{
  "counts": {
    "adjacent": 13,
    "core": 5,
    "errors": 0,
    "negative": 71,
    "total": 89
  },
  "date": "2026-08-29",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-29T18:46:52Z",
  "items": [
    {
      "age_days": 3,
      "arxiv_id": "2608.25449",
      "authors": [
        "Jiaxin Yuan",
        "Connor Martinez Lockhart",
        "Xiaoyu Liu",
        "Jiaqi Wang",
        "Chenghao Deng",
        "Xiayimei Han",
        "Vlasios Mastrantonis",
        "Dmitrii Gudin",
        "Shaopeng Zhu",
        "Abdirisak Abdullahi Mohamed",
        "Bilal Hamdi Aytekin",
        "Jiewen Lang",
        "Zezheng Song",
        "Furong Huang"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.25449",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-26",
      "score": 7.9,
      "source": "arxiv-ai4math-core",
      "summary": "Formal theorem proving enables machine-verifiable evaluation of mathematical reasoning, yet existing benchmarks often emphasize aggregate proof accuracy, concentrate on a narrow range of mathematics, and provide limited evidence of robustness to equivalent reformulations. We introduce MathAdv, a diagnostic benchmark spanning 13 domains across undergraduate- and graduate-level mathematics. Alongside Lean 4 theorem proving, MathAdv provides up to three auxiliary tasks: multiple-choice questions that probe mathematical knowledge, fill-in-the-blank problems that isolate informal reasoning, and expert-crafted transformations that test robustness to problem presentation. Our evaluation of contemporary theorem provers yields four findings: formalization remains a major bottleneck; performance varies substantially across mathematical domains; natural-language guidance helps general-purpose LLMs but can hinder proof-specialized models; and mathematically equivalent reformulations expose substantial robustness limitations. Together, these results show how component-wise evaluation can reveal model capabilities and failure modes that aggregate theorem-proving accuracy obscures. The dataset and evaluation scripts are available at https://github.com/margotyjx/MathAdv.git.",
      "title": "MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.25449"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26334",
      "authors": [
        "Wenqian Ye",
        "Ziwei Guan",
        "Eric Xie",
        "Bohan Liu",
        "Shivani Modi",
        "Buyun Zhang",
        "Ellie Dingqiao Wen",
        "Henry Kautz",
        "Aidong Zhang"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26334",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-26",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Automated theorem proving offers a natural foundation for recursive self-improvement in scientific discovery. However, existing neural provers do not fully preserve this recursive structure, where the learning process should be self-improving over time. Existing methods either embed proof experience into model parameters through expensive weight updates, or keep verified intermediate deductions only within the current problem. In addition, these methods also heavily rely on sparse whole-proof feedback, even when unsuccessful partial attempts contain useful discoveries. To close the gap, we propose ProofEvolve, a neuro-symbolic framework that evolves explicit, formally verified symbolic proof structures with neural models to decisively expand the knowledge boundary. In this framework, the neural model proposes variation operators, including decompositions, repairs, and schema recombinations. The symbolic Lean kernel verifies every proof transition. Over the evolution loops, ProofEvolve computes verified closure over the resulting proof directed acyclic graphs (DAGs). Within each problem, ProofEvolve evolves partial AND-OR proof DAGs in a behaviorally indexed archive. Across problems, kernel-checked schema extraction adds newly proved sub-DAGs to a persistent schema library. Proof DAGs inherit the solved results through typed schema recombination, with every residual premise exposed as a new subgoal. This evolutionary process preserves verified results from incomplete attempts and makes them available for later proofs without weakening formal soundness. Across three competition-level Lean benchmarks, ProofEvolve achieves the highest average solve rate among the evaluated proof systems.",
      "title": "ProofEvolve: Neuro-Symbolic Evolution for Formal Automated Theorem Proving",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26334"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.25117",
      "authors": [
        "Hwei-Shin Harriman",
        "Wode Ni",
        "Yuchen Jin",
        "Dominik Moritz",
        "Joshua Sunshine"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.25117",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-25",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Geometric proof is a foundational yet challenging topic in mathematics, requiring students to integrate visual, logical, and notational skills. While technology has enhanced learning in other mathematical domains, its impact on geometric proof remains limited. To investigate this gap, we interviewed 18 geometry teachers to establish the technical requirements of educational proof tools. These requirements inform our review of 33 commercial and research tools. Our findings reveal a critical mismatch: while teachers value certain digital tools for initial planning and exploration activities, they revert to pen-and-paper for formal proof because it supports diagram annotation and provides space for multiple approaches to proof-solving. Annotating the diagram is a key component of the proof-solving workflow that existing tools do not support. We propose four technical and human-centered design guidelines for educational proof tools to meet teacher needs at scale: integrating diagram and proof, generating problems and feedback automatically, supporting multiple proof formats, and reducing accidental complexity in the user experience.",
      "title": "Teaching Geometric Proof with Tech: Pitfalls and Possibilities",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.25117"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23281",
      "authors": [
        "Ludovic Tagnon"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23281",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-24",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Hermite asked in 1848 for a representation of real numbers whose eventual periodicity characterizes cubic irrationals. The totally real case was solved by Karpenkov's $\\sin^2$-algorithm; the complex case, signature (1,1), is his Problem 4. We study a deterministic algorithm implementing his suggested analytic extension: the score expression is strictly negative on (1,1) data (closed form proved), the most negative score is selected, and exact score ties are resolved by a declared ordering. On a sample of 205 complex cubic polynomials, every run closes projectively with an exact unit certificate, each transition certified by exact comparisons in $\\mathbb{Q}(α)$. An exhaustive campaign over the full box $[-3,3]^3$ closes 194/194. Across 457 deformed bases, the terminal cycle is an invariant of the marked lattice. Certified finite transition graphs are computed for four fields; the plastic case is machine-checked in Lean 4, kernel-only. All data ship in a public archive with a portable verifier.",
      "title": "A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23281"
    },
    {
      "age_days": 8,
      "arxiv_id": "2608.20793",
      "authors": [
        "Sihai Jin"
      ],
      "content_date": "2026-08-21",
      "freshness": "fresh",
      "id": "arxiv:2608.20793",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-21",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "We report a Lean 4 formal verification accompanying the paper \"Subregular Affine Cells and the Level -1 Vertex Algebra of Type D\" (arXiv:2608.11997). The formalization kernel-checks substantial internal parts of the proof architecture, including the Section 4 membership/descent chain, the type-D norm-gap argument, zero-orbit energy and signed-permutation rigidity, node-weight and numerical rigidity calculations, the exhaustion logic, the passage to the candidate quotient classification, the simple-object count, the final additive Grothendieck-group comparison, and the coefficient-substitution layer of the uniform character formula. Higher representation-theoretic results whose foundational infrastructure is not presently constructed in the file are isolated as explicit semantic interfaces rather than introduced as Lean axioms. Thus the precise claim is a kernel-checked internal deduction from explicit representation-theoretic boundary inputs, not a from-scratch formalization of vertex algebras, BRST reduction, finite W-algebras, or affine Hecke theory inside Mathlib.",
      "title": "A Lean 4 Verification Report for Subregular Affine Cells and the Level $-1$ Vertex Algebra of Type $D$",
      "updated": "2026-08-21",
      "url": "https://arxiv.org/abs/2608.20793"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.27451",
      "authors": [
        "Chiké Abuah"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "arxiv:2608.27451",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-27",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Empirical comparisons between systems are a standard form of evidence in computer science research, but few are checked for statistical validity: most are never framed as statistical tests at all. Existing multiple-comparison procedures could control the resulting error, but need inputs (what an analysis examined, and how its observations are arranged) that are not recoverable from a list of p-values. We introduce Tacet, a language in which an analysis declares what it generated, states what it expects to find, and is refused any claim it cannot afford or cannot properly test. Its core calculus T pairs a free estimation sublanguage, carrying a reported footprint and a purity bit that records whether any outcome was consulted in building a value, with a priced claim sublanguage, carrying a wealth transformer, connected only by a mechanism that prices a comparison. A sample selected by reading outcomes sets the purity bit and is recorded as having examined everything it read, permanently, so it can never be granted a one-sided or confirmatory price, without the system ever asking whether the analyst intended to cherry-pick. Whether a comparison is paired or clustered is computed statically from the artifact schema, from declared functional dependencies between key fields alone and before any data is read, and a mechanism that assumes that structure away is refused rather than priced. Because the wealth transformer is antitone in the realized p-value, affordability can be checked before the analysis runs too, turning pre-registration into a typing rule. We prove the metatheory machine-checked in Lean 4 with no admitted gaps, and demonstrate the approach on a reference implementation and two case studies on published artifacts, the SWE-bench Verified leaderboard and BIG-Bench Hard.",
      "title": "Tacet: A Language and Type System for Automatic Statistical Validity Accounting",
      "updated": "2026-08-27",
      "url": "https://arxiv.org/abs/2608.27451"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.27321",
      "authors": [
        "Floris van Doorn",
        "Polona Durcik",
        "Joris Roos",
        "Lenka Slavíková",
        "Christoph Thiele"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "arxiv:2608.27321",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-27",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "This blueprint serves as a companion to a forthcoming, shorter traditional mathematical paper. The purpose of this blueprint is two-fold: first, it has served as the foundation for a formalization in Lean 4 of these results. This formalization has been completed largely automatically, making essential use of current frontier large language models. Second, it will serve as a resource to readers of the main paper who are interested in further technical details of the proofs. The main result concerns norm-variation estimates for multiple ergodic averages associated with $n\\ge 2$ commuting measure preserving transformations, providing a quantitative strengthening of Tao's norm-convergence theorem and answering an open question of Avigad and Rute. At the core of the analysis lies an explicit real-variable estimate for twisted multilinear averages that is closely related to certain singular Brascamp--Lieb inequalities.",
      "title": "A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations",
      "updated": "2026-08-27",
      "url": "https://arxiv.org/abs/2608.27321"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.25057",
      "authors": [
        "Dakota Charles Baker"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.25057",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-25",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "A point lies in the kernel of a polygon if it can see the entire polygon. Thus the kernel measures how much of the polygon is available to a single guard, while the convex hull measures how far the polygon is from being convex. We prove that these two losses are linked by a sharp factor of two: the area lost between a polygon and its kernel dominates twice the kernel-weighted area missing from the polygon's convex hull. In terms of Sibley's guard-point ratio $G$ and exterior ratio $E$, which we denote by $A$, the result is $G \\leq A/(2-A)$, which improves Nakano's inequality $G \\leq A$ whenever $A < 1$. The proof passes through a convex-body cap union. From a compact convex body $K$ and finitely many points whose convex hull contains it, we join every point to $K$ and take the union $U$ of the resulting caps. Cyclically sorting the directed boundary edges of a polygonal $U$ produces a convex companion $H$. A boundary-reversal argument gives $|H| + |U| \\geq 2|\\mathrm{conv}\\, U|$, while a support-function identity and Minkowski's mixed-area inequality give $|U|^2 \\geq |K||H|$. Inner polygonal approximation handles every positive-area compact convex $K$, while a separate null-area branch covers points, segments, and all other lower-dimensional cases. Both main theorems have machine-checked Lean 4 proofs whose final statements were audited against the informal statements after kernel checking.",
      "title": "The Kernel Deficit Dominates Twice the Hull Deficit: A Sharp Strengthening of Nakano's Inequality",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.25057"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.25194",
      "authors": [
        "Ashutosh S. Jogalekar"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.25194",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-25",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "RNA inverse folding asks for an RNA sequence whose prescribed secondary structure is the unique maximum-base-pair compatible fold. In the four-letter Watson-Crick model (A-U and C-G pairs only, no pseudoknots, and zero minimum base-pair span), Hales et al. introduced a separated-coloring certificate and an even-odd device, while Boury et al. generalized this to modulo-$m$ separability, gave an $O(n 2^m)$ decision algorithm, and guaranteed designability when every helix has length at least 3. We prove that the guarantee still holds when a motif-free target has at most two maximal helices of length 2, no maximal helix of length 1, and all remaining helices of length at least 3. The proof builds on Boury et al.'s local helix-coloring transfers and adds a global counting argument showing that the demands created by at most two short helices can always be coordinated. This is a structural success guarantee for the existing modulo-2 algorithm, not a new general decision capability. The resulting coloring yields an explicit sequence whose every distinct compatible noncrossing fold has fewer pairs. No claim is made for nearest-neighbor thermodynamic energy models. The theorem and supporting lemmas are formalized in Lean 4 against pinned Mathlib and reproduced from a frozen public artifact; the kernel-reported axiom set is $\\{\\mathrm{propext},\\mathrm{Classical.choice},\\mathrm{Quot.sound}\\}$. The work was developed with foundational generative-AI assistance under the author's direction and has not yet received independent human expert review.",
      "title": "Designability of RNA Targets with Up to Two Length-2 Helices",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.25194"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.24750",
      "authors": [
        "Ludovic Tagnon"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.24750",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-25",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We develop the structure theory of the deterministic $\\sin^2$-type algorithm for complex cubic fields introduced in the companion paper, addressing the complex-signature case of Karpenkov's Problem 4. The selection rule is shown to be, exactly, the minimization of a conformal module: the hyperbolic cosine of the distance between the transverse complex structure of the state and the round point. All governing quantities are exact elements of the real embedding of the field and satisfy closed dual-type identities; in particular no isotropic candidate ever arises, and the transverse deviation lattice has exactly pinned covolume. We prove an unconditional soft-rebound lemma (the module can grow by at most the factor $\\varphi^2 = 2.618\\ldots$ in one step), a finiteness theorem for states of bounded module and height at fixed coordinate discriminant, with explicit static constants, and a per-field periodicity theorem under two named hypotheses: $(C_κ)$, contraction of the module in the high phase, partially reduced here to a fixed finite minimax over a five-parameter compact with rational objective; and (B), recurrence of bounded height, which we then prove under $(C_κ)$ alone: a height-descent theorem shows the height can never exceed $\\max(H(s_0), C_H)$ with an explicit constant. The remaining program for per-field periodicity is reduced to (R) on the compact and to the proved stretched subcases. All proved statements and certificates are finite and exact. A machine-checked core of the paper is sealed in Lean 4, kernel-only, under the standard axioms: the analytic core of the height-descent theorem, the finiteness pigeonhole, the dual and conformal identity layer, and an abstract assembly theorem composing them through named interface hypotheses.",
      "title": "A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.24750"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23659",
      "authors": [
        "Cătălin I. Cârstea"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23659",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
      ],
      "published": "2026-08-24",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "This reports on an experiment in autoformalization of arxiv:2606.15977, an inverse problems result for piecewise polynomial anisotropic conductivities, using Isabelle/HOL. The proof of the result is relative to a number of external results which were deemed to be well known and generally accepted to be true. The formalization files are made available at a GitHub repository. Translation issues are discussed.",
      "title": "Relative formalization in Isabelle/HOL of a result in inverse problems",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23659"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23247",
      "authors": [
        "Ryuta Arisaka",
        "Hirotaka Ono"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23247",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-24",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We introduce multi-winner voting with argumentative ballots (MVArg) and investigate theoretical properties. As our conceptual contribution, we generalise approval ballots to argumentative ballots, thereby allowing voters to express defeasible preferences over candidates. We accordingly generalise voter cohesion and justified representation axioms JR, PJR and EJR. As our theoretical contribution, we establish several key results. First, MVArg is strictly more expressive than multi-winner voting with approval ballots (MV). Second, our notions of cohesion and justified representation are conservative generalisations of their counterparts in MV. Third, the MVArg counterpart of JR can always be satisfied, whereas the counterparts of PJR and EJR cannot always be. Fourth, although verifying whether a winner set satisfies the MVArg counterpart of JR is already coNP-hard, such a winner set can be constructed in polynomial time. All definitions, propositions, auxiliary lemmas and theorems have been formalised and mechanically checked in Lean 4.",
      "title": "Multi-Winner Voting with Argumentative Ballots",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23247"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23652",
      "authors": [
        "Glauco Rampone"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23652",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-24",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "For integers $k,g \\ge 3$ let $n_g(k)$ denote the minimum order of a graph with chromatic number $k$ and girth at least $g$. Exoo and Goedgebeur (DMTCS 2019) proved $26 \\le n_6(4) \\le 66$; their 66-vertex witness has remained the smallest known 4-chromatic graph of girth 6. We improve both bounds to $29 \\le n_6(4) \\le 64$. The upper bound is witnessed by an explicit 4-chromatic graph of girth 6 on 64 vertices with 152 edges; it is vertex- and edge-critical, and its automorphism group is cyclic of order 8 and acts semiregularly. The lower bound is an exhaustive isomorph-free computation in the SAT modulo symmetries framework with co-certificate learning, driven by the Liu-Postle edge-density bound for 4-critical graphs of girth five; it re-derives $n_6(4) \\ge 26$ by a disjoint method and is validated on the known values $n_4(4)=11$ and $n_5(4)=21$. We complement the bounds with structural obstructions: no smaller witness arises from either known witness by local modifications; no 4-chromatic Cayley graph of girth 6 exists on 54-63 vertices (for orders 59 and 61 no vertex-transitive witness exists at all); and no witness on at most 63 vertices admits a semiregular automorphism group with two or three vertex orbits, for any finite group. Since every known witness of an $n_g(4)$ record with $g \\ge 6$ is a lift of a small base graph along a semiregular action, these results close the most symmetric part of that regime below 64 vertices. All properties of the new graph are verified by independent programs and formally certified in the Lean 4 proof assistant: the non-3-colourability is established inside Lean by a formally verified checker that re-validates a 219,532-node refutation certificate, with a machine-checked soundness theorem.",
      "title": "Improved bounds for the smallest 4-chromatic graph of girth six",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23652"
    },
    {
      "age_days": 7,
      "arxiv_id": "2608.21712",
      "authors": [
        "Deyi Li",
        "Qi Xu",
        "Lingyao Li",
        "Tiansheng Wang",
        "Muxuan Liang",
        "Mei Liu"
      ],
      "content_date": "2026-08-22",
      "freshness": "fresh",
      "id": "arxiv:2608.21712",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-22",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Transformer-based models are widely used for clinical prediction from electronic health records (EHRs), yet their architectures require manual tuning, and the optimal configuration may vary across tasks and hospitals. Neural architecture search (NAS) automates architecture design, but conventional methods are computationally costly for Transformer-based EHR models. Recent large language model (LLM)-guided NAS methods reduce manual search design but conduct each search independently, without reusing architecture knowledge across hospitals. In this study, we propose ATHENA (Agentic Transfer across Hospitals for EHR Neural Architecture Search), a knowledge-guided agentic NAS framework for Transformer-based EHR modeling. ATHENA uses a weight-sharing supernet that is pretrained once per hospital, allowing candidate architectures to be instantiated as inherited subnetworks and evaluated through fine-tuning rather than independent pretraining. It incorporates a two-layer cross-hospital architecture prior. The first layer retrieves high-performing architecture examples from source sites based on task descriptors, while the second estimates the effects of architectural components using SHapley Additive exPlanations (SHAP)-based meta-regression. These priors guide a multi-agent LLM search using validation feedback from the target hospital. Across six clinical prediction tasks evaluated at one held-out OneFlorida+ site and one external MIMIC-IV site, ATHENA significantly outperforms all four baselines in 9 of 12 site-task evaluations under a strict equal-compute comparison. Using a common pretrained AutoFormer supernet for candidate evaluation, ATHENA ranks first in 9 of 12 evaluations at a search budget of 30. It also shows more consistent architecture selection across repeated searches. ATHENA provides a practical approach for reducing manual architecture tuning in Transformer-based EHR modeling.",
      "title": "ATHENA: Knowledge-guided agentic neural architecture search for AutoFormer-based electronic health record modeling",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.21712"
    },
    {
      "age_days": 8,
      "arxiv_id": "2608.21356",
      "authors": [
        "Jason Hickey"
      ],
      "content_date": "2026-08-21",
      "freshness": "fresh",
      "id": "arxiv:2608.21356",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-21",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI inverts this relationship: at AI speed, machine verification is not only economical but essential to productivity --- it is the incorruptible referee that lets one person safely direct autonomous machine work at scale. In five weeks, one researcher on consumer AI subscriptions directed a small fleet of AI agents from application code, through a verified compiler and executive, to a RISC-V processor taped out on a community silicon shuttle; no proof passed through human review, and no RTL was written by a human. The working discipline --- the Salt method --- rests on a proof kernel no hallucinated proof can pass: mathematical claims travel between agents as kernel-checked artifacts, and human attention is reserved for statements, designs, and rulings. Verification is stated link by link, from the Lean 4 kernel to SAT-checked equivalence at the silicon boundary. We publish the complete accounting: theorem provenance, a pre-registered token meter, floor-bounded human time, and an error ledger whose catch numbering runs to #256 --- a monotone counter over the mathematics campaign's append-only flags ledger, maintained 2026-07-07 to 2026-07-20 (one number, #79, was never assigned; later catches are recorded un-numbered) --- against zero incorrect proofs reaching the record.",
      "title": "AI with Authority, from Application to Silicon",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.21356"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26321",
      "authors": [
        "Benjamin Dozier"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26321",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-26",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "We show a birthday paradox for random non-backtracking walk on regular graphs of degree at least $3$: such a walk of length $k$ has high probability of self-intersecting when $k$ is significantly greater than $\\sqrt n$, where $n$ is the number of vertices of the graph. This resolves a conjecture of Noga Alon and Yuval Peres for the fixed degree case.",
      "title": "The Birthday Paradox for non-backtracking walks on regular graphs",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26321"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26310",
      "authors": [
        "Ziyu Wang",
        "Qiming Dai",
        "Yishan Wu",
        "Zaiwen Wen"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26310",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-26",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Large language models can now generate complex, multi-step mathematical proofs, but reliably determining their correctness and localizing early logical errors remains a critical challenge. Existing evaluation approaches largely depend on model-based natural-language judgments, which often overlook local reasoning gaps. While formal theorem provers like Lean offer a path to rigorous verification, using them to evaluate informal text requires solving locality and semantic mismatches: a prover might bypass a local flaw by proving an overly broad target, or validate an auto-formalized statement that drifts from the original mathematical intent. To address this, we introduce FaithSieve, a Lean-assisted framework for fine-grained evaluation of natural-language mathematical proofs. FaithSieve decomposes coarse proof steps into local reasoning units, extracts typed proof obligations, and verifies them through a formal evaluation agent. Formal validation is gated by semantic alignment scoring, so Lean evidence is incorporated only when the formal statement faithfully preserves the context, objects, and logical form of the original claim. We construct two expert-verified datasets, ProofLoc-Olympiad and ProofLoc-University, to benchmark first-error localization. On the 350-problem Olympiad dataset, FaithSieve using a GPT-5.4 backbone achieves 81.43% exact first-error accuracy, outperforming the direct-judging baseline of 72.29%. Furthermore, on the 200-problem ProofLoc-University benchmark spanning six advanced domains, FaithSieve reaches 84.5% exact accuracy, compared to 75.0% for the direct judge. Our work demonstrates that decomposing proofs into fine-grained units and grounding them with faithful formal evidence significantly improves reliable evaluation of natural-language reasoning.",
      "title": "FaithSieve: Fine-Grained Evaluation of Math Proofs with Faithful Formal Evidence",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26310"
    },
    {
      "age_days": 7,
      "arxiv_id": "2608.21749",
      "authors": [
        "Siwei Zeng"
      ],
      "content_date": "2026-08-22",
      "freshness": "fresh",
      "id": "arxiv:2608.21749",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-22",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "The general subgroup permanental-dominance conjecture was previously known only through matrix order three. This paper proves its complete order-four case: for every subgroup $H\\leq S_4$, every irreducible complex character $χ$ of $H$, and every $4\\times 4$ Hermitian positive-semidefinite matrix $A$, it establishes $d_χ^H(A)/χ(1)\\leq \\operatorname{per} A$. Unlike the usual immanant specialization, the result covers all thirty-seven irreducible-character cases arising from the eleven conjugacy classes of subgroups of $S_4$. Thirty-five cases follow from general principal-minor, moment, and block-contraction inequalities. The two non-real $A_4$ characters are reduced to polynomial nonnegativity on the cone of $3\\times 3$ positive-semidefinite Gram matrices and are resolved by a rank-one sum-of-squares identity, an exact positive-definite interior certificate, rational Gram certificates, and closure of the Gram cone.",
      "title": "The General Subgroup Permanental-Dominance Conjecture in Order Four",
      "updated": "2026-08-22",
      "url": "https://arxiv.org/abs/2608.21749"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:696e847a6c07",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: split `Core.Context` into hot and cold subobjects (#14962)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover/lean4/commit/696e847a6c079637186e492f37e22dedf4faf679"
    },
    {
      "age_days": 0,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:482150a8bc3f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: compile mimalloc with `MI_MAX_ALIGN_SIZE=8` (#14948)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover/lean4/commit/482150a8bc3f3834e3f1baed8fb7d785d4bda5f3"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:80e859f8d92a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: link `libLeanExport.a` into executables that link Lake (#14963)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover/lean4/commit/80e859f8d92a2a9680100ff6bece4905544018a1"
    },
    {
      "age_days": 0,
      "authors": [
        "Kyle Miller"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:1584f13f4af0",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: improve `#print` recursor rules (#14960)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover/lean4/commit/1584f13f4af0172204ee16b09955ac205d38abde"
    },
    {
      "age_days": 0,
      "authors": [
        "Joris Roos"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:bbcd1968ee69",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(MeasureTheory/Integral): second mean value theorem for integration (#41964)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/bbcd1968ee6950abe88b85dba6995da346c4b2a8"
    },
    {
      "age_days": 0,
      "authors": [
        "Joël Riou"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:9a2d60ba1f29",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): preservation of `κ`-pure morphisms by `κ`-accessible functors (#41420)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/9a2d60ba1f29e58a687bba9aabaa7184bc2cfe1b"
    },
    {
      "age_days": 0,
      "authors": [
        "Joël Riou"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ec5c964b4983",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): comma categories are `κ`-accessible (#41068)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ec5c964b4983b2427eb57b090e42920b875dff02"
    },
    {
      "age_days": 0,
      "authors": [
        "Joël Riou"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:58e016c6f6c8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(CategoryTheory/Limits): weighted limits commute with limits (#41313)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/58e016c6f6c829b5f25b1a87a88f495f40e70aa7"
    },
    {
      "age_days": 0,
      "authors": [
        "Brian Nugent"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:73ecfd61cc8e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Algebra/Category/ModuleCat): add abbrevs for Presheaves of Modules over commutative rings (#43192)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/73ecfd61cc8e66ff527c3733f2a7af3127178cca"
    },
    {
      "age_days": 0,
      "authors": [
        "Junyan Xu"
      ],
      "content_date": "2026-08-29",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3649549a1e4b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-29",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: doc(AlgebraicGeometry): fix docstring about finite presentation (#42913)",
      "updated": "2026-08-29",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3649549a1e4b19461e912299ca7127d8831b79fa"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b01c874fd8dd",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: test: complete no-concurrency Lean model of refcounting (#14910)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/b01c874fd8dd4e5cfdff5740c6bfa25dc2044bf2"
    },
    {
      "age_days": 1,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:a57be6641c51",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: update to LLVM 23 (#14531)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/a57be6641c51438c02c51fd65c166ca71e137734"
    },
    {
      "age_days": 1,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:3129edaa4cc6",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: working with RAT proofs (#14951)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/3129edaa4cc655915c89f2202a382ea0d86f8e84"
    },
    {
      "age_days": 1,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:4ad88fe794e0",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: do not unfold partially applied constants in `cbv` (#14939)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/4ad88fe794e04a7b8fa5f98218ed7ae87e1a7a4c"
    },
    {
      "age_days": 1,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:41bdd5d01845",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: `deprecated_syntax` warnings for syntax that has `.original` source info (#14940)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/41bdd5d018452ed9f556f9991d0e6ccacc62c2ba"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b5466a1aa841",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: run `lake challenge` dependency resolution inside the sandbox (#14947)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/b5466a1aa841d9a3f533c9ffde1d0dc6ae9c2ad4"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Ullrich"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2a7175c74ba1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: remove deprecated in-kernel native reduction (#14953)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/2a7175c74ba17b160299accd7e6ea6984d7ea86f"
    },
    {
      "age_days": 1,
      "authors": [
        "Henrik Böving"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:35cf6e487c28",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: min/max support in bv_decide (#14956)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/35cf6e487c2825ea83f33ddf717aea523c6da0d5"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Ullrich"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:fe1939c0b3bf",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `lake challenge` as a `comparator` frontend (#14885)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/fe1939c0b3bf148eb2c3e64fa02ce2f9311d8f96"
    },
    {
      "age_days": 1,
      "authors": [
        "Peter Limkilde Svendsen"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:4edc42d4330b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: doc: clarify that BitVec intMin/intMax refer to two's complement interpretation (#13336)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/4edc42d4330b786c3310515d6ce072253930340a"
    },
    {
      "age_days": 1,
      "authors": [
        "Julia Markus Himmel"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:424cc7309957",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: delete bootstrapping workarounds (#14946)",
      "updated": "2026-08-28",
      "url": "https://github.com/leanprover/lean4/commit/424cc73099573b57d6ca8d6f1ceeb443cf6aef69"
    },
    {
      "age_days": 1,
      "authors": [
        "Marcelo Lynch"
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      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:5ba951246811",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
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      "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/Trails): the support of an Eulerian trail equals the support of the graph (#41632)",
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      "url": "https://github.com/leanprover-community/mathlib4/commit/589208471b29b1f0220edd901c62ad81d0b12333"
    },
    {
      "age_days": 2,
      "authors": [
        "Thomas Browning"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:cc2a4a8ff4c7",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Ring/WithAbs): add `AbsoluteValue.under` (#42566)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover-community/mathlib4/commit/cc2a4a8ff4c7143b6bdf4faaa418f97721a3efb5"
    },
    {
      "age_days": 2,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:f988eda5de1a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Combinatorics/SimpleGraph/CycleGraph): golf `cycleGraph_isContained_iff` (#42964)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover-community/mathlib4/commit/f988eda5de1aff03157c116b01178564a2ad1c01"
    },
    {
      "age_days": 3,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:31aea96d017b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: persist code quality entries in an environment extension (#14914)",
      "updated": "2026-08-26",
      "url": "https://github.com/leanprover/lean4/commit/31aea96d017b53c6acf56577b20e4ef48421af9e"
    },
    {
      "age_days": 3,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:940c33d992b8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: support some symbolic `Nat` operations in `bv_decide` (#14928)",
      "updated": "2026-08-26",
      "url": "https://github.com/leanprover/lean4/commit/940c33d992b87d120c1b28e2732bad5ec3790186"
    },
    {
      "age_days": 3,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:ec5816f82fab",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add a `leanchecker-paranoid` binary with mimalloc mitigations (#14884)",
      "updated": "2026-08-26",
      "url": "https://github.com/leanprover/lean4/commit/ec5816f82fabf7d0982f388a19694a926c9ec5ac"
    },
    {
      "age_days": 4,
      "authors": [
        "Joachim Breitner"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:30ad6f54fd4a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: build `casesOn` for propositions from projections (#14925)",
      "updated": "2026-08-25",
      "url": "https://github.com/leanprover/lean4/commit/30ad6f54fd4a9e3193156fbb25c7f0e76a50d927"
    },
    {
      "age_days": 4,
      "authors": [
        "Robert J. Simmons"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b9c9eb9a3ace",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: create asNode/mkNode abstraction for DiscrTree (#14911)",
      "updated": "2026-08-25",
      "url": "https://github.com/leanprover/lean4/commit/b9c9eb9a3acefaa242c1da2a31e3723e94fde3a5"
    },
    {
      "age_days": 4,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8c07c8f7c1c4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add strong (co)induction principles for lattice-theoretic predicates (#14855)",
      "updated": "2026-08-25",
      "url": "https://github.com/leanprover/lean4/commit/8c07c8f7c1c475db22594bc7595472daa0c438b2"
    },
    {
      "age_days": 4,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:e276422fda5c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add hint to transitive `deprecated` usage warning (#14841)",
      "updated": "2026-08-25",
      "url": "https://github.com/leanprover/lean4/commit/e276422fda5ca6cff5999766b98291ffa274d919"
    },
    {
      "age_days": 4,
      "authors": [
        "Julien Cretin"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:174754bba994",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: doc: fix imprecision in IO.FS.Stream.getLine and IO.FS.Handle.getLine (#14754)",
      "updated": "2026-08-25",
      "url": "https://github.com/leanprover/lean4/commit/174754bba9943a578ce980d59a0f5e7f05749182"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26418",
      "authors": [
        "Architect Labs"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26418",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Modern AI workloads and the hardware that runs them evolve on different timescales: architectural definition precedes volume silicon by years, while target workloads shift in months. Design decisions are therefore committed under deep uncertainty and paid for twice, once in the generality added as a hedge, and again when new workloads map poorly onto frozen silicon. As Moore's Law stagnates, specialization is the main remaining source of performance-per-watt and demands a design cycle that runs at the cadence of the workloads. We present an end-to-end AI system that collapses the software-to-silicon stack into a single optimization loop, where hardware and software are co-designed and verified under one objective. Its first demonstration is Redwood, a frontier AI accelerator built for single-batch, low-power, ultra-low-latency inference for physical AI. From a high-level specification by two human architects, the system autonomously generated the performance model, RTL design, UVM environments, formal proofs, firmware, and kernels in under two weeks with no human intervention below the specification. Every block reached 95% coverage via commercial EDA tools, our proprietary formal engine, and hardware-in-the-loop validation. Specification changes were reverified and redeployed to hardware in under 48 hours. Redwood Nano, its ultra-low-power FPGA variant, runs multi-billion-parameter models like Llama and Qwen. Projected onto Samsung 8 nm, the Jetson Orin Nano's process class, Redwood delivers 1.75x the throughput at 1.9x lower power, a 3.4x performance-per-watt gain against a measured Jetson baseline on the same models. Qwen running on Redwood also helped design next-generation Redwood, an early step toward recursive self-improvement. To our knowledge, this is the first production-worthy AI accelerator designed end-to-end by an AI system and running a modern AI model.",
      "title": "Redwood: A Frontier AI Accelerator Designed, Verified, and Deployed from Scratch in 2 Weeks by AI",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26418"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26435",
      "authors": [
        "Chao Xu",
        "Yiqing Wang",
        "Riccardo Scarcelli"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26435",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "In this study, direct numerical simulations (DNS) are employed to investigate NOx formation in turbulent lean premixed hydrogen-air flames under engine-relevant conditions. Various turbulence intensities and molecular transport models are examined to isolate the individual impacts of turbulence intensity, Lewis number, and preferential diffusion on NOx production. Results show that NOx production is significantly enhanced in all turbulent cases relative to the laminar flame, reaching approximately five times the laminar value at a mixture residence time of 0.15 ms. Increasing turbulence intensity is found to have three competing effects on NOx formation: (1) it strengthens turbulence-instability interactions by inducing local super-adiabatic hot spots and elevating key flame radical concentrations within the flame brush, thereby promoting NOx formation locally; (2) it accelerates the turbulent flame speed, reducing the flame-brush residence time and thus suppressing NOx production globally; and (3) it reduces post-flame temperature fluctuations, suppressing thermal NOx enhancement in the post-flame zone. Lewis number effects are identified as the primary mechanism driving thermodiffusive NOx enhancement, with preferential diffusion playing a secondary role, as evidenced by the nearly identical NOx reaction rates between unity Lewis number turbulent flames and their laminar counterparts. Finally, an excellent correlation between the peak conditional mean NOx reaction rate and the stretch factor is identified, and a conceptual model is proposed to predict NOx enhancement in practical engine simulations. The findings highlight that turbulence--chemistry interaction is critical for accurately predicting NOx formation in thermodiffusively unstable hydrogen flames.",
      "title": "Direct numerical simulation of NOx formation in turbulent lean premixed hydrogen-air flames under engine-relevant conditions",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26435"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.26365",
      "authors": [
        "Cynthia Bortolotto",
        "João P. G. Ramos"
      ],
      "content_date": "2026-08-26",
      "freshness": "fresh",
      "id": "arxiv:2608.26365",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-26",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We give a short complex-analytic proof of a square-restricted form of local stable phase retrieval at the Gaussian in one-dimensional Fock space. The main estimate is a coercivity inequality for the map $F\\mapsto F^2$: \\[ \\|F^2-F(0)^2|_{\\mathcal{F}^2(\\mathbb{C})} \\lesssim \\inf_{c\\in\\mathbb{R}}\\||F|^2-c\\|_{L^2(d γ)}. \\] The proof uses a weighted derivative norm, two integrations by parts, and a weighted Cauchy inequality. The proof has been completely verified in Lean with the aid of Large Language Models.",
      "title": "A complex-analytic proof of square-restricted stable phase retrieval in Fock space",
      "updated": "2026-08-26",
      "url": "https://arxiv.org/abs/2608.26365"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.25220",
      "authors": [
        "Henry Robbins",
        "Connor Lawless",
        "Madeleine Udell",
        "Ellen Vitercik"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.25220",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Mixed-Integer Linear Programming (MILP) is a fundamental tool for combinatorial optimization with extensive real-world applications. A central challenge is designing computationally efficient MILP formulations. Large Language Models (LLMs) offer new opportunities to automate the modeling process, from deriving formulations to strengthening them. Reliable automation requires robust methods for verifying that proposed formulations preserve the underlying optimization problem. However, existing approaches evaluate formulations numerically and fail to reason about general problem instances. We resolve this limitation by introducing a constructive definition of MILP reformulation that can be formalized in Lean and machine-checked. We develop FLARE (Formulation-Level Automated Reformulation Evaluation), a method that uses an LLM-based agent and the Lean proof assistant to verify proposed reformulations against a reference formulation. To evaluate our approach, we introduce FormulationBench, a challenging dataset of 20 problems and 109 formulations. FLARE outperforms existing methods, with 100% accuracy on the NP-hard subset of FormulationBench. Furthermore, FLARE produces a machine-checkable certificate for every reformulation it accepts. For cases where formal guarantees are not necessary, we introduce FLARE-NL, a fast and cheap LLM proxy that matches FLARE's accuracy but produces no certificate. These methods enable reliable verification in automated optimization modeling.",
      "title": "FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.25220"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.24964",
      "authors": [
        "Yiheng Feng"
      ],
      "content_date": "2026-08-25",
      "freshness": "fresh",
      "id": "arxiv:2608.24964",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-25",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "This note studies the geometry of full conformal prediction (FullCP) regions generated by an empirical energy-form pairwise score. Candidate-score convexity alone does not guarantee connected FullCP regions, even when the candidate score is an empirical average of a loss convex in its first argument. Direct expansion of the leave-one-out scores shows that each training-point comparison for the energy-form score is exactly a pairwise-dissimilarity sublevel condition. Under symmetry, a constant diagonal, a diagonal lower bound, and attainment of the associated Fréchet-type objective, every comparison region contains a common minimizer; when the comparison regions are convex, the nontrivial exact conformal region is therefore star-shaped about that same point. For power distances $ρ_β(x,y)=\\|x-y\\|^β$, this deterministic geometry holds for $β\\ge1$, while the conventional energy score is strictly proper for $0<β<2$. In the univariate $β=1$ specialization, every nontrivial empirical-CRPS FullCP region is a nonempty closed interval, possibly $\\mathbb R$ in the $m=1$ degeneracy. On the unconditional reconstruction range $1<β<2$ and $m\\ge2$, explicit data-checkable derivative bounds yield Lipschitz control of the comparison-set radial exits and hence of the exact conformal radial function. These score-specific bounds permit existing directional root-search ideas and classical Lipschitz-extension machinery to yield certified inner and outer radial envelopes with width at most $δ+2Lh_{\\mathcal U}$ and corresponding same-ray Hausdorff guarantees. An analytic two-dimensional example shows why retaining star-shaped but nonconvex geometry can matter. The resulting reconstruction perspective is intended for low-dimensional multivariate outputs rather than high-dimensional scaling or runtime improvement.",
      "title": "Common-Center Geometry and Certified Radial Reconstruction for Energy-Form Full Conformal Regions",
      "updated": "2026-08-25",
      "url": "https://arxiv.org/abs/2608.24964"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.22928",
      "authors": [
        "Yusheng Zheng",
        "Xiaoyu Song",
        "Yanpeng Hu",
        "Lebin Cheng",
        "Yuxi Huang",
        "Wei Zhang"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.22928",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-24",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Agent runtimes can Checkpoint an execution, Fork it, Restore a checkpoint, or Merge branches without restarting a task. We call these operations execution edits, with Checkpoint recording the current execution for later use and Fork, Restore, and Merge changing what the Agent will do next. An execution edit cannot undo an earlier authorization or a tool request already sent. An unsafe edit can therefore authorize the same tool action twice, discard a result the task still requires, or conflict with a call that began before the edit. The Agent is untrusted, so the runtime uses its execution record to determine which past actions an edit must account for and which required results it must preserve to keep the subsequent execution safe. Yet existing Agent systems support such operations without deriving what each edit must preserve from the running execution, whereas prior methods for computing safe behavior take that requirement as input. We give an algorithm that decides exactly whether an edit is safe. It returns all safe ways to continue, or proves that none exists. To make this decision, the algorithm lists every way the task can finish without violating policy. It removes any way that could make a still-required result impossible to finish later. If none remain, it returns a checkable proof that no safe implementation exists. Otherwise, the remaining ways describe exactly what the runtime may allow. Our formal results cover Checkpoint and the six forms of Fork, Restore, and Merge, together with extensions, atomic enforcement, and the information every exact checker needs. Lean mechanizes the finite checker and runtime invariant, and tests validate all six edit forms. The source code, Lean proofs, and executable tests are available in the public GitHub repository at https://github.com/eunomia-bpf/agent-check-restore-safety.",
      "title": "When Can Agents Safely Checkpoint, Fork, Restore, and Merge? Exact Checking for Execution Edits",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.22928"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23506",
      "authors": [
        "Michael Emmerich"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23506",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-24",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove that minimum Riesz $s$-energy subset selection in the Euclidean plane is NP-complete already for the fixed exponent $s=2$. To our knowledge, this is the first Euclidean hardness result for exact Riesz-energy subset selection in which both the ambient dimension and the exponent are fixed. The reduction uses Barahona's planar cubic Ising model with uniform field. A spin is encoded by one diagonal of a four-point square. Axis-aligned selector chains implement ferromagnetic consistency, while a $45^\\circ$ terminal geometry yields an antiferromagnetic source interaction. Rational diagonal perturbations realize the magnetic field, and all remaining interactions are dominated by polynomial separation. Because $s=2$ and all coordinates are rational, every constructed energy and the decision threshold are rational exactly.",
      "title": "Riesz Energy Subset Selection in the Euclidean Plane is NP-Hard: A Reduction from the Ising Model on Planar Cubic Graphs",
      "updated": "2026-08-27",
      "url": "https://arxiv.org/abs/2608.23506"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23721",
      "authors": [
        "Daniel Carranza",
        "Chunyi Liu",
        "Emily Riehl",
        "Egbert Rijke"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23721",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-24",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We report our findings and the results of our experiment of autoformalizing the homotopy type theoretic computation of $π_3(S^2)$ in agda-unimath using Codex.",
      "title": "Autoformalizing the calculation of $π_3(S^2)$",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23721"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.23413",
      "authors": [
        "Seiichiro Kusuoka",
        "Shuta Nakajima"
      ],
      "content_date": "2026-08-24",
      "freshness": "fresh",
      "id": "arxiv:2608.23413",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-24",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We consider the Sherrington--Kirkpatrick model with inverse temperature $β>0$ and deterministic external field $h>0$. Let $q$ be the replica-symmetric fixed point: $q=\\mathbb E{\\rm tanh}^2 (h+β\\sqrt q\\,Z)$, where $Z$ is a standard normal. We prove that, uniformly on compact subsets of the strict de Almeida--Thouless region: $β^2\\mathbb E{\\rm sech}^4(h+β\\sqrt{q} Z) <1,$ the overlap satisfies the concentration: $$ \\mathbb E\\langle (R_{12}-q)^2\\rangle=O(N^{-1}). $$ The result of the present paper provides an alternative proof of the replica-symmetric free energy formula in de Almeida--Thouless region recently established by Lopatto [arXiv:2604.11921]. Moreover, our approach yields the stronger conclusion of an explicit quantitative bound. As a consequence, we obtain an $O(N^{-1})$ replica-symmetric free-energy correction and identify the finite-volume replicon susceptibility. Our proof is self-contained and does not use the identification of the limiting free energy with the Parisi variational formula. The main result supersedes the corresponding result in our recent preprint arXiv:2607.23427, extending the replica-symmetric bounds to the strict de Almeida-Thouless region. However, we keep the previous preprint, since its argument is different and substantially simpler than the one given here.",
      "title": "A quantitative replica-symmetric bound of Sherrington--Kirkpatrick model in the entire de Almeida--Thouless region",
      "updated": "2026-08-24",
      "url": "https://arxiv.org/abs/2608.23413"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.22550",
      "authors": [
        "Jan Snellman"
      ],
      "content_date": "2026-08-23",
      "freshness": "fresh",
      "id": "arxiv:2608.22550",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-23",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We consider families of lines that cover every point of the integer lattice $\\mathbf{Z}^2$ in the plane, subject to the constraint that no two lines of different direction in the family meet at a lattice point. Restricting to \\emph{lattice lines} (lines containing at least two, hence infinitely many, lattice points, equivalently of rational direction), we show that the set of directions occurring in such a covering can be made dense in the space of line directions. The construction is a recursive splitting of $\\mathbf{Z}^2$ into nested rank-2 sublattice cosets, each handed off to a freshly chosen direction; the key technical point is a steering lemma showing that at every stage of the recursion a new direction arbitrarily close to any prescribed target can still be realized, via an elementary sieve bound.",
      "title": "On the directions occurring in lattice-line coverings of the integer plane",
      "updated": "2026-08-23",
      "url": "https://arxiv.org/abs/2608.22550"
    },
    {
      "age_days": 7,
      "arxiv_id": "2608.22117",
      "authors": [
        "Joshua Nunley"
      ],
      "content_date": "2026-08-22",
      "freshness": "fresh",
      "id": "arxiv:2608.22117",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-22",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "A standard Transformer block separates cross-token interaction in self-attention from a nonlinear feed-forward network applied independently at each position. We introduce the TANGO model (Token-Aggregated Nonlinear Gating Operators), which replaces these two sublayers with one cross-token gated residual update. Each source token produces a SwiGLU gate vector. Query-key similarities determine a weighted average of source gates for each destination, and the resulting gate rescales projected destination features. TANGO assigns a separate weight to every causally visible source and is quadratic in sequence length. The WANGO model (Windowed Aggregation of Nonlinear Gating Operators) retains the same unnormalized scores within a recent window and uses positive feature-map prefix statistics for older sources, giving linear sequence-length complexity for fixed window and feature dimensions. We compare TANGO and WANGO with Recurrent and Untied Transformer++, full-attention GAU, and FLASH. All models have approximately 44.3M nonembedding parameters and are trained in three matched runs. TANGO, WANGO, and Recurrent Transformer++ apply one shared block four times; the other architectures use four independent blocks. TANGO obtains the lowest mean validation negative log-likelihood on FineWeb-Edu, Lean, and DeepMind Mathematics, although it has the largest analytical forward-pass operation count. WANGO obtains the lowest mean FineWeb-Edu NLL among the architectures with computation linear in sequence length and outperforms Recurrent Transformer++ at nearly the same analytical forward-pass multiply-accumulate count.",
      "title": "TANGO: Token-Aggregated Nonlinear Gating Operators for Natural and Formal Language Modeling",
      "updated": "2026-08-22",
      "url": "https://arxiv.org/abs/2608.22117"
    },
    {
      "age_days": 8,
      "arxiv_id": "2608.21502",
      "authors": [
        "Bennett Chow",
        "Yuan Liao",
        "Ziyang Qin"
      ],
      "content_date": "2026-08-21",
      "freshness": "fresh",
      "id": "arxiv:2608.21502",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-21",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We describe a Lean formalization of Hamilton's 1982 theorem on closed, connected three-manifolds with positive Ricci curvature. The development contains a short-time existence theorem for Ricci flow and substantial geometric-analysis infrastructure: Riemannian tensor calculus, the Levi--Civita connection, Ricci-flow evolution equations, scalar and tensor maximum principles, three-dimensional curvature algebra, preservation of Ricci pinching, and Hamilton's improved pinching estimate. The formalization follows an alternative blow-up route, rather than Hamilton's original normalized-flow proof. Its time-uniform short-time existence, maximal continuation, no-local-collapsing, and Cheeger--Gromov--Hamilton compactness pipelines have been formalized and are included in the artifact, while we give only a brief account of these companion developments and record the interfaces and consequences used by the Hamilton argument; a detailed exposition of their full constructions is deferred to the second author's forthcoming thesis. We interweave representative Lean declarations with their mathematical meaning and record the status and provenance of every major component. All source-level status claims are tied to the source release identified below.",
      "title": "A Lean Formalization of Hamilton's Three-Manifold Theorem",
      "updated": "2026-08-21",
      "url": "https://arxiv.org/abs/2608.21502"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}