{
  "counts": {
    "adjacent": 18,
    "core": 1,
    "errors": 0,
    "negative": 71,
    "total": 90
  },
  "date": "2026-10-01",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-10-01T20:26:35Z",
  "items": [
    {
      "age_days": 3,
      "arxiv_id": "2609.38237",
      "authors": [
        "Ishan K Singavarapu",
        "Manish Bhatt"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.38237",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Verifying large C codebases requires translating them into formally checkable semantics, but most autoformalization work reports a single aggregate success rate that conflates two different failure modes: code the translator declined to handle and code the translator translated incorrectly. We present a deterministic code-property-graph (CPG)-based exporter that translates C source into a small Lean~4 core semantics under a three-tier correctness discipline: hole-free, call-closed, and dynamic-hole-risk, that keeps these modes distinct. Applied to a re-export of the SQLite source tree (8{,}602 functions, over 1.5~million AST nodes), the exporter translates 5{,}222 functions (60.7\\%) hole-free, of which only 2{,}134 (24.8\\%) are call-closed, a $2.4\\times$ gap a single rate would hide. Both figures are reported in a full per-construct trust ledger rather than a single score. Our main contribution is methodological: a protocol for separating constructs that are fundamentally unresolvable by whole-program static analysis (such as public API boundaries) from constructs that only look that way. For example, we retracted our own ``impossible'' classification of function-pointer/vtable dispatch after tracing a concrete counterexample in the target codebase. Separately, a search for ``more holes closed'' surfaced a latent silent-wrong-answer bug: a translation that succeeded with an incorrect result rather than declining, a failure mode we argue is more dangerous than any hole, and one a hole-count-only evaluation would never surface.",
      "title": "A Trust Ledger and an Execution Check for CPG-Based C-to-Lean 4 Autoformalization: Separating Declined from Silently Incorrect Translations",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.38237"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.38286",
      "authors": [
        "Asad Shahab"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.38286",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "For a graph $H$, let $f(n,e,H)$ be the least number of colors in an edge-coloring of some $n$-vertex graph with at least $e$ edges in which every copy of $H$ is rainbow. Burr, Erdős, Graham, and Sós conjectured that $f(n,\\lfloor n^2/4\\rfloor+1,C_{2k+1})=(1/8+o(1))n^2$ for every fixed $k\\ge3$, and Bucić, Chen, and Ma recently proved this for all $k\\ge4$. We prove the remaining case $k=3$: \\[ f\\left(n,\\left\\lfloor n^2/4\\right\\rfloor+1,C_7\\right) =\\left(\\frac18+o(1)\\right)n^2. \\] The lower bound rests on a weighted palette inequality, which we prove with an exact rational certificate on five sampled vertices. Its main ingredients are a fractional matching of compatible triangular edges and private resources attached to nontriangular edges. A stable form of the inequality, combined with regularity, triangle removal, and a direct argument for graphs close to bipartite, transfers the bound to arbitrary edge-colorings. We also describe a Lean 4 formalization of the conjecture for every fixed $k\\ge3$, which combines the new seven-cycle proof with a formalization of the Bucić-Chen-Ma argument for $k\\ge4$.",
      "title": "The Burr-Erdős-Graham-Sós conjecture for the seven-cycle",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.38286"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39009",
      "authors": [
        "Nandakumar Edamana",
        "Piyush P Kurur",
        "Unnikrishnan Cheramangalath"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39009",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-09-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We give a new multiplication algorithm for tristate numbers improving upon the state-of-the-art implementation from the Linux kernel in terms of precision and formal proofs. Our algorithm is significantly more precise as shown by experimental evaluation (at the peak, giving better results in 95.59% cases compared to the previous work for 31-bit samples). Importantly, we achieve this additional precision with performance comparable to the previous algorithm, as demonstrated by benchmarks. Finally, we formalize and prove the soundness of the algorithm in the Rocq proof assistant, adding to the trust in the resulting implementation. Our algorithm is now part of the upstream Linux kernel. Our soundness proof in Rocq for the new multiplication algorithm works for all bit widths, while the SAT/SMT-based machine-checked proof accompanying the previous algorithm was restricted to 8 bits. We also provide Rocq proofs for the soundness and optimality of the newly added tnum union operation and the existing tnum addition algorithm from the Linux kernel. Our optimality proof for tnum addition presents a simpler and straightforward lemma compared to prior work.",
      "title": "Improved Tristate Multiplication With Formalization in Rocq",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39009"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39544",
      "authors": [
        "Jules Viennot",
        "Guillaume Baudart",
        "Marc Lelarge"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39544",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-09-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Recent achievements in AI-assisted mathematics require intensive interaction of agents with proof assistants to generate machine-checked proof certificates. Agents interact with proof assistants such as Rocq or Lean through an interface that controls what the agent receives from the prover and the cost of these interactions. Today, these interfaces are adapted from tools designed for humans and not optimized for agents. We propose an evolutionary method where a frontier model incrementally proposes new features and only keeps the ones that improve the overall performance of smaller models. We demonstrate the effectiveness of our method by growing, on a curated set of mathematical problems, \\rme, a new MCP server for the Rocq prover. On the held-out \\texttt{test} split of miniF2F-Rocq, an agent equipped with \\rme outperforms both the baseline that only exposes the Rocq compiler and an established MCP server, across four models from two families, in success rate, cost per solve, and time per solve. Although evolved for Rocq, the resulting server transfers to Lean, improving cost and time per solve on a subset of PutnamBench. We release \\rme and its port to Lean.",
      "title": "Growing an Agent/Prover Interface: Evolutionary Tool Design for Cost-Efficient Theorem Proving in Rocq and Lean",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39544"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39228",
      "authors": [
        "Wei Zhao",
        "Yangshuo Zou",
        "Chengxiang Ding",
        "Yifan Wu",
        "Xuchuan Wang",
        "Zimu Mao",
        "Lei Zhang",
        "Tao Luo"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39228",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "mathlib_retrieval"
      ],
      "published": "2026-09-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present FYAN, a human--AI harness for document-level mathematical formalization. Rather than treating theorems in isolation, FYAN coordinates an end-to-end workflow spanning specification, proof planning, logical review, Lean proof construction, knowledge curation, and validation, with support for independent supervision and human guidance. A central component is evidence-grounded semantic auditing, which assesses whether formal statements faithfully preserve their informal specifications. A language model constructs structured evidence over local correspondences, omissions, scope, and logical relations, while a deterministic validator checks this evidence and produces reproducible judgments. When a substantive but admissible deviation is accepted, FYAN requires an explicit proof-transfer obligation connecting the formal statement back to a source-facing interpretation. With the same model (DeepSeek-V4.1-Flash) in every stage, FYAN proves 86 of 143 FormalTCS theorems under a strict Lean check, against 69 for a general agent harness, and raises the natural-language proof score from 0.501 to 0.851. On ConsistencyCheck, its semantic audit catches more inconsistent statements than a direct LLM judge, both on labels verified against the source (recall 0.777 vs. 0.636) and on the original labels (0.873 vs. 0.820), and localizes each mismatch it reports to a specific hypothesis, conclusion, or scope. FYAN also built ODENumLib, a 9,355-line Lean library for the numerical analysis of ordinary differential equation.",
      "title": "Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39228"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.40062",
      "authors": [
        "Aparna Gupte",
        "Seyoon Ragavan",
        "Mark Zhandry"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.40062",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We establish a no-go theorem for a broad class of quantum algorithms for the dihedral coset problem (DCP). We consider the Fourier-sampling and subset-sum-measurement template proposed by Regev (SIAM Journal on Computing, 2004), which is one of the main approaches to solving DCP. Suppose that, after measuring the lower $n-1$ bits of the subset sum, the algorithm discards any $ω(\\log n)$ bits from each of the Fourier labels. Then we prove that the algorithm cannot succeed in solving DCP. This shows that any algorithm following this template must make extensive use of the Fourier labels, and thus serves as a useful guide for developing algorithms for DCP. As a main application, we show that the recent algorithm by Simon (IACR ePrint:2026/1591, August 11 2026) does not solve DCP. We show that after the subset-sum measurement, this algorithm can be implemented (up to exponentially-small error) using only the most-significant third of the Fourier labels, and is therefore subject to our general no-go theorem. To help with verifiability, we release Lean 4 code for our results.",
      "title": "A Fourier-Label Information-Loss Barrier for Dihedral Coset Algorithms",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.40062"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.37754",
      "authors": [
        "John Fairfax-Ball"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.37754",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "For integers $m\\geq 2$ and $m\\mid N$, let $G(N;m)=\\gcd\\{\\binom{N}{k}:0<k<N,\\ m\\mid k\\}$. We prove a complete $p$-adic valuation formula for $G(N;m)$ at primes $p\\equiv -1\\pmod m$, under the hypotheses $m\\geq 3$, $m\\mid N$, and $m<N$. Writing $N=\\sum_i d_i p^i$, put $A=\\sum_{i\\text{ even}}d_i$ and $B=\\sum_{i\\text{ odd}}d_i$. Then $v_p(G(N;m))$ is $2$ in the exceptional mixed case $(A,B)=(1,1)$ with $p=m-1$, is $1$ in the mixed case $(A,B)=(1,1)$ with $m<p$, is $1$ in the one-parity cases $(A,B)=(m,0)$ and $(A,B)=(0,m)$, and is $0$ otherwise. The proof uses Kummer's theorem to translate the problem into digitwise borrow counts and a minimal signed zero-sum classification. A source-level literature audit through 25 September 2026 located no equivalent prior theorem for the full minus-one classification: McTague's corrected same-residue extension covers the one-parity $p>m$ subcases, but not the mixed-parity branch or the $p=m-1$ regime. The theorem, its plus-one companion, a scaling reduction, and the $m=3,4,6$ specializations have been formalized in Lean 4 / Mathlib.",
      "title": "Restricted Binomial GCDs at Primes Congruent to -1",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.37754"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.38492",
      "authors": [
        "Volkan Dağlı",
        "Zerrin Dağlı",
        "Dağhan Dağlı"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.38492",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present gap-lean4-port (Release v0.2.0), a machine-checked formalization of foundational algorithms in computational discrete algebra and permutation group theory within the Lean 4 interactive theorem prover and Mathlib4. While modern proof assistants feature extensive abstract algebraic hierarchies, constructive and operational permutation group algorithms, such as Charles Sims' 1970 Schreier-Sims algorithm, transversal tree lookups, and backtrack ordered partition refinement, have remained largely unformalized in dependent type theory. Here, we formalize the operational algorithmic core of the Groups, Algorithms, Programming (GAP) system library across four foundational modules, proving 35 machine-checked theorems with zero unproven conjectures (sorry) and zero custom axioms under standard Lean 4 foundations (propext, Classical.choice, Quot.sound). We machine-check: (1) Schreier-Sims stabilizer chain hierarchies (StabLevel, StabChain) and the invariance of incremental transversal tree extensions (extendSchreierPoint_invariant); (2) single-level and multi-level Schreier sifting reductions (siftOneLevel, siftFull), proving that full sifting strictly fixes all base points (siftFull_fixes_all_basePoints); (3) constructive soundness and completeness of Base and Strong Generating Set (BSGS) membership testing (membershipTestKnownBase_iff_mem); (4) backtrack ordered partition cell refinement (splitCellByPred), proving mutual cell disjointness, union conservation, and exact cardinality preservation; (5) cyclotomic extension rings Z/nZ(eps_m) and machine-check GAP's exact size theorem |Z/nZ(eps_m)| = n^m; and (6) executable Bezout inverses via Extended Euclidean GCD (Nat.gcdA) over residue rings Z/nZ. The entire codebase compiles deterministically under 'lake build RequestProject' and is openly available at https://github.com/pCwOrM/gap-lean4-port.",
      "title": "Machine-Checked Computational Group Theory in Lean 4: Operational Schreier-Sims Stabilizer Chains, BSGS Sifting, and Backtrack Ordered Partitions",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.38492"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.38384",
      "authors": [
        "Pauline Bourigault"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.38384",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Verified proof edits offer a natural source of supervision for improving language-model-generated Lean proofs. Yet verification establishes that an edit is correct, not that its training signal is free of search artifacts. We introduce LeanPolish, a symbolic Lean 4 pipeline that releases 33,402 accepted local edits and 65,596 same-state failed attempts, and use it to study what models learn from this supervision. First-success search admits a goal-independent rule with perfect ranking accuracy; teacher-selected evaluation sites also reward trivial deletions. Continuing menu evaluation beyond the first success removes the ordering shortcut: a trained ranker selects the best candidate on 70.1% of evaluated held-out states, versus 36.9% for the strongest frozen baseline. For compression, iterating the symbolic pass raises miniF2F savings from 19.7% to 27.5%, exceeding the neural hybrids we test there. Verified neural editing helps on other proof sources, but matched frozen-model controls show that its gains need not come from training. The supervision does improve whole-proof rewriting: fine-tuning raises verified token reduction from 2.8% to 5.5% on 19 PutnamBench proofs. Together, the released edits, complete candidate pools, and controlled evaluations separate learning to imitate a search policy from improving on that search. They provide a reproducible basis for studying proof improvement while keeping correctness, compression, and edit policy distinct.",
      "title": "LeanPolish: Verified Supervision for Lean Proof Compression",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.38384"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.36663",
      "authors": [
        "Shuangping Li",
        "Peng Zhang"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.36663",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present GenLimitLib, a source-aligned Lean 4 library for language generation in the limit. Introduced by Kleinberg and Mullainathan at NeurIPS 2024, language generation in the limit studies a theoretical question motivated by LLMs: how to generate valid new strings from observed examples. This young and rapidly evolving field offers a natural testbed for studying large-scale formalization. GenLimitLib contains formal developments for 30 papers. It extracts shared definitions and reusable proof components while preserving paper-specific assumptions and statements, and records relationships across papers. In this way, GenLimitLib provides a concrete and structured view of the literature. We show through mathematical case studies and LLM experiments how our library can support both human mathematical research and AI-assisted research. Our Library: https://github.com/pengzhang91/generation-in-the-limit-lib.",
      "title": "GenLimitLib: A Formal Library for Language Generation in the Limit and AI-Assisted Mathematical Research",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.36663"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.38242",
      "authors": [
        "Eric Allen"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.38242",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-29",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Programs that compute with physical quantities often need to convert between units of measurement, and as the Mars Climate Orbiter showed, these conversions can be a rich source of errors. Meanwhile, typed unit calculi, our most rigorous formalisms for checking physical units in a program, have excluded unit conversions. Through this exclusion, they have established a powerful property: well-typed programs are invariant under rescaling (no program can depend on how big a meter is). But losing the ability to convert between units is a significant cost. In contrast, practical languages provide conversion but no invariance theorem. We present $Λ_S$, a typed lambda calculus with conversion, quantification over units and dimensions, and vectors and linear maps with per-component units, and we determine exactly how much invariance survives conversion. For terms without unit constants we prove two abstraction theorems: (i) a convert-free term is invariant under every rescaling; (ii) a term with conversions is invariant under every rescaling that scales all units of one dimension by the same factor. The condition in (ii) cannot be weakened: under any other rescaling, some conversion of a nonzero value is not invariant. For first-order programs, a verified decision procedure returns one of three verdicts: it certifies that no error in the declared conversion factors can change the program's answer, names the accumulated ratio through which such an error would scale it, or declines. A verified checker decides whether unit declarations are consistent and determine every conversion factor, and extracts each factor exactly. We also prove adequacy, erasure, and the $n$-variable Pi theorem of dimensional analysis with conversion. Every theorem is mechanized in Lean 4, and the evaluator compiles to a native binary.",
      "title": "A Calculus for Units of Measure with Conversion",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.38242"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.34927",
      "authors": [
        "Alexandre Zua Caldeira"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.34927",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove that the state space of every well-formed session type, quotiented by strongly connected components, forms a bounded lattice; n-ary parallel composition yields product lattices. Two consequences follow: duality preserves the lattice up to isomorphism, and Gay-Hole width subtyping corresponds to lattice embedding for non-recursive types. We validate this on 108 benchmark protocols across networking, databases, distributed systems, AI, and fault tolerance: all form lattices, 93 distributive, 15 non-distributive. Mechanised in Lean 4 with two independently developed tool implementations.",
      "title": "Session Type State Spaces Form Lattices",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.34927"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.36279",
      "authors": [
        "Christoph Benzmüller"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.36279",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzmüller and Scott's Notes on Gödel's and Scott's variants of the ontological argument (2025), reaches beyond the modal object language of the arguments: its property quantifiers range over terms that may also express nominals and satisfaction operators of hybrid logic, and a proof using one proves a theorem of the embedding that need not be one of the modal logic. That the framework affords this is not new, and whether a result is one of the modal logic can be settled in two ways: by replaying it in an explicit proof calculus, done by hand for chosen theorems, or by analysing the proofs the embedding itself produces, which this article does mechanically, for every result at once. Every statement the Notes prove has a proof inside the object language: 294 written out by hand and machine-checked, none using a nominal. The proofs the Notes themselves give instantiate no nominal either; what the detector flags there are terms a prover substituted. The three questions the Notes leave open are settled too, and without nominals, but the conjunction axiom has to be emended: generalised in the Notes to Gödel's \"any number of summands\", it covers the conjunction of no properties, and of one; the empty one alone settles all three, and the two together yield what a separate axiom of Gödel's is for. This article restricts the conjunction axiom to at least two different conjuncts, the reading Gödel's footnote suggests, and the questions are settled again, by proofs that turn on the argument rather than a degenerate instance. The restriction holds of the object language only: with a nominal the axioms make the accessibility relation the identity and the readings coincide. Every theorem is verified in Isabelle/HOL and independently in Lean 4; the countermodels are Nitpick's, certified by the build.",
      "title": "Proofs Without Nominals: Gödel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.36279"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35762",
      "authors": [
        "Jaewook J. Suh",
        "TaeHo Yoon",
        "Edward Duc Hien Nguyen",
        "Bicheng Ying",
        "Shiqian Ma"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35762",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "This paper presents Peppy, an AI-assisted workflow for discovering tight, analytic convergence proofs for first-order optimization algorithms. Generic approaches to using LLMs to conduct mathematical research target an unspecified, broad spectrum of problems and sometimes use the Lean 4 proof assistant for formalization. On the other hand, Peppy leverages domain-specific knowledge more heavily and is thereby capable of constructing the proofs in a more structured manner, which allow a minimal and accessible verification through SymPy. We experimentally demonstrate through examples that Peppy provides a rigorous, practical, and reproducible paradigm for AI-assisted theorem synthesis in optimization. We further highlight its capability of closing several open problems on tight convergence analysis of first-order optimization algorithms, including conjectures for Nesterov's FGM. Overall, Peppy is designed to turn the art of optimization algorithm analysis into a science.",
      "title": "Peppy: An AI-Assisted Workflow for Tight Convergence Analysis of Optimization Algorithms",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35762"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35187",
      "authors": [
        "Xinyu Wang"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35187",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Let $f$ be a Steinhaus random multiplicative function and let $g$ be a polynomial of degree $d$. Write $S_N=N^{-1/2}\\sum_{n\\le N}f(n)\\,e(g(n))$. We prove a quantitative dichotomy for the moments of $S_N$: for each integer $s\\ge 2$, either $\\mathbb{E}|S_N|^{2s}$ is close to the Gaussian moment $s!$, or the coefficients of $g$ can be approximated by rationals with a small denominator. In particular, if the coefficients of $g$ satisfy a Diophantine condition, then $S_N$ converges in law to a complex normal distribution with mean $0$ and variance $1$. Lean 4 code for the proofs is provided, for convenience of verification.",
      "title": "Moments of random multiplicative functions with polynomial coefficients",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35187"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35062",
      "authors": [
        "Shuo Li Liu"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35062",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We give a finite simplex theorem. When the number of states equals the number of source signals and the source posterior likelihood-ratio vectors form a simplex, Blackwell dominance is characterized by a universal barycentric-coordinate condition. We also give an explicit countable-state, countable-signal diagnostic-monitor theorem with a closed-form universal criterion and a closed-form garbling; tensorization yields dominance at every sample size. Finally, we provide a three-state, two-signal counterexample to the sufficiency conjectured by Mu, Pomatto, Strack, and Tamuz for their many-state moment-generating-function conditions for large-sample Blackwell dominance. The pair satisfies strict comparisons on both parameter domains, all ordered Kullback-Leibler inequalities, bounded likelihood ratios and pairwise genericity, but dominance fails at every positive sample size. The finite theorem, obstruction, and continuum inequalities are verified in Lean 4.30 with Mathlib; the countable diagnostic proof is given analytically.",
      "title": "Blackwell Boundaries",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35062"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.37471",
      "authors": [
        "Shisheng Li"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.37471",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-09-28",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Call a set $A$ of positive integers admissible if, whenever $a_1\\cdots a_r=b_1\\cdots b_s$ with $a_1,\\dots,a_r$ distinct elements of $A$ and $b_1,\\dots,b_s$ distinct elements of $A$, necessarily $r=s$. Erdős asked whether admissible sets can have density $1-\\varepsilon$ for every $\\varepsilon>0$, and whether $\\{1,\\dots,N\\}$ always contains an admissible subset of size $(1-o(1))N$. For the variant in which repetitions are allowed both questions were answered negatively by Erdős, Ruzsa and Sárközy and by Granville and Soundararajan; for products of distinct elements, the first question was answered only recently (with density bound $7/8$), and the second has remained open. We show that every admissible $A\\subseteq\\{1,\\dots,N\\}$ satisfies $\\sum_{a\\in A}1/a\\le\\tfrac12\\log N+(\\log\\log N+2)^2$, and that there is an absolute constant $η>0$ such that every admissible $A\\subseteq\\{1,\\dots,N\\}$ has $|A|<(1-η)N$ for all large $N$. Both questions therefore have negative answers. The proofs are elementary; the second rests on a coupling that replaces the largest divisor of an integer composed of small primes, which avoids the divisor-function losses inherent in counting quotients along a multiplication table. Both negative answers are formally verified in Lean 4 against the statements of the Formal Conjectures project.",
      "title": "A negative answer to Erdős Problem #786",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.37471"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35632",
      "authors": [
        "Tejasvi Singh Tomar"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35632",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-09-28",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "We prove that for every choice of four positive masses and every cyclic ordering of the bodies there is exactly one strictly convex planar central configuration with that ordering, up to similarity. This answers Problem 10 in the list of Albouy, Cabral and Santos, which Santoprete calls the Simó-Yoccoz conjecture. The main step is a uniform lower bound for the Hessian at convex central configurations: it is at least one quarter of its radial part, which vanishes only on translations and rotations. Dziobek's relations turn the indefinite part of the Hessian into a negative multiple of a square, and a Cauchy-Schwarz argument bounds this term by the radial part times the trace of an explicit $2\\times 2$ matrix in which the masses do not appear. We prove that this trace is less than 3/4 by interval arithmetic on the three-dimensional set of normalized convex central configurations, in the coordinates of Corbera, Cors and Roberts. Uniqueness then follows by a covering argument from the case of four equal masses. The computation has been repeated with a second, independently written program. The Hessian bound and the uniqueness theorem, including the computation, have been formalized in the Lean proof assistant and checked by its kernel, using only the standard axioms. As consequences, every degenerate four-body central configuration is concave, the convex central configuration depends analytically on the masses, and the known symmetry theorems for kites, isosceles trapezoids and rhombi follow in a few lines. The analytic dependence and the symmetry theorems are also formalized.",
      "title": "Uniqueness of four-body convex central configurations for all masses",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35632"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.34960",
      "authors": [
        "Feiming Wang",
        "Daibo Li",
        "Kun Yuan"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.34960",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "tool_use_agents"
      ],
      "published": "2026-09-28",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Formalizing research-level stochastic optimization in Lean requires both an algorithm model and domain theory connecting foundational libraries to convergence proofs. Revising a model to restore provability can change the mathematical claim. We introduce ProofLoom, a fully automated LLM-agent system for Proof-Obligation-Driven Theory Construction. Given a published algorithm, target theorem, and source proof, ProofLoom autonomously constructs the Lean model and supporting theory. Open proof obligations drive the development of definitions, interfaces, lemmas, and proof plans. Signature contracts record evidence and obligations for model revisions; an independent Judge rejects unsupported assumptions and weakened conclusions. Planner expands the published argument into intermediate claims, and Audit checks whether the Lean proof follows it. Across tasks, SOptLib accumulates verified mathematics and construction experience: reusable results are extracted, generalized, and verified, while modeling decisions and failed proof routes are recorded. Later tasks retrieve these results and records and contribute new developments, forming a cycle of construction, accumulation, and reuse. On fifteen textbook and research-paper tasks, ProofLoom obtains mean human ratings of 6.3/7 and 6.4/7, compared with 4.9/7 and 5.0/7 for the strongest of six baselines. Across 33 developments, it produces 490,693 lines of algorithm-local Lean code with no sorry. The formalizations also expose 28 incorrect formulas, proof gaps, and algorithm-analysis mismatches in published sources across 22 developments, each with checked evidence.",
      "title": "ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.34960"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:e70fdc77742c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: make `Decidable` And/Or `macro_inline` again (#15430)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/e70fdc77742cc2511d5699b484ce534588c2212c"
    },
    {
      "age_days": 0,
      "authors": [
        "David Thrane Christiansen"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:7050b7be21ee",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: remove extraneous `atomic` from Verso blockquote parser (#15425)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/7050b7be21ee5ecfe8b6bcbdc44ce871a6da639f"
    },
    {
      "age_days": 0,
      "authors": [
        "Robin Arnez"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c908828b7afd",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: remove duplicate `BEq (Option a)` instance (#15316)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/c908828b7afd2e5a8e36c398971ba1608ec13034"
    },
    {
      "age_days": 0,
      "authors": [
        "Robin Arnez"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8687bce592f6",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: `Array.compareLex` to be specialized correctly (#15315)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/8687bce592f6f985d7f5e1f3a18bf77020b929f7"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:300eacaf66ef",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: support mutual recursion between macro_inline and csimp (#15429)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/300eacaf66eff77c7269d8f8d4fd2a264cd18a97"
    },
    {
      "age_days": 0,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:481c47acf685",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: missing order instances for `ByteArray` (#15329)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/481c47acf6858f135c7f86af3697504c5104ff7c"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:023b7c477951",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add a CEGAR solver with support for UF to bv_decide (#15398)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/023b7c4779513894d4f29053d82e55fde60d6382"
    },
    {
      "age_days": 0,
      "authors": [
        "Robin Arnez"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:13f0cbd311c4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `Expr.hasAnyMVar` analogous to `Expr.hasAnyFVar` (#15319)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/13f0cbd311c4a5bcac53be37c15182dbb5a86105"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c346b4898ee8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `grind norm` lemmas for the lattice theory (#15299)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/c346b4898ee83ec6df177ce8b3a4249511384b18"
    },
    {
      "age_days": 0,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c28dd4565fbe",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: doc: more Grove tables for order instances (#15428)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/c28dd4565fbe7e98e559d9a70380fea9050d2ac5"
    },
    {
      "age_days": 0,
      "authors": [
        "Lean stage0 autoupdater"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:64c1a7ee2c5d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: update stage0",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/64c1a7ee2c5dbe3b0bc51686cd8d566804668cc1"
    },
    {
      "age_days": 0,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:71bae769f911",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: missing order instances for `List`, `Array` and `Vector` (#15304)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover/lean4/commit/71bae769f9116db7bc70baf4c367ad3e551bfea9"
    },
    {
      "age_days": 0,
      "authors": [
        "Dagur Asgeirsson"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:53cd6f8a6867",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: refactor(CategoryTheory): use quadrifunctors for the localized pentagon (#43009)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/53cd6f8a6867bb8d75f05a0175574b850ced5400"
    },
    {
      "age_days": 0,
      "authors": [
        "Jovan Gerbscheid"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:a04f5a63d974",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: perf: disable the unreachable tactic linter (again) (#44391)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/a04f5a63d9743efa2fb83ab2912169caebecfe83"
    },
    {
      "age_days": 0,
      "authors": [
        "Jovan Gerbscheid"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:033c22e2f1d9",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: perf(Linter/UnusedTactic): replace `IO` with `BaseIO` (#44377)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/033c22e2f1d9a1a3d694d8354cb3c4892caee931"
    },
    {
      "age_days": 0,
      "authors": [
        "Jovan Gerbscheid"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:26804a9ffeb8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix(Order/Heyting/Regular): fix `Lattice` instance diamond (#41776)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/26804a9ffeb88d5b10ff493822c64f427d76a7a1"
    },
    {
      "age_days": 0,
      "authors": [
        "Aaron Liu"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:c7eec1400d29",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(SetTheory/Ordinal): definition of addition and multiplication (#43588)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/c7eec1400d29a52e5944bd5aa31e999195854dfe"
    },
    {
      "age_days": 0,
      "authors": [
        "Michael Graham"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:bc9cec55beb0",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Matrix/Rank): linearly independent rows give a surjective mulVec (#43956)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/bc9cec55beb0c3c8c28749378d9e54f9c3a145ff"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:8b426c3abbed",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Data/Sym/Sym2/Card): cardinality theorems about `Sym2 α` (#36442)",
      "updated": "2026-10-01",
      "url": "https://github.com/leanprover-community/mathlib4/commit/8b426c3abbedb0514dc6b25c4992ba2b776183c7"
    },
    {
      "age_days": 0,
      "authors": [
        "Jesse Alama"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1f2e1a8c80f3",
      "kind": "github_update",
      "label": "negative",
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      "matched_signals": [],
      "published": "2026-09-30",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Matrix/NonsingularInverse): generalize some lemmas from `Field` to `IsArtinianRing` (#44054)",
      "updated": "2026-09-30",
      "url": "https://github.com/leanprover-community/mathlib4/commit/69452e2479125f8a0dc95426b82034884873f20e"
    },
    {
      "age_days": 1,
      "authors": [
        "Yaël Dillies"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:afbe9eae3227",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Algebra/Group/Torsion): deprecate `zpow_eq_zpow_iff'` (#44349)",
      "updated": "2026-09-30",
      "url": "https://github.com/leanprover-community/mathlib4/commit/afbe9eae32276e014bb57f6525ea96dec05cf30a"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:a332ad100000",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: test: re-enable the `grind_bitvec2` benchmark (#15408)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/a332ad1000004723f3fedf2990e775762dbe6ecd"
    },
    {
      "age_days": 2,
      "authors": [
        "Hongyu Ouyang"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:62e2afd1a5a7",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: memoize the search path root of each package in `findOLean` (#15291)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/62e2afd1a5a79562d37cabc44fb1619b7e0556d6"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:633a200e4aac",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: sharing violation in the `Sym.Arith` normalizer (#15405)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/633a200e4aac7eba2b6f85719eb6e3679a7a2320"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c266b91ed310",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: introduce `__`-prefixed binders as implementation details in `Sym.intros` (#15322)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/c266b91ed31065c5ebfa6000329f1f1d9a6e35fc"
    },
    {
      "age_days": 2,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:6dae63ba38d3",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: avoid sharing bug in bv_decide (#15403)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/6dae63ba38d3c288288e34cb3dfda27c1a2c79a9"
    },
    {
      "age_days": 2,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:089d938f77b5",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: make codegen for ctorIdx O(1) (#15407)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/089d938f77b5249b8eaf945de42f533c5e617313"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:67a862927484",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: lattice lemmas and `PredTrans` rules for `do` notation (#15387)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/67a8629274847c29155324086f6c0f49ba20ec8d"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:58d47647ae50",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: control-flow reduction in the `Sym.simp`-based `grind` normalizer (#15409)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/58d47647ae5036505c6452f36e2ea871121c67a9"
    },
    {
      "age_days": 2,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:4ac30d495e49",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add support for incremental (partially verified) bitblasting (#15404)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/4ac30d495e4917a6de26ceae7163abc440938a6a"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:791e095296b9",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `Char` ground evaluation in `Sym.simp` (#15411)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/791e095296b9a29cc2c27e7fbf1389fff7bcf276"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8d338845e5de",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: disable broken `grind_bitvec2` benchmark temporarily (#15397)",
      "updated": "2026-09-29",
      "url": "https://github.com/leanprover/lean4/commit/8d338845e5de0a87977768f0d0bd7536620d3245"
    },
    {
      "age_days": 3,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8dd5d448291e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-28",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: sharing violation in `Sym.dsimp` binder telescopes (#15389)",
      "updated": "2026-09-28",
      "url": "https://github.com/leanprover/lean4/commit/8dd5d448291eb0ca0180c8ae1f9d248b2c8a2a7b"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39460",
      "authors": [
        "Carlotta Schneeberger",
        "Kevin Tang"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39460",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Rechtsrock is a subgenre of rock music that spreads right-wing ideology, often instrumentalized to recruit adolescents into the radical scene. Monitoring institutions counteract this by manually examining and, in some cases, banning extremist content; however, there are border cases that evade regulation. We present a study aimed at determining whether such a case, the band Frei.Wild, should be classified as politically right-leaning or as part of the general German rock genre. We sampled a German rock dataset and created a corpus for right-wing rock to use as reference in this analysis and found that we can confirm the intuitions from previous investigations that Frei.Wild successfully maintains an ambiguity with regard to their political affiliation. However, the tendency is towards the right-wing spectrum. Lexical analyses reveal nationalistic narratives and two high-performing classifiers (up to 97% ROC-AUC score) label more than half of their songs as right-wing extremist. Our analysis provides insight into how computational methods can improve the process of identifying right-wing extremist tendencies in music, especially in borderline cases like Frei.Wild. The code and data are made available for future research.",
      "title": "Right-Wing Rock or Just Rock? A Computational Linguistic Analysis of Frei.Wild",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39460"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39872",
      "authors": [
        "Bruno Le Floch"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39872",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We consider the 653 equational laws of order up to 4 for an associative binary operation, and all of their conjunctions. We determine that there are only 456 equivalence classes of such conjunctions (associative equational theories), and find all implications between them. The conjunction operation makes this set of theories into a semi-lattice. These results are formalized in Lean. This is a semigroup analogue of the Equational Theories Project, but extended to conjunctions of equations.",
      "title": "Lattice of 456 semigroup varieties from equations of order up to 4",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39872"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.38919",
      "authors": [
        "Fengqi Hou"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.38919",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We encode the vertices of every finite complete bipartite graph as binary strings at each scale. The information distances between these strings approximate the scaled graph distances with an additive error bounded by a constant independent of the scale. We also assign one fixed infinite binary sequence to each vertex; suitable prefixes satisfy the same distance estimate with logarithmic error. This extends Hutter's construction for $K_{3,3}$ and resolves his open problem on scale-embeddings of finite complete bipartite graphs. Combined with his complete bipartite obstruction, these embeddings show that no positive power of information distance can be represented exactly by distances in a real Hilbert space, resolving his question about such representations. For conditional prefix complexity, we further prove that at most $2^{δ+C}$ strings lie between any two strings with total distance exceeding their mutual distance by at most $δ$, where $C$ is independent of the endpoints. This bound rules out scale-embeddings of the integer line and every positive-dimensional integer lattice, resolving Hutter's lattice embedding problem for both string and sequence embeddings. Restriction to the integer lattice gives the same conclusion for $(\\mathbb R^m,\\|\\cdot\\|_1)$ for every $m\\ge1$.",
      "title": "Complete bipartite embeddings, lattice non-embeddability, and non-Euclidean powers of information distance",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.38919"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.38959",
      "authors": [
        "Rohit Sharma",
        "Pavani Ayinampudi",
        "Aditya B. M. V.",
        "Jinal Gupta",
        "Prakash Hegade",
        "Sakshi Sharma",
        "Meenakshi V",
        "SRS Iyengar"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.38959",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Real-time classroom polls are widely used and increasingly generated with automated assistance, yet the questions themselves are rarely evaluated as measurements. We audit a large corpus of authentic classroom polls, 604 items across 47 sessions answered 340,668 times by 2,807 learners, as a measurement instrument. For the 539 items whose correct answer could be established and verified from the lecture transcript, we place every item and every student on a common scale using item response theory and analyse the answer structure of the True/False items. Two findings emerge. First, the polls form a coherent but easy scale of moderate precision (marginal reliability about 0.60), on which roughly a quarter of items barely separate stronger from weaker students. Second, students show a robust tendency to answer True, present at the individual level (77% of students lean True), which meets a milder tendency for items to be keyed False; as a result answer direction predicts difficulty, False-keyed items being about thirteen points harder, and the effect survives controls for item content and for selective answering. Both findings rest on signals a polling system already records, so the same checks can be run as items are generated, before they reach students.",
      "title": "An Audit of Measurement Quality and Answer Bias in a Large Classroom-Poll Corpus",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.38959"
    },
    {
      "age_days": 1,
      "arxiv_id": "2609.39633",
      "authors": [
        "John Fairfax-Ball"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2609.39633",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We study a support-collapse version of graph pebbling on paths. A configuration is stackable if a sequence of legal pebbling moves can produce a nonzero configuration supported on a single vertex. On the path P_n, we choose a configuration uniformly from all weak compositions of total n times mu_n, where mu_n is a positive integer. We prove a two-sided fixed-offset transition for the logarithmic density. The transition is centred at sqrt(log_2 n) - (1/2) log_2 log_2 n + log_2(3e). For every fixed epsilon greater than zero, the stackability probability tends to zero when log_2 mu_n is eventually at most the centre minus epsilon, and tends to one when it is eventually at least the centre plus epsilon. No assertion is made at zero offset. The proof uses an exact recursive stackability score on trees, a one-dimensional path-message recurrence, binary-partition asymptotics for rare dyadic deficit excursions, a constant-cost regeneration argument, and an exact deep-message necessity theorem. Conditioning independent geometric occupancies on their sum returns the uniform fixed-total model. The finite deterministic necessity theorem and its exact fixed-total corollary are formalised in Lean and registered with Palomar; the full probabilistic asymptotic theorem is not part of that registration.",
      "title": "A Fixed-Offset Transition for Random Stackability on Paths",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2609.39633"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.38035",
      "authors": [
        "Jeff Calder",
        "Nadejda Drenska"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.38035",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting. The solution formula establishes that the adversary's rank strategy $(1,0,1,0,0)$ is globally optimal, and the COMB strategy $(1,0,1,0,1)$ is optimal exactly on the set where $x_1=x_2$ and $x_3=x_4$. The formula is derived from the solution of the geometric-stopping problem given in our companion paper through the transform principle of Bayraktar, Ekren and Zhang, which links the two problems by a Laplace transform. Inverting the transform term by term expresses the solution through a series of Gaussian and complementary error function kernels. The optimality of $(1,0,1,0,0)$ is reduced to the signs of $41$ one-variable Gaussian series, which are certified with computer assistance by Poisson summation, first-mode domination and interval arithmetic on $1616$ rational cells. The proofs of our main theorems, certificates included, are also formalized in the Lean proof assistant.",
      "title": "The finite-horizon five-expert prediction problem",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.38035"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.36534",
      "authors": [
        "Andrew Tang",
        "Nicholas Deas",
        "Kathleen McKeown",
        "Vishal Misra"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.36534",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Dense retrievers decide which documents reach users and the language models that use them, yet they are typically evaluated with neutral queries. We ask whether the identity signals that real users express in their queries---political ideology and dialect---bias what a retriever returns. We design evaluations in two domains, political news and consumer-health questions, each pairing a controlled synthetic set that varies only the identity signal with naturalistic queries. Across five dense retrievers and a sparse baseline, every retriever (i) retrieves articles that align with the query's own political lean and (ii) performs worse for questions written in African American Language (AAL) than in White Mainstream English (WME). Two analyses tie these gaps to queries' identity signals beyond surface vocabulary: partialling out an aggregate lexical-asymmetry score leaves the synthetic gaps largely intact, and linear probes recover lean and dialect from the retrievers' query embeddings beyond token-level features. Left unaddressed, such retrieval biases risk contributing to polarization and reinforcing the health disparities already faced by AAL speakers. Code is available at https://github.com/Andrewtcr/bias-ret.",
      "title": "Retrieval Sensitivity to Identity Signals in Queries",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.36534"
    },
    {
      "age_days": 2,
      "arxiv_id": "2609.37728",
      "authors": [
        "Moussa Labbadi",
        "Rupak Majumdar",
        "V. R. Sathiyanarayana",
        "Sadegh Soudjani"
      ],
      "content_date": "2026-09-29",
      "freshness": "fresh",
      "id": "arxiv:2609.37728",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-29",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Discrete-event simulation is a standard technique for modelling and analysing the performance of computer systems, networks, and services. Although simulation tools are widely used, reasoning about the correctness and performance guarantees of the models they implement remains largely ad hoc: simulation outputs are interpreted statistically, but there is no logical foundation for deductive reasoning about their behaviour. We present a core imperative calculus that captures the essential constructs common to discrete-event simulators: asynchronous execution, continuous and discrete sampling from distributions, and time-based event scheduling through a global event queue. On top of this calculus, we develop a proof system for reasoning about almost-sure reachability and expected reaching time properties. Our main result is a sound and complete proof rule for these properties. Our framework generalizes deductive reasoning for discrete-time probabilistic programs to the setting of performance models, in which continuous time and continuous probability distributions are central. We have implemented the proof rules in a tool embedded in Lean. We demonstrate the applicability of our proof rule by deriving proofs of almost-sure reachability and expected reaching time for a number of case studies, including client-server examples that go beyond analytic solutions from queueing theory as well as convergence behaviours in network routing protocols. Establishing the soundness and completeness of our proof rules requires significantly more complex arguments than in the discrete-time setting. This is due to the fundamentally discontinuous nature of the operational semantics and the measure-theoretic challenges of continuous time and probability distributions.",
      "title": "Formal Reasoning about Performance Models",
      "updated": "2026-09-29",
      "url": "https://arxiv.org/abs/2609.37728"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.34889",
      "authors": [
        "Isabela Drǎmnesc",
        "Tudor Jebelean",
        "Sorin Stratulat"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.34889",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-28",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "This is a case study on a specific version of the Patience Sort algorithm in which we illustrate the evolution of it from an intuitive but inefficient nested recursion into a more complex but more efficient tail recursion, together with its formal implementation and certification in Theorema and Rocq (formerly Coq). We identify some general principles of algorithm transformation, and we develop the necessary background theory and proof methods. As a significant distinctive aspect, the approach in Theorema uses multisets, which simplifies the whole process and makes it more intuitive. The certification process reveals significant differences between the Theorema and Rocq approaches, about which we provide a comparative analysis with respect to algorithm definition, proof development, and proof effort. This analysis offers insights into how algorithm design influences the complexity and structure of formal proofs and demonstrates how non-trivial algorithms can be effectively verified across different formal frameworks.",
      "title": "Certification of Bilateral Patience Sort in Theorema and Rocq",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.34889"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35719",
      "authors": [
        "Sergey Gusev",
        "David E. Bernal Neira"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35719",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-28",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Artificial intelligence (AI) agents, language models connected to tools and run in a loop, can now carry out long, multi-step tasks with little supervision. We gave swarms of off-the-shelf coding agents a short statement of scope, from a narrow topic to a whole field, access to the literature and to computing tools, and one standing instruction: make real, correct, useful progress, and do not stop. We supplied no scientific ideas. Within weeks, the agents produced a large body of research notes, paper-length drafts, and formal proofs in five areas of optimization theory and physical science, and proposed untested laboratory experiments in a sixth. We do not claim that all of it is correct or new, but it is not noise: in what we have checked so far, we found no major scientific error, and several results are proved in a proof assistant. The agents produced results faster than we could review them; we estimate that a full review would take us months. Together with two widely discussed 2026 results in mathematics obtained with swarms, our runs suggest that agents can already do a large part of routine theoretical research, at least in areas that we experimented with. This raises questions we cannot yet answer: how to trust results when review, not production, is the scarce resource; what credit and publication counts mean when the human input is a prompt, and why institutions would pay researchers rather than buy computing time; and how people can learn a field, add to what agents do, and stay in control of research they cannot keep up with. Research institutions are not ready: models improve faster than institutions change, so they should decide now how to respond as capabilities increase. We offer tentative positions, release the agents' unedited output as of 25 September 2026, and invite readers to repeat the experiment in their own fields.",
      "title": "AI Agent Swarms as Researchers: Progress, Challenges, and Open Questions",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35719"
    },
    {
      "age_days": 3,
      "arxiv_id": "2609.35229",
      "authors": [
        "Christian Hägg",
        "Anders Mörtberg"
      ],
      "content_date": "2026-09-28",
      "freshness": "fresh",
      "id": "arxiv:2609.35229",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-28",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit $2\\times 2$ matrix has no Smith normal form. The obstruction is topological and is detected by the Möbius line bundle.",
      "title": "A Bézout domain that is not an elementary divisor domain",
      "updated": "2026-09-28",
      "url": "https://arxiv.org/abs/2609.35229"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}