Hilbert's 16th problem is one of the most fundamental open problems in the qualitative theory of ordinary differential equations and dynamical systems. A central unresolved question is whether the Hilbert number $H(d)$ is finite for arbitrary polynomial degree $d$. (A very recent manuscript from OpenAI asserts the finiteness of $H(d)$; see the remark at the end of this paper.) In the absence of a general upper bound theory, most existing work constructs explicit perturbed polynomial systems to obtain improved lower bounds for $H(d)$, while rigorous upper bound estimates remain largely unavailable. This paper focuses on improving the quantitative lower bound for polynomial systems through a systematic Hierarchical Melnikov Realization framework. We construct perturbed dynamics based on an anisotropic Chebyshev Hamiltonian, where hierarchically selected perturbation coefficients generate simple zeros of the first-order Melnikov function simultaneously across multiple disjoint period annuli. Two distinct 3-adic filtrations supply the necessary logarithmic correction factors, and a Borel--Gauss analysis establishes the required local rank condition under sufficiently strong anisotropy. As the main result of this work, we prove that $H(d)=Ω\\bigl(d^2\\ln^2 d\\bigr)$, which improves the previously known lower bound by a factor of $\\ln d$. The full construction of limit cycles and the resulting dynamical bounds are formally certified using Lean 4 formal verification.", "title": "Hierarchical Melnikov Realization: Logarithmic Factor Improvement to Hilbert Number Lower Bounds", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12218" }, { "age_days": 3, "arxiv_id": "2610.13897", "authors": [ "Yuan Liao", "Ziyang Qin", "Jui-Hui Chung", "Ayush Khaitan", "Zhengyang Zhang", "Hongzhou Lin", "Zijian Zhang", "Ligeng Zhu", "Peng Lu", "Bennett Chow" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13897", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "seed_author:Hongzhou Lin", "seed_author:Jui-Hui Chung" ], "published": "2026-10-09", "score": 4.3, "source": "arxiv-ai4math-core", "summary": "We formalize the Hamilton--Perelman Ricci-flow proof of Thurston's geometrization conjecture. The public Lean declaration is reproduced in this paper. Its geometric interpretation follows, and verification is recorded in 4.", "title": "A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13897" }, { "age_days": 3, "arxiv_id": "2610.13461", "authors": [ "Pablo Manrique", "Hai Xia", "Stefan Szeider" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13461", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-10-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "AI systems are making rapid progress in mathematics, but this progress is hard to measure. Benchmarks of solved problems saturate, and in benchmarks of open problems each problem can be resolved for the first time only once. We present SqueezeBench, a benchmark that is resilient to saturation: a success raises the bar instead of removing the problem. Each problem fixes an integer function $f(n)$ whose values are known only for small $n$, and the benchmark keeps a lower and an upper record on it. A record is a computable Lean function with a machine-checked proof that it bounds $f$. A submission proposes a new function and proves that it bounds $f$, that it is no worse than the current record at any $n$, and that it is strictly better at some $n$. Once accepted, it becomes the record that the next submission has to beat. The system thus chooses the bound as well as its proof, and it may improve the record at a single $n$ or its growth rate. At every $n$, the gap between the two records shows how far the certified bounds are from determining $f(n)$. Every proof is checked by two independent Lean kernels, so no referee needs to check the mathematics. The checks also reject a function that computes $f$ by exhaustive search at small $n$, and a maintainer only reads the submitter's report and looks for such a search at larger $n$. We release ten problems from extremal combinatorics with twenty proved initial records and the admission tools. As a baseline, agents based on a frontier language model, with at most one hour per record, had 82 submissions accepted and improved every record, without going beyond the published literature. Agents based on two newer models then started from these records, had 60 more submissions accepted and improved 19 of the 20 records again. For eight of the ten problems, at least one record is still asymptotically behind the best published bound.", "title": "SqueezeBench: Saturation-Resilient Evaluation of Mathematical Capability", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13461" }, { "age_days": 3, "arxiv_id": "2610.13463", "authors": [ "Dakai Guo", "Ruichen Qiu", "Yichuan Cao", "Ruyong Feng", "Xiao-Shan Gao" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13463", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the cyclic sum $\\sum_{i=0}^{10}(x_i-x_{i+1})/(x_{i+1}+x_{i+2})$ is nonnegative for every strictly positive real eleven-tuple, with indices taken modulo eleven. Clearing denominators reduces the problem to a homogeneous polynomial. Subtracting the smallest coordinate then separates the proof into nonnegativity of a common-translation derivative and nonnegativity on a full boundary face. We supply exact rational polynomial certificates in Gram-matrix form for both statements. The derivative certificate uses a linear multiplier, centered monomials and cyclic averaging; the boundary certificate uses a strictly positive quadratic multiplier and uncentered monomials. Their verification requires 6,069 cyclic coefficient comparisons and 34,304 literal coefficient comparisons. All 606 certificate matrices are certified by integer congruences with strictly diagonally dominant images. A Lean 4 development formally verifies the certificate checks and their connection to the original inequality. The exact certificate data, replay programs, and formal sources are publicly available.", "title": "Exact rational certificates and a Lean formalization of the eleven-variable Vasc inequality", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13463" }, { "age_days": 4, "arxiv_id": "2610.11324", "authors": [ "Sebastien Kawada" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.11324", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We resolve Erdős Problem #522, posed in 1961, by proving that for random Littlewood polynomials the proportion of zeros in the closed unit disk converges almost surely to $1/2$. More generally, for partial sums of random power series with i.i.d. coefficients that are bounded, nondegenerate, and centrally symmetric, real Gaussian, or circular complex Gaussian, we prove that the proportion of zeros in the disk of radius $1+x/n$ converges almost surely to $\\frac12(1+\\coth x-1/x)$, uniformly in $x\\in\\mathbb{R}$. Thus almost all zeros lie at distance $O(1/n)$ from the unit circle. For random Littlewood polynomials, even with arbitrary dependence between degrees, the convergence at the unit circle holds at the almost-sure rate $O(n^{-1/4}\\sqrt{\\log n})$. We establish a law-of-the-iterated-logarithm criterion for dependent sequences and, for real Gaussian coefficients, obtain the sharp law of the iterated logarithm over all integer degrees, variance and cross-degree covariance asymptotics, quantitative central limit theorems, joint Gaussian limits, and increment bounds. For symmetric coefficient laws with bounded density and all moments finite, the number of zeros in the closed unit disk has variance $(c_G+κ_4/12)n+O_ξ(n^{399/400})$, and for random signs the constant is $c_G-1/6$. Thus the radial law is universal, while the fluctuations depend on the coefficient law through its fourth cumulant $κ_4$. All our main results are formally verified in Lean 4, and our proof of Erdős Problem #522 has been accepted as a solution to its formal statement in Google DeepMind's Formal Conjectures project.", "title": "Universal Radial Laws for Random Polynomials: Erdős Problem #522 and Non-Universal Fluctuations", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.11324" }, { "age_days": 4, "arxiv_id": "2610.11823", "authors": [ "Tejasvi Singh Tomar" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.11823", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The rank of the tensor of $3\\times 3$ matrix multiplication over the field with two elements is at most $23$ by Laderman's algorithm, and Rudich and Rousseau recently proved that it is at least $22$. We prove that it equals $23$. Hence Laderman's algorithm uses the fewest multiplications among all bilinear algorithms over $\\mathbb{F}_2$ and among all bilinear algorithms with integer coefficients. The proof uses the substitution method in the form developed in recent work of D'Ambrosio, Wang and Yang et al.: a subspace $S$ of the space of first factors contains at most $r-R(S)$ first factors of a decomposition of length $r$, where $R(S)$ is the rank of the tensor modulo $S$. We raise the known lower bounds on $R(S)$ for $111$ of Wang's $496$ symmetry classes of subspaces. One of these bounds, $R(S)\\ge 21$ for a point spanned by a matrix of rank one, forces the $22$ first factors of a decomposition of length $22$ to be distinct. A $27\\times 27$ flattening of the tensor gives further constraints on the ranks of the first factors, and a separate enumeration shows that, when at least $14$ first factors have rank one, no line in a certain orbit of lines contains two first factors. A computer search then lists, up to symmetry, all sets of $22$ matrices that satisfy these constraints, and an exact completion search shows that none of them is the set of first factors of a decomposition. The computation emits certificates, which are checked in the Lean 4 proof assistant by checkers whose soundness is proved in Lean. The largest checks are evaluated as compiled code, so the proof relies on the Lean compiler in addition to its kernel.", "title": "The rank of $3\\times 3$ matrix multiplication over $\\mathbb{F}_2$ is 23", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.11823" }, { "age_days": 4, "arxiv_id": "2610.12030", "authors": [ "Andrea Brunello", "Cristian Curaba", "Luca Geatti", "Michele Mignani", "Angelo Montanari", "Nicola Saccomanno" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12030", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-10-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Large Language Models (LLMs) have renewed interest in autoformalization. Yet, when First-Order Logic (FOL) is considered as the target formalism, the field still lacks a unified task formulation and a systematic survey. This paper addresses this gap: we first provide a principled definition for the FOL-autoformalization task by distinguishing Ontology Extraction from Logical Translation, showing how their conflation obscures (cross-study) evaluation; we review existing datasets, evaluation metrics, and LLM-based methods, including fine-tuning, prompting, and verification-based refinement; we identify open challenges in benchmarking, semantic evaluation, ontology-aware methods, and end-to-end applications.", "title": "Natural Language to First-Order Logic LLM-based Autoformalization", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12030" }, { "age_days": 5, "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": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-10-07", "score": 3.5, "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 1417152 equations in 1889684 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": "2026-10-08", "url": "https://arxiv.org/abs/2610.10248" }, { "age_days": 4, "arxiv_id": "2610.12700", "authors": [ "Qiang Gao" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12700", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-10-08", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "A recent preprint by OpenAI resolved the spherical fermionic Laughlin spectral-gap conjecture for the full $V_1$ interaction by a Fock-space inequality: $H_Q^2\\ge γH_Q$ on the lowest-Landau-level Fock space for all large flux $Q$ and every $γ$ below $0.0461673\\ldots$, so that the gap above the Laughlin state at filling $1/3$ is at least $1/25$. That proof, with its original constant, has also been formalized in Lean. We show that the same argument supports a much larger constant. Two sharper estimates, a product-twirl bound for the three-body tail and a staircase price for the four-body allowance, raise the constant above $0.0601$ without changing the original certificate. Treating the auxiliary operators as the variables of a semidefinite program (SDP) and enlarging the finite set of orbital modes on which they act then gives $H_Q^2\\geγH_Q$ for every $γ<γ_*=0.2190037845063196\\ldots$, certified by exact rational arithmetic. Consequently the gap above the Laughlin state is at least $1/5$ for all sufficiently large spheres, and the untruncated planar $V_1$ Hamiltonian has positive spectrum bounded below by $γ_*$, uniformly in particle number and angular momentum. A heuristic extrapolation of the SDP optima suggests that auxiliary operators of the present form can give at most about $0.222$, while exact diagonalization of finite systems places the true gap near $0.4$. A larger family of auxiliary operators could push the bound further towards the true gap, and the SDP formulation makes such families easy to test. The proof of the improvement and the SDP search were completed by the AI model Claude Opus 5.5 (Anthropic) under the author's direction.", "title": "Improving the lower bound on the Laughlin gap: An SDP search", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12700" }, { "age_days": 5, "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": 5, "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": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:e630960677d2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: `UInt8.isUTF8ContinuationByte` (#15634)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/e630960677d2390570a6a81c73d3e627cc271087" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:8dddb8da755b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: simplify repeated cases on let bound variables (#15636)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/8dddb8da755bb2f253025435ce7a65b460bc62ef" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:80eb4a11e49e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: mark `Char.utf8Size` as inline (#15629)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/80eb4a11e49ebcaa0a5f541fcf0b989915961ee1" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:4b4ede5f438f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: faster `String.push` (#15631)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/4b4ede5f438fe27724eccc8ce001ead3ce75d03f" }, { "age_days": 0, "authors": [ "Joachim Breitner" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:157bd5b80cfc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: reject duplicate object keys in `Lean.Json.parse` (#15628)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/157bd5b80cfc0c5e8b8fa4936a044fc5acb42e08" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:db7f10e90a71", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: normalize `BitVec.ofNat w k` literals with symbolic width in `grind` new normalizer (#15624)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/db7f10e90a71899cfd531a040360b1365f5fd92f" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:caf3cb08d091", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: bv_decide imports under module system (#15635)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/caf3cb08d09110dad5f541c507ed6faedb746c89" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:a6eb9d4f2b77", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support constructors with more than 255 object fields (#15516)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/a6eb9d4f2b77770927e2cf7c6c74829b7e109090" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:6216cc198b26", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: switch releases to use stage2 (#15637)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/6216cc198b26843e792ee07fa80f5288c478f2a9" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover/lean4:f7f7bf42084f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: enable `linter.redundantVisibility` in lean4 (#15553)", "updated": "2026-10-12", "url": "https://github.com/leanprover/lean4/commit/f7f7bf42084fa1242378bf3c73395dc2ea416049" }, { "age_days": 0, "authors": [ "Nailin Guan" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ff787258a3d9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Ideal/Cotangent): make `Ideal.Cotangent` implicit reducible (#43158)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/ff787258a3d97c4079c6dd8906211832dff5a00d" }, { "age_days": 0, "authors": [ "Joseph Myers" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0d7500e26682", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Geometry/Euclidean/Incenter): move to Incenter/Basic (#44772)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/0d7500e26682a081cc80fbf5efa0e7fa24d72c9c" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:dde65624ecc7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(CI): check the PR number in decls-diff against the built commit (#44505)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/dde65624ecc7ebb09c14a4c2d5a13bedc94c939c" }, { "age_days": 0, "authors": [ "Oliver Nash" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4e6064a4a3a6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add alternate constructor for bases of root systems (#43555)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/4e6064a4a3a617a3ba6739b50152b02e4d6ad3ea" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b594c9e734b1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(SimpleGraph/Star): the star graph is the only triangle-free graph with a universal vertex (#41218)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/b594c9e734b10b452544da4681b50e6279b32e85" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8eccd619360a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(SimpleGraph/Coloring/Constructions): `turanGraph n r` is `r`-colorable (#44232)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/8eccd619360a34db3b70877fe3785de84ea1cea5" }, { "age_days": 0, "authors": [ "Gaëtan Serré" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:196a7cca6267", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Monoidal): fix order of arguments (#44543)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/196a7cca62679af383ddad79a91f8b87d47b9075" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e773223b7a9a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Logic/Function/Basic): add `Injective.existsUnique_iff_exists` (#43795)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/e773223b7a9ad921948f71a66614a520ac5c7011" }, { "age_days": 0, "authors": [ "Jakub Štepo" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1afbf2aa6325", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/Hasse): more properties of Hasse graphs of linear orders (#40728)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/1afbf2aa63258589e575eca6d06bf10bd62a3018" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:69fa9d75e94c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Limits): commutation of limits and colimits (#43977)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/69fa9d75e94c9a7cd518829a3fb26524b670e602" }, { "age_days": 0, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:56557d86ab23", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AffineSpace): exists affinely independent set of a cardinality dim + 1 (#43910)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/56557d86ab23b9c4a2982a2d9d21dd4fde7dd02a" }, { "age_days": 0, "authors": [ "Justus Springer" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9454a4c25a2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(*): add missing bib entries for keys (#44767)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/9454a4c25a2b923eb55dba3098f2d6ae0484d09b" }, { "age_days": 0, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fad34067088f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: replace `{a a : α}` with `{a : α}` in `variable`s (#44739)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/fad34067088f101a9a302d9393aacbffa190694c" }, { "age_days": 0, "authors": [ "Keith Adler" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:715a03a90adf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename four lemmas named `sub` that state `+` (#44777)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/715a03a90adf491de40fbec8b456c179a623435f" }, { "age_days": 0, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e7dbfbe916d3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove unnecessary set_option lines (#44785)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/e7dbfbe916d30f3f261cee4622102b2fffea4ca3" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:54c01c3314d3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RepresentationTheory/Basic): automated extraction from #44776 (#44780)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/54c01c3314d33d15d77893cbe4e0472ff26bb34d" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1ce668c19c4f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(GroupTheory/Commutator/Basic): golf some proofs (#44193)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/1ce668c19c4f4d6810db48ede3b86734f7f52618" }, { "age_days": 0, "authors": [ "Joseph Myers" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:48192e08dfcf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Geometry/Euclidean/Incenter): `deprecated_module` for #44772 (#44781)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/48192e08dfcf79f1ff190f1762d1e3b617f7138f" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9bb8be11d7e9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/Cones): automated extraction from #44765 (#44792)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/9bb8be11d7e995aaee9ff31050708f32293fdaa2" }, { "age_days": 0, "authors": [ "Justus Springer" ], "content_date": "2026-10-12", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8018a6565e36", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-12", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Group/Pointwise/Set/SelfInv): put into lemmas into Set namespace (#43792)", "updated": "2026-10-12", "url": "https://github.com/leanprover-community/mathlib4/commit/8018a6565e366597e5f20d4c3deded3f4441b1dc" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:fe2da218b955", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep a `Prop` hypothesis when `grind` applies eager `cases` to it (#15612)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/fe2da218b955ca5219f04e9e9a696bab7bc26f0f" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:2bbdc293f6ca", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: generate a script for every goal in `grind?` when parameters split the goal (#15611)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/2bbdc293f6ca050a67ebc7ec2a8250d571482a9c" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:1aacc7a9b6de", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: drop metadata on the arithmetic spine in the `Sym.Arith` normalizer (#15619)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/1aacc7a9b6de1cf33bc7e0b0ba0505ddc12417fd" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:12ae34c29a6b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: canonicalize class fields that are not global instances in `Sym.canon` (#15618)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/12ae34c29a6b5df76fc2641ae1671784c19f527f" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:29a05d3f4d38", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: simplify propositional binder domains in `Sym.simp` (#15623)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/29a05d3f4d389f648aaa9d640092f59169047a65" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover/lean4:0ec09562d639", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add a few more BitVec terms to bv_decide (#15616)", "updated": "2026-10-11", "url": "https://github.com/leanprover/lean4/commit/0ec09562d6398d0fab6ed92a696f03d0837ae725" }, { "age_days": 1, "authors": [ "Keith Adler" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:591130056fe5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(Data/DFinsupp,Order/Preorder/Finsupp): make `coe_strictMono` state `StrictMono` (#44705)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/591130056fe555daaae6fa337f3a19e0d7c846c2" }, { "age_days": 1, "authors": [ "Keith Adler" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d6416ab0f09d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(AlgebraicTopology/ModelCategory): state `homEquivLeft_symm_apply` about `homEquivLeft` (#44703)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/d6416ab0f09d3a2e090f403fc80f37754f6181a9" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1619863c2b37", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add `ContMDiffWithinAt.contMDiffWithinAt_tangentMapWithin` and friends (#44710)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/1619863c2b37930e217c20c40ea1e3ce0cc78500" }, { "age_days": 1, "authors": [ "Weiyi Wang" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:021c46bdd042", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FieldTheory): field equivalences for bot subfield (#41909)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/021c46bdd042f67b538b9f9871d556a93713a9a9" }, { "age_days": 1, "authors": [ "Yaël Dillies" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a78af439fb34", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/{ENat,ENNReal,EReal}): missing coercion lemmas (#41101)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/a78af439fb3422dbd6528baf0747ede0193ca629" }, { "age_days": 1, "authors": [ "Justus Springer" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:be54e3f266c1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: fix references.bib keys whose year does not match the entry (#44758)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/be54e3f266c15cb52e61d18debe1a95fdc854954" }, { "age_days": 1, "authors": [ "Justus Springer" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:40130aac5fa6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(*): use existing citation keys for free-text citations (#44673)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/40130aac5fa6beb6ca371ee462d239d5e89138dc" }, { "age_days": 1, "authors": [ "Yaël Dillies" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:939d5d5d9e6f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: use the `Finset.card` notation more widely (#44638)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/939d5d5d9e6f07d1d8c80a16fa3fa39a7518b716" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:051bc081081f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/SuccPred/Relation): use `to_dual` (#44412)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/051bc081081f2bb77b81d47ee69146c4cef28bbe" }, { "age_days": 1, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-10-11", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:feefa3237dfe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-11", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Matrix/DualNumber): automated extraction from #44776 (#44779)", "updated": "2026-10-11", "url": "https://github.com/leanprover-community/mathlib4/commit/feefa3237dfed481db898e96db56d47f6f992c15" }, { "age_days": 2, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:07c4dc383411", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: share error and promise helpers in the libuv bindings (#15594)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/07c4dc383411a38473a390bd4351d184a43efecc" }, { "age_days": 2, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:50541c319404", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: embed libuv handles in the uv socket, timer and signal objects (#15545)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/50541c3194040b253c3e835340683227a5c462f0" }, { "age_days": 2, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:ca7a383af084", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: add RAII-based scoped lock guard (#15547)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/ca7a383af084133dcf631c6b4db41d4ed958bfab" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:62801e856156", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: validate `finish?` suggestions at the goal before its parameters are asserted (#15606)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/62801e856156a7485568696a868d3b4b49ec1e7c" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:d285f8dd8efc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: queue solver callbacks replayed during `grind` internalization (#15599)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/d285f8dd8efc8f29d839ce91fd1a15beb8751761" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:d77ee81096a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: preserve `inj` and `funCC` parameters in `grind?` and `finish?` suggestions (#15602)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/d77ee81096a7ffc43952454127ec4699b1125a8f" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:825446302d83", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: compare instances at `.implicit` transparency in `isDefEqI` (#15600)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/825446302d837108227daa4e7c345a90957bb844" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:9f9ee910ae84", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: assert non-indexable ground theorems as facts in `grind` parameters (#15609)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/9f9ee910ae84a732bb1a7a745b35d84502fd63c8" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-10-10", "freshness": "fresh", "id": "github:leanprover/lean4:b8182f642813", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: lake: clear IR artifacts before `leanir` (#15570)", "updated": "2026-10-10", "url": "https://github.com/leanprover/lean4/commit/b8182f6428135d8de524313001fffe7434bfacad" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "github:leanprover/lean4:5e96ee1153f9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: reuse the goal's WP instance when building vcgen spec rules (#15555)", "updated": "2026-10-09", "url": "https://github.com/leanprover/lean4/commit/5e96ee1153f945234f126ed024043a0697c9d6f3" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "github:leanprover/lean4:7cd10322fcb4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: missing zero check when propagating implied equalities in `grind ring` (#15589)", "updated": "2026-10-09", "url": "https://github.com/leanprover/lean4/commit/7cd10322fcb4c2f4fd3827c9082422a49ac2dd1f" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "github:leanprover/lean4:b70afe029893", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: evaluate `cond` lazily in `cbv` (#15582)", "updated": "2026-10-09", "url": "https://github.com/leanprover/lean4/commit/b70afe0298938afe3c8354b045103ef2ce52957d" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "github:leanprover/lean4:c1f2fc66e14c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: builtin component instances in the `grind` canonicalizer (#15588)", "updated": "2026-10-09", "url": "https://github.com/leanprover/lean4/commit/c1f2fc66e14cf8632e9dd0e0702d407fdc67b9c6" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "github:leanprover/lean4:d10dc23fa535", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-10-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: guard WP.Frames by the ambient precondition (#15497)", "updated": "2026-10-09", "url": "https://github.com/leanprover/lean4/commit/d10dc23fa5351c1d09cfccb7ae4609fdd9f83806" }, { "age_days": 3, "arxiv_id": "2610.13940", "authors": [ "Ahmed Bou-Rabee" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13940", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In the abelian sandpile model on $\\mathbb{Z}^d$, a site with at least $2d$ grains topples by sending one grain to each neighbor. In a box $[-L,L]^d$ whose boundary absorbs grains, adding grains at random sites and toppling defines a Markov chain, and Athreya and Járai (2004) constructed the stationary state on $\\mathbb{Z}^d$ as the limit of its stationary distributions as $L\\to\\infty$. By a formula of Dhar (1990), when a grain is added at the origin of a sandpile in the stationary state, the expected number of topplings at a site in the resulting avalanche is proportional to the Green function of simple random walk from the origin. This Green function is finite for $d\\geq3$, where Járai and Redig (2008) proved that avalanches are almost surely finite, and infinite for $d=2$. We prove that for $d=2$ avalanches are nevertheless almost surely finite: the probability that an avalanche reaches distance $R$ is at most a negative power of $\\log R$. The proof follows the avalanche backward and reduces the question to an estimate for the uniform spanning tree, which we prove by a multiscale electrical argument.", "title": "Sandpile avalanches in two dimensions are finite", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13940" }, { "age_days": 3, "arxiv_id": "2610.12831", "authors": [ "Alex Burgin", "Anastasios Fragkos", "David Kruzel", "Michael Lacey", "Amelia Stokolosa" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.12831", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Given an integer $k \\geq 2$ and a prime $p$ large enough depending on $k$, we show that, if $A \\subseteq \\mathbb F^n_p$ does not contain a restricted polynomial progression of the form \\begin{align*} x, x+\\begin{pmatrix} y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n \\end{pmatrix}, x+\\begin{pmatrix} y_1^2 \\\\ y_2^2 \\\\ \\vdots \\\\ y_n^2 \\end{pmatrix}, \\ldots, x+\\begin{pmatrix} y_1^{k-1} \\\\ y_2^{k-1} \\\\ \\vdots \\\\ y_n^{k-1} \\end{pmatrix}, \\end{align*} where $x \\in \\mathbb F^n_p$ and $y \\in \\{0,2, 3, \\ldots, M_k\\}^n \\backslash \\{\\vec{0} \\}$, for some fixed $M_k$, then $A$ must have density bounded above by $\\frac{C}{(\\log^{(k^{O(k)})} n)^c}$, where $C, c>0$ only depend on $k$ and $p$. For $k\\geq 4$, the best previously known bound came from the density Hales--Jewett theorem and was of inverse Ackermann type. The proof uses a recent inverse theorem for noise stability of Bhangale, Khot, Liu and Minzer, which arose in the study of constraint satisfaction problems. The main new ingredient is a proof that the underlying distribution counting restricted polynomial progressions does not admit a nontrivial abelian embedding.", "title": "Reasonable bounds for Restricted Polynomial Progressions in $\\mathbb F^n_p$", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.12831" }, { "age_days": 3, "arxiv_id": "2610.13717", "authors": [ "Aravind Reddy", "Deeraj S K", "Mohd Wasif Raza", "Saurav Prakash" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13717", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Federated clustering can support applications such as patient stratification across hospitals and customer segmentation across distributed financial datasets. Responsible AI calls for fair representation of demographic groups and support for data deletion, motivated in part by rights such as the GDPR's right to erasure. These goals interact: deleting records can change the balance between groups and alter the clustering of the remaining population. We study exact machine unlearning for federated socially fair $k$-means, whose objective is to minimize the largest group-average squared distance to the nearest center. Our approach keeps separate local summaries for each group, so summaries at unaffected institutions remain valid as global fairness weights change. For two groups, we prove an initialization approximation guarantee independent of client group proportions under ideal sampling, and we show that same-seed replay reproduces retraining exactly. Reuse pays off most when a whole client withdraws: across three datasets, replay is $35.8\\times$ faster than retraining for the initialization-only model and remains $2.4\\times$ and $1.7\\times$ faster with one and two fair-refinement rounds, which improve worst-group cost. For individual record deletions, gains are modest (about $1.06\\times$), and certifying cached assignments can cost more than it saves. These results map where exact unlearning can profitably reuse computation. Code and reproducibility materials are available at https://github.com/arareddy/mufsc.", "title": "Machine Unlearning for Federated Socially Fair k-Means Clustering", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13717" }, { "age_days": 3, "arxiv_id": "2610.13924", "authors": [ "Tianyi Wu" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13924", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A parallel sampler can choose at random which coordinates to generate together. For a target $p$ and the output law $q_U$ of a schedule $U$ drawn afresh for each output, we compare the schedule-averaged divergence $\\mathbb{E}_U D_{\\mathrm{KL}}(p\\|q_U)$ with the output-law divergence $D_{\\mathrm{KL}}(p\\|\\mathbb{E}_U q_U)$, in nats. Rounds commit independent draws from exact conditional marginals frozen at the round's start, each output's schedule is drawn before sampling from a finite mixture of schedules, and every scheduled round is charged. For the uniform distribution on binary strings of even length $n$ with $n/2$ ones, the least expected number of rounds at a fixed tolerance $\\varepsilon>0$ is $Θ_\\varepsilon((\\log n)^2)$ under the first criterion but $(e^{-\\varepsilon}+o(1))\\log_2\\ln n$ under the second, and the double-logarithmic order is attainable with the same round count on every run. For this target, a count-state recursion gives the exact least output divergence at every round cap over all causal randomized policies. The separation extends to weighted fixed-count targets with bounded weight ratios and quota fractions bounded away from zero and one, without permutation symmetry, and to the full-support Beta$(1,1)$--Bernoulli target, where the sharp expected cost under the output-law criterion is $(e^{-\\varepsilon}/2+o(1))\\log_2\\log_2n$, attained with rare $n$-round runs. Prior work implies the order of the schedule-averaged cost on the balanced target and its $O_\\varepsilon((\\log n)^2)$ upper bounds on both extensions.", "title": "KL Before and After Mixing: A Round-Complexity Separation in Parallel Sampling", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13924" }, { "age_days": 3, "arxiv_id": "2610.13100", "authors": [ "Tejasvi Singh Tomar" ], "content_date": "2026-10-09", "freshness": "fresh", "id": "arxiv:2610.13100", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove that for every choice of five positive masses the planar five-body problem has finitely many central configurations up to similarity. This settles Smale's sixth problem for five bodies in the plane. Albouy and Kaloshin proved it for masses outside a closed algebraic subset of codimension two. We follow their method. Infinitely many central configurations would give an algebraic curve of complex solutions. At the places at infinity of the curve the valuations of the mutual distances must balance. We determine the possible valuation vectors at all positive masses, together with the mass conditions under which each can occur. We treat limits in which four bodies form a cluster of zero potential energy by expanding the potential, which is constant along the curve, at a place. This excludes, at every positive mass, one of the two diagrams in which such clusters occur, and part of the other. The same expansion excludes one further diagram at every positive mass. What remains is an exact analysis, by computer algebra, of the sets of mass conditions that can hold together at positive masses. Exact rational certificates show that the balance fails under each of them, except on a few one-parameter families of masses, which we treat separately. On the rays through $(1,4,4,4,4)$ and $(1,1,4,4,4)$ the certificates do not apply. On the first ray they cannot apply: there the complex equations have a continuum of solutions, as Albouy and Kaloshin observed. On these rays we count the real central configurations: there are 306 and 294 up to orientation-preserving similarity. The certificates, the programs that check them and a proof of the theorem in the Lean proof assistant are available.", "title": "Finiteness of planar central configurations of five bodies for all positive masses", "updated": "2026-10-09", "url": "https://arxiv.org/abs/2610.13100" }, { "age_days": 4, "arxiv_id": "2610.12234", "authors": [ "Baiying Liu" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12234", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Recently, a uniform $\\frac{7}{8}$ zero-free half-plane for finite-order Hecke $L$-functions over $\\mathbb Q(\\sqrt{-3})$ and its transfer to Dirichlet $L$-functions was given by OpenAI in [1]. In its proof, there are two chosen parameters $b=\\frac{1}{8}, \\ell=\\frac{1}{6}$. In this note, via varying $b$ and $\\ell$, following the same strategy, we slightly improve the bound $\\frac{7}{8}=0.875$ to be $$B_{\\mathrm r}=\\frac{34999}{40000}=0.874975, (\\text{when }b_{\\mathrm r}=\\frac{1}{8}, \\ell_{\\mathrm r}=\\frac{1}{6} + \\frac{1}{10000});$$ and \\[ \\begin{gathered} B_{\\mathrm{new}}=\\frac{1507-2\\sqrt{921}}{1653} =0.874957069799\\ldots, (\\text{when }b_{\\mathrm{new}}=-\\frac{4}{29}+\\frac{230\\sqrt{921}}{26709}, \\ell_{\\mathrm{new}}=\\frac{33+8\\sqrt{921}}{1653}). \\end{gathered} \\] This result has been formalized by Lean ([15]).", "title": "Slightly improved zero-free half-planes for the quasi-Riemann hypothesis", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12234" }, { "age_days": 4, "arxiv_id": "2610.12168", "authors": [ "Lars Simon", "Holger Eble", "Manuel Radons" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12168", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.", "title": "Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12168" }, { "age_days": 4, "arxiv_id": "2610.11879", "authors": [ "Scott Armstrong", "Benny Avelin", "Tuomo Kuusi", "Aatu Turpeinen" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.11879", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We extend the theory of De Giorgi-Nash-Moser to elliptic equations with symmetric coefficients $\\mathbf{a}(x)$ which are possibly degenerate and unbounded but satisfy a coarse ellipticity condition. We prove local upper bounds for weak subsolutions, a weak Harnack inequality for nonnegative supersolutions, and a Harnack inequality for nonnegative solutions. The coarse ellipticity hypothesis requires spatial moments of coarse-grained matrices, suitably discounted and summed across scales, to be finite. In particular, it holds if, for some $α,β\\geq0$ and $10$. For $α=β=0$, it corresponds to the results of Bella and Schäffner [8].", "title": "Coarse ellipticity and De Giorgi-Nash-Moser theory in the optimal range", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.11879" }, { "age_days": 4, "arxiv_id": "2610.12335", "authors": [ "Scott Armstrong", "Ahmed Bou-Rabee", "Tuomo Kuusi" ], "content_date": "2026-10-08", "freshness": "fresh", "id": "arxiv:2610.12335", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We study a Brownian particle in $\\mathbb{R}^d$, $d\\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The proof uses a renormalization group induction: at each scale, the elliptic operator is well approximated by a Laplacian with effective diffusivity decaying as a power of scale. We compute this exponent exactly in dimension two.", "title": "Anomalous scaling limit of a Brownian particle in a log-correlated potential", "updated": "2026-10-08", "url": "https://arxiv.org/abs/2610.12335" }, { "age_days": 5, "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": 5, "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": 5, "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": 5, "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": 5, "arxiv_id": "2610.11014", "authors": [ "Hanyue Shen", "Pavel B. Dubovski" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.11014", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-10-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We determine the minimum volume product of centrally symmetric polytopes obtained by adding facet apices to a cube while fixing their total outward height. Heights and tangential coordinates vary subject to a product condition on the polar-cap denominators. In every dimension at least two, the minimum has an explicit formula, attained by concentrating the height at one opposite pair of corner apices. For positive height in dimensions at least three, every minimizing array has this structure. The product condition strictly extends coordinatewise quadratic constraints. We also obtain two bounds without that condition: a four-dimensional Mahler bound for a specified height range, and a correction measuring volume generated jointly by two apices. The latter certifies a continuous family outside the preceding sufficient conditions. The proof combines known cap volumes with a sharp aggregate height estimate and a double-pyramid construction. Lean~4 verifies the actual-volume minimum, the necessary equality structure and both extensions.", "title": "A sharp minimum for cube-apex bodies in every dimension", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.11014" }, { "age_days": 5, "arxiv_id": "2610.10673", "authors": [ "Alfredo Guevara" ], "content_date": "2026-10-07", "freshness": "fresh", "id": "arxiv:2610.10673", "kind": "paper", "label": "negative", "matched_signals": [ "negative:vision_world_models" ], "published": "2026-10-07", "score": -2.5, "source": "arxiv-ai4math-core", "summary": "We argue that the scattering amplitude of a single minus helicity gluon with arbitrarily many positive helicity gluons is topological. The amplitude is constant in chambers of kinematic space, its resonances are located at walls and its factorization is determined by wall-crossing. Yangian invariance dictates the amplitude to be determined by a 2d null Wilson loop that can be lifted into a positive and transverse 3d link. By reinterpreting wall-crossing and the Weinberg soft theorem as skein relations and Reidemeister moves of the subknots, we construct a state-counting description consisting of adding the `corners' of their HOMFLY-PT polynomials. Beyond the classical limit, we argue that this provides a conjectured but precise connection to topological field and string theory. The new formula is rigorously derived via a Lean-formalized dependency graph (DAG) as detailed in a companion paper, laying out the precise assumptions including Reidemeister III invariance. It is further tested exhaustively, including novel `star' kinematics where the amplitude and state count are shown to become Catalan numbers, in agreement with knot theory literature.", "title": "Gluons and Knots", "updated": "2026-10-07", "url": "https://arxiv.org/abs/2610.10673" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }