{
  "counts": {
    "adjacent": 15,
    "core": 5,
    "errors": 0,
    "negative": 69,
    "total": 89
  },
  "date": "2026-08-31",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-31T21:00:24Z",
  "items": [
    {
      "age_days": 5,
      "arxiv_id": "2608.25449",
      "authors": [
        "Jiaxin Yuan",
        "Connor Martinez Lockhart",
        "Xiaoyu Liu",
        "Jiaqi Wang",
        "Chenghao Deng",
        "Xiayimei Han",
        "Vlassis Mastrantonis",
        "Dmitrii Gudin",
        "Shaopeng Zhu",
        "Abdirisak Mohamed",
        "Bilal 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": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.25449"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.28433",
      "authors": [
        "Shuze Chen",
        "Kunal Marwaha",
        "Xiaoyang Lu",
        "Henry Yuen",
        "Tianyi Peng"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28433",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-28",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Proof assistants such as Lean 4 promise the paradigm of formally verified mathematics, but large-scale formalization projects have faced major barriers to entry, including the need for expertise in formal verification (as well as the underlying mathematics) and the significant time required for writing formal proofs. AI coding agents have dramatically reduced these barriers; human users can now use natural language to prompt agents to write complex proofs in Lean. This opens up the intriguing possibility of internet-scale mathematical collaboration involving both humans and AI agents, where correctness is machine-checked. To realize this possibility, we introduce Prove2Me (https://prove2.me), an open collaborative platform for formalizing mathematics. Users launch formalization \"missions\", to which AI agents contribute formal proofs toward completion. We designed mechanisms and a specialized harness in Prove2Me that enable large-scale collaboration so that agents can build on one another's work and freely reuse existing results. In doing so, Prove2Me aims to turn math formalization into a scalable, crowd-sourced effort open to anyone with an agent.",
      "title": "Prove2Me: An Open Collaborative Platform for Scaling Math Formalization",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28433"
    },
    {
      "age_days": 5,
      "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": 6,
      "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": 7,
      "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": 3,
      "arxiv_id": "2608.28133",
      "authors": [
        "Zhaorui Wu"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28133",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "A $p$-ary bent partition of $\\mathbb{F}_p^n$ is a partition into $K$ nonempty cells such that every balanced assignment of its cells to $\\mathbb{F}_p$ produces a bent function. It was asked whether every possible depth $K$ is a power of $p$; for general $p$, previous affirmative results required regularity or cell-symmetry hypotheses. We prove the stronger unconditional statement that, for every nonzero $h$, exactly $p^n/K$ points remain in the same fine cell under translation by $h$. Thus the fine cells form a partitioned difference family and the fine label map is zero-difference balanced. Consequently $K\\mid p^n$, so $K=p^t$; nonempty cells further give $1\\le t<n$. In even dimension, the classical cell-size theorem yields $K\\mid p^{n/2}$. Together with the known odd-dimensional ternary three-fibre parameter restriction, this gives the global bound $t\\le\\lfloor n/2\\rfloor$. The proof is an exact finite average over balanced coarsenings. The main counting identity and selected consequences are formalized and kernel-checked in Lean 4.",
      "title": "Fine Difference Structure and Prime-Power Depth of Bent Partitions",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28133"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.28337",
      "authors": [
        "Julien Grain",
        "Hugo Holland",
        "Lucas Pinol"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28337",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "General relativity coupled to multiple scalar fields is a diffeomorphism-invariant constrained system. Consequently, a naive counting of the perturbative degrees of freedom unavoidably overestimates the true number of physical modes propagating in the theory, as gauge redundancies and constraint equations remove non-dynamical ones. While this problem has been solved for linear fluctuations, this work presents the first explicit calculation of all large-scale gauge-invariant phase-space variables in multifield inflation and at second order in perturbation theory, in a Hamiltonian language. Building upon the well-known Sasaki-Mukhanov variables, we show how to construct a finite-dimensional basis of quadratic corrections which are invariant under gauge transformations. Although our procedure is generic to any number of fields and at any scale, we restrict to super-Hubble scales for their explicit solution, which we deliver. Henceforth, we prove that it is possible to recover the usual flat-gauge and comoving-gauge fluctuations as large-scale gauge-invariant combinations, making for a robust consistency check of the gauge-fixed procedure to connect theoretical predictions above the horizon to observations. We derive the quadratic and cubic Hamiltonian of multifield inflation in a gauge independent manner, then we gauge fix our theory by going into the flat gauge, and we show perfect agreement with the literature on this topic, usually based on a Lagrangian approach. After these concrete steps, we propose a more formal proof of the existence of gauge-invariant variables at quadratic order, and we provide a sketch of the procedure that should allow to go to higher orders in perturbation theory.",
      "title": "Explicit gauge-invariant variables in multifield inflation beyond linear order and Hamiltonian dynamics",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28337"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.28432",
      "authors": [
        "Jiayan Lin",
        "Yujia Liu",
        "Zijin Hong",
        "Zheng Yuan",
        "Yilin Xiao",
        "Hao Chen",
        "Qinggang Zhang",
        "Xiao Huang",
        "Feiran Huang"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28432",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Recent advances in in-context learning (ICL) text-to-SQL have substantially improved execution accuracy on public benchmarks by assembling increasingly elaborate pipelines around the base generator, yet existing studies typically report aggregate end-to-end accuracy, without quantifying the marginal accuracy-cost contribution of individual design choices. Consequently, providing a unified, paradigm-level cost-accuracy quantification remains a critical challenge for understanding and configuring modern text-to-SQL. To address this, we instantiate 17 paradigm-level configurations across five recurring modules of the ICL text-to-SQL pipeline under a single controlled implementation, and attribute each paradigm's marginal contribution and incurred cost across all four backbones spanning diverse capability levels and reasoning styles. Our analysis reveals that execution-feedback refinement is the only paradigm whose benefit holds universally at consistently low cost, while most other modules help only under backbone-dependent conditions. Token accounting shows that input demand is more closely tied to pipeline structure, whereas output demand is more sensitive to backbone generation behavior. Cross-module analysis further shows that stacking improves accuracy on most backbones, although how the gains compose varies with backbone capability. We also find that a fixed budget is often better spent engineering a more elaborate pipeline over a mid-tier backbone than upgrading to a frontier model with a lean pipeline. These findings distill into an actionable, cost-aware tiered guideline that transfers to five additional backbones without per-paradigm search.",
      "title": "Are These Modules Worth Their Cost? A Paradigm-Level Accuracy-Cost Analysis of In-context Learning Text-to-SQL",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28432"
    },
    {
      "age_days": 4,
      "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": 4,
      "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": 6,
      "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": 6,
      "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": 6,
      "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": 7,
      "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": 7,
      "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": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.23247"
    },
    {
      "age_days": 7,
      "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": 4,
      "arxiv_id": "2608.27718",
      "authors": [
        "Colin Defant",
        "Sidharth Hariharan",
        "Kenny Lau",
        "Ken Ono"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "arxiv:2608.27718",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-27",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "The rows and columns of the character table of the symmetric group $S_n$ are both naturally indexed by partitions of $n$. Let $D(n)$ denote the number of conjugacy classes of $S_n$ whose column contains no zero entry. The identity column is always zero-free, so $D(n)\\geq 1$. It is known that $D(n)\\ll n^2$. We prove that $D(n)\\ll n^{3/4}$. Second, we prove for almost all positive integers $n$ that $D(n)\\ll_B n^{1/2}(\\log n)^B$ for every $B>5/6$, with a quantitative bound for the exceptional set, using work of Matomäki and Radziwill. Finally, we offer a heuristic supporting our conjecture that $D(n)\\ll_{\\varepsilon} n^{\\varepsilon}$. AxiomProver formalized the results in this paper in Lean assuming preexisting literature.",
      "title": "Zero-free columns in character tables of symmetric groups",
      "updated": "2026-08-27",
      "url": "https://arxiv.org/abs/2608.27718"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.27708",
      "authors": [
        "Colin Defant",
        "Ken Ono"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "arxiv:2608.27708",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-27",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Let $D_n$ be the dihedral group of order $2n$. Consider a continuous-time random walk on $D_n$ driven by arbitrary symmetric rates whose support generates $D_n$. For $p\\in[1,\\infty]$, we say the pair $(D_n,p)$ is rate-monotonic if for each fixed time $t$, the $\\ell^p$-distance between the random walk's distribution at time $t$ and the uniform distribution is monotonically decreasing as a function of the rates. Lyons and White proved that $(D_n,2)$ and $(D_n,\\infty)$ are rate-monotonic. Somewhat counterintuitively, they found several pairs $(D_n,p)$ with ${p\\in[1,1.997]\\cup[2.001,3.999]\\cup[4.001,5.995]}$ that are not rate-monotonic, and they asked whether any such pairs exist with $p=4$ or $p=6$. We resolve their question, proving that $(D_n,2m)$ is rate-monotonic for all positive integers $m$ and $n$. In fact, we prove a generalization of this result to a broader family of groups that includes generalized dihedral groups, dicyclic groups, and generalized quaternion groups. In the other direction, we prove that for every real $p\\geq 1$ that is not an even integer, there exists a positive integer $n$ such that $(D_n,p)$ is not rate-monotonic. The results of this paper were formally verified in Lean by AxiomProver assuming standard literature.",
      "title": "Proof of the Lyons--White Conjecture",
      "updated": "2026-08-27",
      "url": "https://arxiv.org/abs/2608.27708"
    },
    {
      "age_days": 5,
      "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": 5,
      "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": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:1e67d51928ad",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: avoid `setTransparency` when the transparency is already in effect (#14967)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover/lean4/commit/1e67d51928ad6394f643c32fb36b222e03fcee48"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c8e19cca2547",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: use the correct calling convention when over-applying a closure in `lean_apply_m` (#14969)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover/lean4/commit/c8e19cca2547a89c3aba401afaab9a8808f490a2"
    },
    {
      "age_days": 0,
      "authors": [
        "Siddharth"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:138ca9f20763",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: characterize when T-division equals zero (#8204)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover/lean4/commit/138ca9f20763523c4093baa092cf371e89535098"
    },
    {
      "age_days": 0,
      "authors": [
        "Kitamado"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:f0b9e56cd455",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `Repr` instance for `Vector` (#14545)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover/lean4/commit/f0b9e56cd4556b014e13f8b121eda8d9c922c73d"
    },
    {
      "age_days": 0,
      "authors": [
        "Lean stage0 autoupdater"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0e6944a82599",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: update stage0",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover/lean4/commit/0e6944a825993b20d0834f2f825a3439bad58515"
    },
    {
      "age_days": 0,
      "authors": [
        "DavidLedvinka"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:7b51d193d4cb",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: refactor(Tactic/Linter): rename and generalize `linter.style.nativeDecide` to `linter.style.native` (#43194)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/7b51d193d4cbc4afdf95445d826a52782c2d6754"
    },
    {
      "age_days": 0,
      "authors": [
        "Attila Gáspár"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:29cc1eef29dd",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: homogenization of an affine space (#39368)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/29cc1eef29dd8d04bd7718f6d3895b589997678d"
    },
    {
      "age_days": 0,
      "authors": [
        "jfab"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:cae66e9de4ec",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: add zero lemmas for even powers (#43161)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/cae66e9de4eccd03eb566d07361a07dc1e3ff021"
    },
    {
      "age_days": 0,
      "authors": [
        "mcallisto"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3b6f3a681724",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: add IsNowhereDense.union (#43188)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3b6f3a68172496e3808977d9593fe199ca46d6e2"
    },
    {
      "age_days": 0,
      "authors": [
        "Xavier Roblot"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:7c72847433f7",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal/HasFiniteQuotients): Finite instance for a quotient by a nonzero ideal (#41943)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/7c72847433f7784f32989be58d4f040df96de34a"
    },
    {
      "age_days": 0,
      "authors": [
        "Wenrong Zou"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:cde48137b3b3",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Padics): add an instance `IsValuativeTopology ℚ_[p]` (#42998)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/cde48137b3b391cec6216283121d245c478cd082"
    },
    {
      "age_days": 0,
      "authors": [
        "teorth"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:5961c0e3b76e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(NumberTheory/Harmonic): pointwise inv_riemannZeta_eq_sub_mul (#43207)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/5961c0e3b76e3df1d36818da5b14e846e307cbca"
    },
    {
      "age_days": 0,
      "authors": [
        "M. Winter"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1ed178f0ecb4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(LinearAlgebra/SesquilinearForm): add basic lemmas for bilinear forms (#34487)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/1ed178f0ecb4003157c8dd82fd7b293603b4e083"
    },
    {
      "age_days": 0,
      "authors": [
        "Nailin Guan"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:664cbbe52927",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(LinearAlgebra): exterior algebra of product module (#41026)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/664cbbe52927ce6acaa39ca35498336116e123b8"
    },
    {
      "age_days": 0,
      "authors": [
        "Nailin Guan"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3fc586a5f01d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Homology): interaction of projective and injective dimension and SES (#36643)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3fc586a5f01db5e02a1f442bce948ee63dd9feaa"
    },
    {
      "age_days": 0,
      "authors": [
        "Thomas Krishna Waring"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:486d3e6030df",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(GroupTheory): results on normal subgroups of nilpotent groups (#43061)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/486d3e6030df11a906b5641c752b57699f9b4ed7"
    },
    {
      "age_days": 0,
      "authors": [
        "Weiyi Wang"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:d00a6cc5b8af",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Geometry/Euclidean): cross section perpendicular to the altitude of the simplex (#43054)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/d00a6cc5b8af00f88c5aa26d30bdae6107280b09"
    },
    {
      "age_days": 0,
      "authors": [
        "M. Winter"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:72d626e0ada7",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-31",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Geometry/Convex/ConvexSpace): consistency adjustments for convexity on module and affine space (#41305)",
      "updated": "2026-08-31",
      "url": "https://github.com/leanprover-community/mathlib4/commit/72d626e0ada7f25d1847989be06fe2e804d4cb23"
    },
    {
      "age_days": 0,
      "authors": [
        "Joël Riou"
      ],
      "content_date": "2026-08-31",
      "freshness": "fresh",
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      "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": 3,
      "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": 3,
      "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": 3,
      "authors": [
        "Sebastian Ullrich"
      ],
      "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": 3,
      "authors": [
        "Henrik Böving"
      ],
      "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": 3,
      "authors": [
        "Sebastian Ullrich"
      ],
      "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": 3,
      "authors": [
        "Peter Limkilde Svendsen"
      ],
      "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": 3,
      "authors": [
        "Julia Markus Himmel"
      ],
      "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": 4,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:f3c6b8462d6c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: new LRAT checker (#14842)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover/lean4/commit/f3c6b8462d6cbfcd2fb09599bf5820c59ca6773c"
    },
    {
      "age_days": 4,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:e991a05e359a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: initialize only the core modules `leanchecker-paranoid` needs (#14936)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover/lean4/commit/e991a05e359a25988f49bff3ab8af986e959b866"
    },
    {
      "age_days": 4,
      "authors": [
        "Salkutsan Aleksey"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:459d43013417",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: avoid exposing Fin.foldl implementation (#14554)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover/lean4/commit/459d4301341708de7c16350aeea647b112c62321"
    },
    {
      "age_days": 4,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b66d310c2420",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: sane `rwa` (#14937)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover/lean4/commit/b66d310c242069d99fccc0d5dd30ef72aec090c7"
    },
    {
      "age_days": 4,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-27",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:61bb5655d092",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-27",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: lake: read persisted code quality entries in `lake lint --code-quality` (#14933)",
      "updated": "2026-08-27",
      "url": "https://github.com/leanprover/lean4/commit/61bb5655d092c910d5f1b9f671ceeab87db6a964"
    },
    {
      "age_days": 5,
      "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,
      "arxiv_id": "2608.28031",
      "authors": [
        "Nima Anari"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28031",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-28",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The canonical Bethe approximation gives a deterministic approximation to the permanent of every nonnegative matrix within a factor of $(\\sqrt{2})^n$. We improve the base of this exponential factor: for some absolute constant $c<\\sqrt{2}$, there is a deterministic polynomial-time $c^n$-approximation for the permanent of every nonnegative matrix. This shows that the canonical Bethe guarantee is not a barrier for deterministic approximation of the permanent. The proof augments the Bethe lower bound with a new certificate tailored to matrices on which that lower bound loses nearly the full factor. The author supplied the high-level plan of attack, and the proof was developed in an interaction with ChatGPT 5.6 Sol Pro. The author subsequently verified the results. Codex assisted with proof checking, manuscript assembly, and typesetting.",
      "title": "Beyond the Bethe Approximation of the Permanent",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28031"
    },
    {
      "age_days": 5,
      "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": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.26418"
    },
    {
      "age_days": 5,
      "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": 5,
      "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": 6,
      "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": 6,
      "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": 7,
      "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": 7,
      "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": 7,
      "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": 3,
      "arxiv_id": "2608.28541",
      "authors": [
        "Javier Aguilar Martín"
      ],
      "content_date": "2026-08-28",
      "freshness": "fresh",
      "id": "arxiv:2608.28541",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [
        "negative:vision_world_models",
        "tool_use_agents"
      ],
      "published": "2026-08-28",
      "score": -1.1,
      "source": "arxiv-ai4math-core",
      "summary": "A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. We characterize what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. The gate quotient makes the question precise: acceptance-with-certainty determines the model exactly on the reachable query set; beyond reach is gauge. On a minimal ring instrument we prove the extreme case (a wrong-topology filled-disc artifact unfalsifiable by any sampling gate and bitwise harmless at play) and measure, with LLM synthesis across three model families, how one knob (a channel of width gamma) walks the same artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified. Three principles organize the empirics. First, danger is topology relative to reach: a channel the planner can use collapses the blind model's exploitation (play cost 1.09 to ~0 over a knee at gamma ~ 0.1), while a hidden channel with the same first Betti number keeps it at full strength (1.12). Second, repair is parameter-bound and sensor-bound: no family recovers the region from outside evidence; from inside, models pose the right topology but cannot pin its parameters, and the posed topology tracks the guiding persistent-homology summary's wrong beta_1 (a sensor with a measured geometric resolution limit), not the truth. Third, mitigation must match the error's dimension and direction: point fences fail against the one-dimensional boundary, a dimension-matched persisted fence collapses exploitation to a two-lesson transient (0.999 to 0.058), and the dual freedom certificate collapses the invented-mode failure symmetrically (1.769 to 0.029). In n dimensions the shell makes misidentification near-certain while the danger stays fully exploitable: the two axes are independent.",
      "title": "An Enclosed Mode Is a Gauge Choice: Topology Relative to Reach in Certified Code World Models",
      "updated": "2026-08-28",
      "url": "https://arxiv.org/abs/2608.28541"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}