{
  "counts": {
    "adjacent": 16,
    "core": 2,
    "errors": 0,
    "negative": 72,
    "total": 90
  },
  "date": "2026-10-02",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-10-02T20:05:51Z",
  "items": [
    {
      "age_days": 1,
      "arxiv_id": "2610.01799",
      "authors": [
        "Kuo Zhou",
        "ZiXion Yang",
        "Lu Zhang"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01799",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-01",
      "score": 12.3,
      "source": "arxiv-ai4math-core",
      "summary": "Skill evolution offers a promising way to improve large language model agents without updating their parameters, but its use in formal theorem proving remains underexplored. Existing methods mainly target natural-language reasoning, improving skills by analyzing successful and failed trajectories and incrementally revising solving strategies. Although the Lean verifier provides reliable execution feedback, when all sampled trajectories fail, existing skill evolution methods lack successful trajectories from which to infer effective update directions. Furthermore, these methods also focus mainly on the root instruction file, thus underexploring the evolution of reference knowledge including mathematical concepts and proving techniques. To address these limitations, we propose a mutation-enhanced skill self-evolution framework for building skill-augmented Lean provers. The framework jointly evolves a high-level solving policy and its reference knowledge through progressive and mutation-based updates. Progressive evolution derives local improvements from successful and failed trajectories, while mutation is triggered when no complete proof can be generated, sampling mathematical concepts to produce and select new skill candidates under verifier feedback. We evaluate our method on MiniF2F, PutnamBench, the 2025 International Mathematical Olympiad (IMO 2025), and the 2026 USA Mathematical Olympiad (USAMO 2026). Under the same backbone model, trajectorysampling budget, and test-time compute, our method achieves proof success rates of 100.0%, 90.6%, 4/6, and 4/6, respectively, with GPT-5.5, outperforming the baseline methods. Further analysis shows that concept-guided mutation outperforms random-text-guided mutation by 6.9 and 8.2 percentage points on MiniF2F and PutnamBench, respectively, while solving one additional problem on both IMO 2025 and USAMO 2026.",
      "title": "SkillEvoLean: Mutation-enhanced skill evolution for Lean provers",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01799"
    },
    {
      "age_days": 2,
      "arxiv_id": "2610.00760",
      "authors": [
        "Chenjun Guo",
        "Manooshree Patel",
        "Arnav Mehta",
        "Krishiv Kothari",
        "Thomas Lu",
        "Niels Voss",
        "Rayna Bhattacharyya",
        "Peter Donovan",
        "Bjoern Hartmann",
        "Gireeja Ranade"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2610.00760",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-09-30",
      "score": 9.5,
      "source": "arxiv-ai4math-core",
      "summary": "Large language models are increasingly used as collaborators on deductive-reasoning tasks, but their outputs can hallucinate or pull users away from intended reasoning. Formal proof assistants provide machine-checked verification, but have a steep learning curve and require more granular reasoning than human written proofs. We explore an interface that combines these strengths, allowing users to write and revise free-form natural-language proofs while a verified backend checks their reasoning and returns feedback at the user's granularity. We study this interface in the context of undergraduate mathematics education by developing LeanSide, a formally verified co-reasoning system, which auto-formalizes student reasoning into Lean and informalizes verifier output into understandable feedback. We conducted user studies through classroom deployment and analyzed which system properties helped students make progress and which caused them to get stuck. We use these findings to derive design implications for using a formally verified backend in human-AI co-reasoning systems.",
      "title": "LeanSide: A Formally Verified Co-Reasoning System for Natural-language Proofs",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2610.00760"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.01939",
      "authors": [
        "Ruiyang Si",
        "Jianxin Bi",
        "Shunyu Yang",
        "Rui Ni",
        "Wenbo Huang",
        "Qiang Wang",
        "Shulong Jiang",
        "Duomin Wang",
        "Xiuyu Li",
        "Haiwen Feng",
        "Zhen Dong",
        "Daquan Zhou"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01939",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "tool_use_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-01",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "Vision language model (VLM) agents can control robots through visual feedback and action primitives, but repeated model invocations and redundant observations incur substantial token overhead. We introduce PyRUA-Lean, an interactive code-execution framework that couples feedback-driven primitive composition with selective observation: the agent composes classical robot primitives and learned vision-language-action (VLA) policies into Python cells that perform conditional checks and local retries, returning only explicitly requested images and state feedback for replanning. Across 700 simulated task instances from LIBERO-PRO, RoboTwin 2.0, and RoboCasa365, we compare PyRUA-Lean with a tool-calling baseline using the same GPT-6 Astra planner and underlying robot primitives. Under equal LLM-call budgets, PyRUA-Lean increases overall success from 63.1% to 71.7%. On instances solved by both agents, it uses 49% fewer LLM calls and 65% fewer input tokens.",
      "title": "Fewer Tokens, Better Action: GPT-6 Astra Robot Agents with 14% Higher Success Rate but 65% Fewer Tokens",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01939"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.02035",
      "authors": [
        "Teng Zhang"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.02035",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-01",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "In this paper, we prove Borcea's 2-variance conjecture. The Lean 4 formalization of the main results are also provided.",
      "title": "Borcea's 2-variance conjecture",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.02035"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.02009",
      "authors": [
        "Teng Zhang"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.02009",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-01",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "Let $m$ denote the normalized Haar measure on the unit circle $\\mathbb{T}$. For $0<r<\\infty$, define $\\lVert f\\rVert_{r}:=\\left(\\int_{\\mathbb{T}}|f|^{r}\\,\\mathrm{d} m\\right)^{1/r}$, with $\\lVert f\\rVert_{0}$ and $\\lVert f\\rVert_{\\infty}$ interpreted as the geometric mean and the supremum norm, respectively. Set $Q_n(z)=1+z^n$. We prove that, for every nonzero polynomial $p$ of degree $n$ whose zeros all lie on $\\mathbb{T}$, $$ \\frac{\\lVert p\\rVert_s}{\\lVert Q_n\\rVert_s} \\le \\frac{\\lVert p\\rVert_t}{\\lVert Q_n\\rVert_t}, \\qquad 0\\le s\\le t\\le\\infty. $$ This settles Baernstein's quasi-norm monotonicity conjecture. As corollaries, we obtain an $L^r$ extension of Visser's coefficient inequality, the sharp O'Hara--Rodriguez inequality and its higher-power analogues, the Erdős--Szekeres product bound $ \\left\\lVert\\prod_{j=1}^N(1-z^{s_j})\\right\\rVert_\\infty\\ge2\\sqrt N $ for all positive integers $s_1,\\ldots,s_N$ and Agler--McCarthy's entropy conjecture. We also provide a Lean 4 formalization of the main results.",
      "title": "Baernstein's quasi-norm monotonicity conjecture for polynomials with unimodular zero",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.02009"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.01240",
      "authors": [
        "Tom Verhoeff"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01240",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-01",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "In 1965, D. H. Lehmer conjectured that the permutations of every multiset admit an imperfect Hamiltonian traversal by adjacent swaps: a walk in the neighbor-swap graph that visits every word, with some words visited twice in order to reach a neighbor and return. The question is posed as an unsolved research problem in Knuth's Art of Computer Programming. Verhoeff (2017) chose the stutter words, in which every domino is a double, as the words to be reached this way, and reformulated the conjecture as the Hamiltonicity of the graph $N(S)$ on the non-stutter words, with two exceptional families --- binary signatures with an odd multiplicity, and the permutations of $(2k,1,1)$ --- that admit a Hamiltonian path but no cycle. This article proves the reformulated conjecture, and with it Lehmer's conjecture. The key structure is a partition of the words into hypercubes: the swaps inside dominoes turn each class of words with the same domino contents into a hypercube, and the stutters are exactly the $0$-dimensional classes. When every multiplicity is even, Hamiltonian cycles of the hypercubes are glued along a spanning tree, with no finite check. The case of exactly one odd multiplicity reduces to the all-even case and to a theorem of Stachowiak (1992), the one inherited Hamiltonicity input, which also settles two or more odd multiplicities. The only finite ingredients are two explicit cycles, of 28 and 84 words. Every construction is implemented in Python and checked against brute-force graphs, and the proof is formalized in Lean 4 over Mathlib.",
      "title": "A proof of Lehmer's permutation conjecture for neighbor-swap graphs",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01240"
    },
    {
      "age_days": 3,
      "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": "2610.01527",
      "authors": [
        "Kabir Murjani",
        "Nisarg Patel"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01527",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-01",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Non-Markovian environments are often modeled as Regular Decision Processes (RDPs), where dynamics depend on the interaction history through a finite automaton. Existing offline guarantees for RDPs rely on a distinguishability assumption on the behaviour policy but provide no means of verifying it. When the assumption is violated, distinct models may explain the data equally well. We study when data collected under a fixed behaviour policy can distinguish two candidate RDPs. We prove that the posterior odds between observationally equivalent candidates remain equal to the prior odds at every sample size, even when the policy visits every automaton state, and verify both results formally in Lean 4. We then characterize this equivalence exactly and derive PEC, an algorithm that decides it in time linear in the size of the product automaton. The distinguishability assumption of prior work fails on three of our four test environments, and the experiment identified by PEC restores it in each case.",
      "title": "Exact Distinguishability in Non-Markovian Decision Processes",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01527"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.01121",
      "authors": [
        "Youngwoo Kwon"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01121",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-01",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Gibbs samplers, and more generally component-wise Markov chain Monte Carlo algorithms such as Metropolis-within-Gibbs, can be implemented using either random-scan or deterministic-scan updates. How much convergence can depend on this choice of scanning rule has been a longstanding question. We study this problem through $L^2$ spectral gaps, measuring computational cost in units of component updates. For a $d$-block Gibbs sampler, the cost of random scan is at most twice that of any fixed deterministic scan, while the reverse cost ratio is at most of order $d^2$. We extend these comparisons to general reversible component-wise updates under the global block-wise contraction condition. If $K_j$ denotes the update of block $j$ and $P_j$ its Gibbs counterpart, and $\\|K_j-P_j\\|\\leq λ_0<1$ for $j=1,\\ldots,d$, then the cost of random scan is at most $2/(1-λ_0)$ times that of deterministic scan, while the reverse cost ratio is of order at most $d^2/(1-λ_0)$. Examples show that the cost bounds for random scan relative to deterministic scan are asymptotically sharp and that the joint dependence on $d$ and $(1-λ_0)^{-1}$ in the reverse comparison cannot be improved uniformly. This work was assisted by generative AI, including for formal verification of mathematical results in Lean. The human author reviewed and verified the mathematical content and takes full responsibility for the results.",
      "title": "Cost Comparisons for Random and Deterministic Scans in Component-Wise Markov Chains",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01121"
    },
    {
      "age_days": 2,
      "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": 2,
      "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": "2026-10-01",
      "url": "https://arxiv.org/abs/2609.39544"
    },
    {
      "age_days": 2,
      "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": 2,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 1,
      "arxiv_id": "2610.02159",
      "authors": [
        "Scott W. Viteri",
        "Laura Gomezjurado Gonzalez",
        "Clark Barrett"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.02159",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "reasoning_rl_distillation"
      ],
      "published": "2026-10-01",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Intrinsic rewards are designed to guide exploration in reinforcement learning by assigning value to an agent's experience, for example through prediction error or learning progress. However, maximizing these rewards need not produce the most informative experience available. We propose a formal criterion for exploration that compares policies by the counterfactual information they acquire: how well their histories can substitute for experience under alternative policies. We construct a single, simple environment in which specified count-based, prediction-error, empowerment, and information-gain objectives have maximizing policies that are Pareto-suboptimal at acquiring counterfactual information. We explain these failures and establish conditions under which existing intrinsic rewards successfully encourage optimal exploration. We also construct an objective that assigns a higher value whenever exploration strictly improves under our criterion.",
      "title": "When Do Intrinsic Rewards Lead to Exploration?",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.02159"
    },
    {
      "age_days": 2,
      "arxiv_id": "2610.00413",
      "authors": [
        "Haruhisa Enomoto"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2610.00413",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-09-30",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Børve, Horiatakis, and Kalck defined the magnitude of the module category of a representation-finite algebra as the sum of the entries of the inverse of the matrix of Hom dimensions between indecomposable modules. They showed it is an Euler characteristic, the alternating count of vertices, arrows, and meshes of the Auslander--Reiten quiver, and conjectured that it is at least the number of simple modules, with equality precisely for special biserial algebras. We prove this conjecture over an algebraically closed field. For a representation-directed algebra, we relate the magnitudes of the module category, the subcategory of modules without a given simple composition factor, and the ideal quotient by it. By the theory of hammocks of Ringel and Vossieck, this quotient is equivalent to a category of representations of a finite poset, whose magnitude we compute. The general case reduces to the representation-directed case through algebras obtained by grading a standard form.",
      "title": "Magnitude of module categories and special biserial algebras",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2610.00413"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:7c383e282482",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: solve equations in nonzero characteristic in the `Sym.simp`-based `grind` normalizer (#15434)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover/lean4/commit/7c383e282482431c98704e259ea1cf7303f2fb50"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:463678649cf9",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `Fin` ground evaluation in `Sym.simp` (#15433)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover/lean4/commit/463678649cf906a3125ff63386c76f8b1756f76b"
    },
    {
      "age_days": 0,
      "authors": [
        "Yi.Yuan"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:16b46e224221",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Order): generalize distance lemmas to solid norms (#44072)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/16b46e2242213b8a9b02c9ac393bfa788b8e74e1"
    },
    {
      "age_days": 0,
      "authors": [
        "Weiyi Wang"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:6620c780867f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Analysis/Normed): sup norm of Function.extend by one (#44378)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/6620c780867f0a52446e9c728bc69f50c020eef7"
    },
    {
      "age_days": 0,
      "authors": [
        "Xavier Roblot"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:24f1bff09e32",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Algebra/QuadraticAlgebra): base change of quadratic algebras (#42977)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/24f1bff09e3257ebfe3c8846698e6d9aaabdf36e"
    },
    {
      "age_days": 0,
      "authors": [
        "Joël Riou"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:41d19bc71c2b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Algebra/Homology): more API for Ext in linear categories (#44190)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/41d19bc71c2b66d8a124371a5bd85fde6309d665"
    },
    {
      "age_days": 0,
      "authors": [
        "Hang Lu Su"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:a2d2c3e3baad",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: doc(Geometry/Group/WordMetric): correct wordLength_le_iff docstring (#44418)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/a2d2c3e3baade4f72dfba80d0562b0bf1377b1de"
    },
    {
      "age_days": 0,
      "authors": [
        "Bryan Gin-ge Chen"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:2d1b80eb2f58",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: ci: restore the `DownstreamTest` cache check (#44409)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/2d1b80eb2f589c2587305e521c4902ba75131c91"
    },
    {
      "age_days": 0,
      "authors": [
        "mathlib-update-dependencies[bot]"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:0272bbe1c093",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-10-02 (#44416)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/0272bbe1c093d038d7257ab15306abd58245f9ff"
    },
    {
      "age_days": 0,
      "authors": [
        "David Kurniadi Angdinata"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:19cdde902931",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: rename `sFinite` to `sfinite` in declaration names (#44292)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/19cdde90293121f0047bb385278520a5cb5392c0"
    },
    {
      "age_days": 0,
      "authors": [
        "Yaël Dillies"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:f8412f2c8c13",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: deprecated modules for #43253 (#44401)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/f8412f2c8c13a84a5a04e15191b49e58cfbf9c82"
    },
    {
      "age_days": 0,
      "authors": [
        "Yi.Yuan"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ac77769fabe2",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: address localization algebra TODO (#44422)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ac77769fabe23cb237559e7f56578dbead91499f"
    },
    {
      "age_days": 0,
      "authors": [
        "Kim Morrison"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:282fbb865d53",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(CI): update pinned actions to their SHA-pinned releases (#44415)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/282fbb865d53622ef7f9ef29f6763a0327ee6b5f"
    },
    {
      "age_days": 0,
      "authors": [
        "mathlib-splicebot[bot]"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:97b8c4425c99",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Analysis/CStarAlgebra/Module/Synonym): fix implicit instance diamond (#44406)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/97b8c4425c99103e6bfba90324c1f547d2113edd"
    },
    {
      "age_days": 0,
      "authors": [
        "Xavier Roblot"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:af914e734396",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Algebra/QuadraticAlgebra): make C the simp normal form (#44417)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/af914e734396f29c5c847c99f8e36dbe41ce63a6"
    },
    {
      "age_days": 0,
      "authors": [
        "Xavier Roblot"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:8e30cac82f69",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Algebra/QuadraticAlgebra): define all the casts through C (#43583)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/8e30cac82f69c18f6cbe88799bdc3ebd74cc592d"
    },
    {
      "age_days": 0,
      "authors": [
        "mathlib-splicebot[bot]"
      ],
      "content_date": "2026-10-02",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:014e37aeb813",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-02",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Algebra/Module/Shrink): fix non-reducible instance diamond (#44405)",
      "updated": "2026-10-02",
      "url": "https://github.com/leanprover-community/mathlib4/commit/014e37aeb813aba1ac753e19bbd70f282c194106"
    },
    {
      "age_days": 1,
      "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": 1,
      "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": 1,
      "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": 1,
      "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.",
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      "freshness": "fresh",
      "id": "github:leanprover/lean4:82fdd8ea6791",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: `grind` hom hooks fail on `let`-bound literals (#15417)",
      "updated": "2026-09-30",
      "url": "https://github.com/leanprover/lean4/commit/82fdd8ea67911b4590015937284ad5ba97015782"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0689378b062e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `Char.val` ground evaluation in `Sym.simp` (#15419)",
      "updated": "2026-09-30",
      "url": "https://github.com/leanprover/lean4/commit/0689378b062ea179f494f6cfcfe4339dbf3ec8f4"
    },
    {
      "age_days": 2,
      "authors": [
        "Paul Reichert"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d6ab933716c5",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: make nestedDeciable test more robust (#15413)",
      "updated": "2026-09-30",
      "url": "https://github.com/leanprover/lean4/commit/d6ab933716c575bab56dd45d74110a8e0378b278"
    },
    {
      "age_days": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 3,
      "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": 1,
      "arxiv_id": "2610.01728",
      "authors": [
        "Jakob Paul Zimmermann",
        "Moritz Grillo",
        "Andrei Balakin",
        "Georg Loho"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01728",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Understanding loss landscapes is central to explaining neural-network training, yet their structure remains only partially understood even in simple models. We study the Gaussian population loss of shallow, bias-free ReLU networks in the teacher--student setting. This provides a simple model for studying essential aspects such as feature learning and overparameterization. For teacher networks with positive output weights and planar features, we show that including a learned linear skip removes all spurious local minima with non-negative student output weights once the student network is at least as wide as the teacher network. In contrast, without the skip, we construct a fixed teacher network with positive output weights and only three hidden neurons in input dimension two whose spurious local minima persist at every student width at least three. Thus, a learned linear skip can remove spurious minima that persist under arbitrary overparameterization. Furthermore, we show that a positive output weight student network always learns the subspace spanned by the teacher features: student features at local minima with non-negative student output weights lie in the span of the teacher features. For ReLU networks in two dimensions, even heavily overparameterized student networks have effective width controlled by the teacher width: every critical point with positive student output weights has at most twice as many distinct student feature directions as teacher neurons. Finally, we transfer the benignity result to empirical minima over parameter balls of any prescribed radius, with the required sampling accuracy depending on that radius.",
      "title": "Removing spurious minima for planar features by skip connections",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01728"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.01639",
      "authors": [
        "Isaac Rudich",
        "Louis-Martin Rousseau"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.01639",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Strassen showed that two 2x2 matrices can be multiplied with 7 multiplications instead of 8. Applied recursively, his algorithm multiplies two nxn matrices with O(n^2.807) multiplications, beating the naive O(n^3). The best known 3x3 recursive matrix multiplication algorithm uses 23 multiplications O(n^2.854). The best published lower bound of 21 (on algorithms with integer constants) leaves room for an algorithm with O(n^2.771) multiplications, and thus does not rule out the possibility of an algorithm that would beat Strassen's. We prove a lower bound of 22 multiplications for any 3x3 recursive algorithm with integer constants, proving that no such algorithm can do better than O(n^2.814) multiplications, and eliminating the possibility of a 3x3 algorithm that beats Strassen's 2x2 method. The proof builds on a recent decomposition method from Wang, who approached the problem by turning it into 496 subproblems. We provide exact solutions for 359 of them. The proof is in Lean; verification requires auditing only a few short files. The Lean formalization directly encodes statements about the limitations of recursive algorithms for matrix multiplication, as opposed to just a statement about the rank of the problem.",
      "title": "Lower Bound of 22 for 3x3 Matrix Multiplication over the Integers",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.01639"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.00917",
      "authors": [
        "Yixuan Li",
        "Yiyun Zhou",
        "Yao Long Teng",
        "Fuchao Yang",
        "Yanchen Deng",
        "Zhiyi Lyu",
        "Xuyu Dong",
        "Feng Chen",
        "Bo An"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.00917",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Choosing an agent system means choosing both a language model and the harness through which it acts. We ask whether a strong model, harness, or pairing stays strong when the setting changes. We evaluate 66 configurations: four configurable harnesses (OpenHands, DeepSeek Harness, PI, and openJiuwen) paired with five models on TUA-Bench, ALE-CLI, and Terminal-Bench 4, plus the native Codex-GPT and Claude Code-Claude pairings. Model rankings reverse across harnesses. On Terminal-Bench 4, Claude leads GPT by 7.94 points in OpenHands but trails it by 30.16 points in PI. For four of the five models, the best harness changes from one benchmark to another, yet some pairings hold: openJiuwen gives Kimi its highest score on all three benchmarks, by 5.61 to 11.11 points. A model's own vendor harness is not reliably its best, and higher cost does not reliably buy a higher score. On Terminal-Bench 4, GPT scores higher under PI than under DSH at less than a quarter of the cost per task. Matched trajectories suggest why fit varies. Models start almost all repairs themselves, so much depends on whether the harness hands failures back in a form the model can use. GPT does best with PI's lean scaffold, while Kimi, which often issues malformed tool calls, does best in openJiuwen. We argue that the model, the harness, and the task should be evaluated together, and we release the harness adapters, evaluation code, and all 6,204 scored trajectories at https://github.com/liyix/finding-the-right-fit and https://huggingface.co/datasets/yixuanli97/finding-the-right-fit.",
      "title": "Finding the Right Fit: Model-Harness Interactions across Agent Tasks",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.00917"
    },
    {
      "age_days": 1,
      "arxiv_id": "2610.00885",
      "authors": [
        "Naing Oo Lwin"
      ],
      "content_date": "2026-10-01",
      "freshness": "fresh",
      "id": "arxiv:2610.00885",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Coding agents increasingly automate Lean proof development, but successful compilation alone does not establish that a candidate proves the intended statement under acceptable assumptions. We present FORALL-LEAN-AGENT, a frontend-agnostic framework for auditable reasoning in formal mathematics and software verification. The framework combines isolated workspaces, Lean tools, and fresh review with statement comparison, axiom audits, and independent proof checking where supported. Verification evidence and reviewer decisions are bound to the same candidate artifact, making acceptance traceable. We evaluate the framework on VeriSoftBench, PutnamBench, and both problems in the Lean Eval softwareverification track. On the 100-task VeriSoftBench subset, integration with FORALLLEAN-AGENT raises benchmark-rule success from 93 to 100 for GPT-5.6 Sol at low effort while reducing cost from $69 to $62. The PutnamBench evaluation accepts all 672 problems at an average of $4.72 each. These results show that agent harness design can improve correctness and efficiency while providing evidence beyond aggregate solve counts.",
      "title": "FORALL-LEAN-AGENT for Auditable Reasoning in Formal Mathematics and Software Verification",
      "updated": "2026-10-01",
      "url": "https://arxiv.org/abs/2610.00885"
    },
    {
      "age_days": 2,
      "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": 2,
      "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": 2,
      "arxiv_id": "2610.00530",
      "authors": [
        "Chengxi Yang",
        "Tej Chajed",
        "Thomas Reps"
      ],
      "content_date": "2026-09-30",
      "freshness": "fresh",
      "id": "arxiv:2610.00530",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-09-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Modern incremental computation theories like DBSP have enabled efficient incrementalization of general recursive computations. To do so, they require a runtime Fixpoint Detection (FPD) mechanism to detect whether an iterative computation has reached the fixpoint and thus should terminate. However, we show that the commonly suggested \"FirstZero\" strategy is unsound even in naturally arising cases, and that exact FPD is impossible for arbitrary DBSP circuits with expressive primitive nodes. This issue reveals a fundamental gap between the mathematical specification and implementations of such theories. To fill this gap, using DBSP as a core calculus, we develop a formal theory of convergence detection. Within this theory, we define internal convergence (IntConv) as a declarative criterion corresponding to the internal-state-stability strategy used by practical implementations, and prove that IntConv is a sufficient condition for external convergence. We then define the state fixpoint (StFP) predicate and a sound and complete StFP detector. Combining the StFP detector with fixed-input and zero-output checks yields a sound and complete IntConv detector. Moreover, for a large class of useful circuits (programs) including Datalog queries, nested while queries, and their incrementally optimized versions, we show that IntConv is not only sound but also complete (meaning any convergence in the theory implies the convergence in our criterion). As a result, our theory provides semantic guarantees for convergence detection on all these circuits. Our results are formally verified in Lean, with the formalization available at https://github.com/Arcadia-Y/fixing-the-fixpoint/.",
      "title": "Fixing the Fixpoint: A Formal Theory of Convergence Detection for Incremental Recursive Computation",
      "updated": "2026-09-30",
      "url": "https://arxiv.org/abs/2610.00530"
    },
    {
      "age_days": 2,
      "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": 2,
      "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": 2,
      "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": 3,
      "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": 3,
      "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"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}