arXiv:2606. 06136v1 Announce Type: cross Abstract: We prove the positive-real $n=9$ case of the Vasc cyclic inequality.
arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.
arXiv:2606. 03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$.
arXiv:2606. 15096v1 Announce Type: new Abstract: The Riemann Hypothesis remains one of the central unsolved problems in mathematics.
arXiv:2609.00706v1 Announce Type: new Abstract: The SAIR Mathematics Distillation Challenge on Equational Theories asks a solver to classify whether one magma identity implies another and, for either...
arXiv:2607.00815v2 Announce Type: replace-cross Abstract: If the certificate produced by a SAT solver is checked by a verified checker, we get a verdict which convinces. But this verdict cannot be na...
The paper addresses the asymmetry in verifying optimality claims for synthesis pipelines, distinguishing between the upper bound (existence of a program) and the lower bound (non-existence of a smaller program). It introduces a pipeline that synthesizes minimal linear straight‑line programs over GF(2) and produces DRAT proofs for every UNSAT result, thereby closing the so‑called refutation gap for 121 previously uncertified optimality claims. The authors report that the median proof size is 1.1 MB, checking takes 1.9× the solving time, and that their verification process uncovered defects missed by code review, highlighted interface obstacles, and exposed a budget‑related audit failure.
arXiv:2609.39123v1 Announce Type: new Abstract: When optimizing an expensive black-box function sequentially, as in hyperparameter optimization, we may want to stop once the best evaluated value is c...
arXiv:2607. 00815v1 Announce Type: cross Abstract: SAT solvers settle combinatorial problems beyond the reach of interactive theorem provers and produce LRAT certificates for independent verification.
arXiv:2606. 23858v1 Announce Type: cross Abstract: A primary challenge in AI safety is the existence of adversarial examples -- slightly distorted inputs that cause a neural network (NN) to misclassify.
The paper investigates the reliability of machine‑parsed statutes by developing a passive survival certificate for the Duquenne‑Guigues implication basis of extracted legal contexts. It measures inter‑extractor disagreement, runs 1,000 Monte‑Carlo trials, and certifies an implication only when a one‑sided Wilson 95% lower bound on survival reaches 0.95, providing premise spans and minimal counterexamples. Applied to 29,365 Missouri sections and 502 Indian central‑Act sections, the method passes a held‑out gate for many statute families, yet a global error model shows that 93.2% of held‑out chapters fall below the informativeness floor, attributing this to calibration‑rate transfer rather than selection bias.
arXiv:2606. 13473v1 Announce Type: cross Abstract: We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series.
arXiv:2606. 07316v2 Announce Type: replace-cross Abstract: Can a committee of LLM agents reach agreement that is certifiable at the level of meaning, not only at the level of a label?