{
  "counts": {
    "adjacent": 11,
    "core": 3,
    "errors": 0,
    "negative": 73,
    "total": 87
  },
  "date": "2026-08-18",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-18T15:58:18Z",
  "items": [
    {
      "age_days": 3,
      "arxiv_id": "2608.15432",
      "authors": [
        "Tadd Mao",
        "Tianjun Zhong",
        "Dhruva Arekar",
        "Yuming Feng",
        "One An",
        "Jiani Huang",
        "Xujie Si",
        "Ziyang Li"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.15432",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-15",
      "score": 12.5,
      "source": "arxiv-ai4math-core",
      "summary": "In formal verification, both the autoformalization of statements and automated proof search have been studied extensively. While automated proof search can produce a formal proof that compiles, the generated proof does not necessarily reflect how the natural-language argument arrives at its conclusion--a property we refer to as faithfulness. With faithfully formalized proofs, one can check the reasoning behind a human- or AI-written argument, and assist mathematicians in formalizing their proof sketches. However, it is particularly challenging due to misalignment of formal proof tactics and natural language reasoning. In this work, we rigorously describe a set of five necessary conditions a faithful formal proof must satisfy, and introduce Pistis, an agentic, oracle-guided proof search that produces formal Lean proofs that satisfy them. At its core is a novel faithfulness-preserving divide-and-conquer search, which we name OrderDecompose, that tracks citation dependencies and blocks unfaithful shortcuts, paired with a refutation search, that surfaces gaps and errors in the natural language proof source. OrderDecompose completes proofs that baselines cannot close even within a 12-hour budget, and its artifacts compile over 33$\\times$ as fast as prior work's. We apply Pistis on the first three books of Euclid's Elements, producing high-quality artifacts containing faithful formal proofs. Under a blinded human study and an LLM-as-a-judge protocol on rigorous rubrics, Pistis-generated proofs are favored over prior works--2.89$\\times$ and 5.2$\\times$ as often by human reviewers and the LLM judge, respectively. It further uncovers gaps in Euclid's proofs and their translation, and can accept or refute natural language proofs written by humans or AI, demonstrating that faithful formalization is useful as a proof-checking tool.",
      "title": "Does the Proof Prove It That Way? Faithful Formalization of Elements Proofs",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.15432"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.14221",
      "authors": [
        "Lushi Pu",
        "Weiming Zhang",
        "Xinheng Xie",
        "Zixuan Fu",
        "Bingxiang He",
        "Hengyu Zhao",
        "Hongya Lyu",
        "Xin Li",
        "Jie Zhou",
        "Yudong Wang"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.14221",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "lean_formal_proving_agents",
        "reasoning_rl_distillation",
        "tool_use_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-14",
      "score": 12.3,
      "source": "arxiv-ai4math-core",
      "summary": "Autoformalization is commonly framed as translating natural-language mathematical statements into machine-verifiable formal languages such as Lean 4. However, faithful formalization requires more than translation. Models must map mathematical concepts to the complex hierarchy of types and definitions in formal libraries such as Mathlib, while ensuring that generated statements preserve the meaning of the source propositions. Existing approaches struggle because they rely heavily on the model's parametric memory for library-specific knowledge, while common data construction pipelines often resort to filtering single-pass outputs and lack mechanisms for feedback-driven revision. To address these challenges, we introduce MathForm, an autoformalization framework for constructing verified training data through Mathlib knowledge retrieval and verification-guided iterative refinement. Before generation, a retrieval planner gathers relevant definitions and existing formalizations from Mathlib to guide the formalization generator. Generated statements are then revised using compiler diagnostics and semantic-consistency feedback. Using this framework, we construct FormalVerse, a Lean 4 dataset containing approximately 367K verified examples across diverse mathematical domains and sources. We then train MathForm-8B through supervised fine-tuning followed by reinforcement learning. Across six benchmarks, MathForm-8B achieves average Pass@8 rates of 88.06% under Syntax Check (SC) and 72.37% under Consistency Check (CC), outperforming multiple specialized 32B autoformalizers. On the challenging FATE-H and FATE-X subsets, it attains CC pass rates of 63% and 37%, exceeding the strongest specialized baselines in both cases.",
      "title": "MathForm: Scaling Mathematical Autoformalization with Knowledge Retrieval and Verification-Guided Refinement",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.14221"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.13522",
      "authors": [
        "Zhe Ye",
        "Hantao Lou",
        "Yuechun Sun",
        "Peiyang Song",
        "Zhengxu Yan",
        "Timothe Kasriel",
        "Qingyang Zhang",
        "Kaiyu Yang",
        "Soonho Kong",
        "Jingxuan He",
        "Dawn Song"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.13522",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "seed_author:Kaiyu Yang",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-13",
      "score": 7.7,
      "source": "arxiv-ai4math-core",
      "summary": "AI agents are increasingly used for programming, but do not provide any guarantee on the correctness of generated code. Verified code generation, in which an agent produces both an implementation and a machine-checked proof of its specification, offers a stronger path toward trustworthy AI-generated software. Existing benchmarks in this direction either focus on individual functions or only evaluate proof generation with provided implementations. It is still an open question whether agents can make coherent implementation and proof choices across real multi-module codebases. To bridge this gap, we introduce Vero, the first benchmark to evaluate joint implementation and proof synthesis at the repository level. Vero contains 43 multi-module instances sourced from real-world repositories spanning Python, Dafny, Verus, and Coq, and covering diverse domains from cryptographic protocols to distributed systems. Each instance consists of a multi-module Lean 4 repository with predetermined API interfaces, manually curated formal specifications, and reference implementations, supporting both proof-only and code-and-proof evaluation modes. To improve benchmark reliability, Vero also includes an audit mechanism where agents are allowed to formally prove unsatisfiability of provided specification or incorrectness of reference code, which surfaces and corrects latent code and specification errors during curation. We evaluate frontier coding-agent configurations with Lean toolchain access. The strongest agent fully solves only 27 of 43 instances and closes no specifications on the hardest repositories. Vero provides a concrete testbed for measuring progress toward repository-scale verified software synthesis, where current agents still fall short. We release the benchmark, curation pipeline, and evaluation harness at https://github.com/sunblaze-ucb/vero.",
      "title": "Vero: Can AI Agents Build Formally Verified Software Repositories?",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.13522"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.16649",
      "authors": [
        "Hardik Jain"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "arxiv:2608.16649",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-17",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "The tensor rank of a bilinear map is the least number of multiplications any bilinear algorithm needs to compute it; for the multiplication of an algebra it measures how cheaply the algebra can be multiplied at all. For the even-dimensional real normed division algebras it is $3$ for the complex numbers and $8$ for the quaternions, both classical, while for the octonions $\\mathbb{O}$ only a range was known: at least $15$ (Fiduccia and Zalcstein, 1977) and at most $30$ (Cariow and Cariowa). We prove $$18 \\le \\operatorname{R}_{\\mathbb{R}}(T_{\\mathbb{O}}) \\le 25.$$ The lower bound peels the eight slices of $T_{\\mathbb{O}}$ down to two and bounds the rank of the surviving pencil through the octonion norm. Nothing in it is special to dimension $8$: the same steps give $\\operatorname{R}_{\\mathbb{R}}(T_A) \\ge \\frac{5}{2}n - 2$ for every real normed division algebra $A$ of even dimension $n$, sharp for $\\mathbb{C}$ and $\\mathbb{H}$ and the best bound we know for $\\mathbb{O}$. The upper bound is a separate construction, an explicit rank-$25$ decomposition certified by a Krawczyk argument, in exact rational arithmetic, to sit within $10^{-6}$ of an exact one. The same two arguments pin down the rank of a smaller three-slice quaternion tensor $τ$, giving $\\operatorname{R}_{\\mathbb{R}}(τ) = 7$. The Lean 4 kernel checks the lower bounds and the Krawczyk existence principle; the accompanying scripts check the certificate's finitely many exact-rational inequalities.",
      "title": "Bounds on the real tensor rank of octonion multiplication",
      "updated": "2026-08-17",
      "url": "https://arxiv.org/abs/2608.16649"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.15810",
      "authors": [
        "Fanzhe Wei",
        "Li Liu"
      ],
      "content_date": "2026-08-16",
      "freshness": "fresh",
      "id": "arxiv:2608.15810",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-16",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-level risk by a union bound over a pre-declared event count. We show the union budget exhausts on every long request in a production serving stack (100% of requests), and replace it with an anytime-valid, physically accounted ledger whose bound holds at every one of 352,333 admission calls on live traffic and which, in a pre-registered held-out confirmatory round, halves the exact-fallback rate at matched risk (0.30 -> 0.14) -- coverage is bought at a price the account states. We then price the remaining distance from the certified witness to what a user experiences: a machine-checked design law (TV <= tanh(a_q w_thr)) turns the served-TV target into a threshold knob, and a three-layer audit of its instantiation -- an operator-norm query envelope measured 1.5x from tight, a measured-ellipsoid replacement for the Cauchy-Schwarz ball that buys nothing (0.89x, held-out sound), and the gate's operating point (~700x) -- localizes the entire 1064x gap to the operating point, a price the law now states rather than an unknown. A priced bound is worth nothing on a request one has not seen, so the third link is the quantifier: exchangeable extrapolation across 80 serving histories replaces binary conformal prediction's vacuous certificates with order-statistic bounds that discriminate (0.41 against 0.51 calibration risk). All probabilistic kernels are Lean 4-checked (228 exported theorems, no sorry); which object deserves this machinery at all is settled empirically in a companion paper that adjudicates -- and rejects -- the natural alternative of certifying routing. What ships is an account: risk you can spend, a gap you can read off a law, and a bound that survives the request you have not seen.",
      "title": "Pricing the Risk of Runtime Compression: Anytime-Valid Admission and a Served-Output Law for Compressed Serving State",
      "updated": "2026-08-16",
      "url": "https://arxiv.org/abs/2608.15810"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.15914",
      "authors": [
        "Benny Avelin"
      ],
      "content_date": "2026-08-16",
      "freshness": "fresh",
      "id": "arxiv:2608.15914",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-16",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We study Gaussian random dynamical systems with coordinatewise $\\tanh$ nonlinearity, where finite precision is modeled by nearest-grid rounding after each step. Gaussian symmetry reduces the dynamics to an exact Markov chain for the normalized squared radius. Rounding makes the origin absorbing, and the total variation distance to the absorbing equilibrium equals the survival probability of the absorption time. At fixed width, we identify the critical gain and prove an absorption cutoff with Gaussian profile as the mesh tends to zero. At fixed precision, global contraction yields a large-dimension absorption cutoff, while positive drift produces metastability. In the supercritical regime, we prove a large-dimension cutoff to a nonzero invariant law and show that, at fixed dimension, its mass near the repelling origin has a power-law asymptotic. All six main results are formalized in Lean 4 on top of Mathlib and independently checked against restatements that import only Mathlib.",
      "title": "Absorption cutoff and stationary singularities for rounded Gaussian random dynamical systems",
      "updated": "2026-08-16",
      "url": "https://arxiv.org/abs/2608.15914"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.15337",
      "authors": [
        "Michele Caprio"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.15337",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-15",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows. For the standard cellular flow in dimension two $V_A(x_1,x_2)=A(-\\sin x_1\\cos x_2,\\cos x_1\\sin x_2)$, if $0<d<20/399$ and $\\sqrt{1+4d^2}<Ad\\le1+d/10$, then for every unit planar slope the periodic correction develops oscillations at least linearly in time. The solution remains bounded below on an explicit horizontal channel through $(π,0)$, while at $(π/2,0)$ it decreases at rate at least $CA/\\log A$, with $C>0$ universal. The same conclusions hold for arbitrary continuous periodic perturbations of planar initial data. Under the physical scaling $V_A(x/\\varepsilon)$ and $d_\\varepsilon=\\varepsilon d$, an order one value gap persists between points at distance $O(\\varepsilon)$ at every positive macroscopic time, so the rescaled solutions have no locally uniformly convergent subsequence. The proof uses the Hamiltonian sandwich $H_{\\mathrm{unc}}\\le H_+\\le\\widehat H$. The upper comparator $\\widehat H$ is a rectangular support function, equivalently an upper expectation over a state-dependent credal set, whose reversed control dynamics possess an invariant comparison channel. We also prove that for any $C^2$ incompressible periodic flow, every $\\varepsilon$-outward barrier certificate has covering radius at most $2d\\varepsilon$ for all sufficiently small $\\varepsilon$. We further discuss implications for statistics and machine learning: rectangular, time-consistent local uncertainty need not imply forgetting of the initial state in the long run, so additional global stability or ergodicity conditions are needed in robust sequential decision making. Two Lean 4 appendices record conditional formalizations of a sufficient $p=e_1$ subregime and of the logical assembly of the rigidity theorem for barrier certificates.",
      "title": "The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.15337"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.13864",
      "authors": [
        "Arttu Malkamäki",
        "Antti Gronow"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.13864",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-14",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Studies often attribute the polarisation of climate politics in majoritarian democracies to differing treatment of climate change by conservative and liberal media. How then does such polarisation occur in a system, where mainstream media do not systematically align with party positions? Focusing on how users in different ideological blocs posted and commented on news articles on Finnish Twitter between 2015 and 2023, we address four mechanisms: audience capture, where outlets adapt to increasingly differentiated audiences, reinforcing their divergence through feedback between audience engagement and editorial incentives; selective exposure, where users post ideologically congruent articles from the same outlets; affective assimilation, where users communicate identical content with ideology-consistent valence; and ideological sorting, where identity-driven alignment structures news-posting behaviour across multiple issues. Bayesian regression models indicate increasing divergence in outlet choice, with conservative-leaning users posting more tabloid content, in line with audience capture, and partial support for selective exposure, as within-outlet article posting becomes increasingly differentiated. Valence divergence increases only slightly over time, providing moderate support for affective assimilation, while issue-specific communities show weak alignment with blocs despite convergence over time. Our work refines theories of media effects beyond majoritarian democracies and contributes to understanding the current impasse in climate politics.",
      "title": "Audience capture, selective exposure, affective assimilation or ideological sorting? Polarisation of climate politics under low media-party parallelism",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.13864"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.13501",
      "authors": [
        "Kevin Guan"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.13501",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-13",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "In the transversal achievement game on the $n\\times n$ board, two players alternately claim cells, and the first to own a transversal---a set of $n$ cells of which no two share a row or column---wins. Ranđelović showed that the first player wins for every $n\\ge4$, while the game is a draw for $n=2,3$. We give an independent proof that the first player wins for $n\\ge4$ that additionally establishes a bound on the length of the win: the given strategy forces a win by ply $2n+3$, i.e.\\ on the first player's $(n+2)$-nd move, for every $n\\ge4$. The proof yields a strategy that is fully determined by a fixed rule on the current position and can thus be implemented directly. We isolate the use of the hypothesis $n\\ge4$ to two steps in the analysis, explaining why the argument fails at $n=3$. An exhaustive computational search implementing the strategy verifies it against every legal defense for $n=4,5,6$, confirming both the strategy's validity and that the $2n+3$ bound is attained in these cases. The main theorem has also been formalized and machine-checked in Lean 4.",
      "title": "The transversal achievement game on a square grid",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.13501"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.13637",
      "authors": [
        "Levent Alpöge",
        "Ralph Furman"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.13637",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-13",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove unconditionally that at least two thirds of the nontrivial zeros of the Riemann zeta function, counted with multiplicity, are simple and lie on the critical line, and that at least five sixths are distinct; the previous unconditional records are $\\frac{5}{12}$ and $0.6603$. With the Montgomery--Taylor window the constants become $0.6725$ and $0.8362$. The argument makes Montgomery's 1973 deduction unconditional: the Riemann hypothesis, classically needed to read the zero side as a positive sum over real ordinates, is replaced by a rank-trace inequality applied to a finite compression of Weil's Hermitian form, with Sylvester's law of inertia handling off-line pairs. The analytic inputs are those of Aryan and of Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh. The results extend to primitive Dirichlet $L$-functions and are formally verified in Lean 4.",
      "title": "More than two thirds of the zeta zeros are simple and on the critical line",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.13637"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12242",
      "authors": [
        "Hongru Zhao"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12242",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-12",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Let $\\widehat R$ be the Pearson sample correlation matrix formed from $n$ independent Gaussian observations in $p$ dimensions, and write $m=n-1\\ge p$. Under the null correlation $R=I_p$, the classical independent beta product, exact cumulants, and full Fourier inversion yield, along every sequence $p\\to\\infty$ with $m\\ge p$, a uniform first Edgeworth expansion for $\\log\\det\\widehat R$, centered by its exact mean and scaled by its exact standard deviation. The expansion identifies the exact finite dimensional skewness correction and gives the sharp Kolmogorov equivalent $A_{m,p}/\\{6\\sqrt{2π}V_{m,p}^{3/2}\\}$, where $V_{m,p}$ is the exact variance and $A_{m,p}$ is the absolute third cumulant. This equivalent unifies the square, fixed gap, growing gap, proportional, and dilute regimes; in the square regime the error has order $(\\log p)^{-3/2}$ with an exact constant. For every positive definite population correlation matrix $R$, we prove a uniform finite sample Berry-Esseen bound that explicitly tracks population dependence. All theoretical results have exact or proved equivalent Lean 4 formulations whose declarations and dependencies are kernel checked.",
      "title": "Sharp Berry-Esseen Bounds for the Log Determinant of a Gaussian Sample Correlation Matrix",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12242"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12280",
      "authors": [
        "Lukas Liehr",
        "Mitchell A. Taylor",
        "Peiyang Yu"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12280",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-12",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We establish a sharp version of Grothendieck's theorem for Bessel sequences. Precisely, given a Bessel sequence $\\{ x_j \\}_{j\\in\\mathbb{N}}$ with Bessel bound $1$ in a Hilbert space, we show that there exists functions $\\{ f_j \\}_{j\\in\\mathbb{N}}$ belonging to the unit ball of $L^\\infty([0,1])$ such that for all $j,k \\in \\mathbb{N}$ one has $$ \\langle x_j,x_k\\rangle = \\int_0^1 f_j(x)\\overline{f_k(x)}\\,dx.$$ As an application, we give an affirmative answer to an extension problem of Olevskii: if $E \\subset [0,1]$ is a Lebesgue measurable set such that $[0,1]\\setminus E$ has positive measure, then every Bessel sequence in $L^2(E)$ with Bessel bound $1$ extends to an orthonormal system in $L^2([0,1])$ that is bounded by the (optimal) constant $λ([0,1]\\setminus E)^{-1/2}$ on $[0,1]\\setminus E$. A formalization of our main result in Lean 4 accompanies the paper.",
      "title": "Grothendieck's theorem for Bessel sequences",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12280"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.15219",
      "authors": [
        "Yifeng Huang",
        "Kenny Lau",
        "Ken Ono",
        "Peter Paule"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.15219",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-15",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "The Rogers--Ramanujan identities equate a $q$-series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~$5$. Identities of this shape are scarce, and a central problem is to identify the structures that produce them in families. Huang, Jiang, and Oblomkov have proposed a source of a new kind: to each pair of coprime integers $a,b>1$ they attach an infinite-rank $q$-series $Z_{a,b}(q)$, assembled from counts of commuting nilpotent matrix pairs $(A,B)$ with $A^a=B^b$ over finite fields, and they conjecture that it equals an explicit product of $(a-1)(b-1)/2$ modular units of level $a+b$. The $a=2$ cases are the Andrews--Gordon identities; no case with $a>2$ was known. We prove the conjecture for $(a,b)=(3,4)$, $(3,5)$, $(3,7)$, and $(3,8)$. Our proofs pass through a finer sum-to-sum identity, which we conjecture for all $b$ coprime to $3$ and establish for all $b$ when $q=1$. Lau and Ono have since proved that identity in general, and with it the full $a=3$ case. These identities have been formalized and verified in Lean by AxiomProver.",
      "title": "Algebraic geometric framework of Rogers--Ramanujan identities",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.15219"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.14836",
      "authors": [
        "Michele D'Adderio",
        "Giovanni Interdonato",
        "Alessandro Iraci",
        "Roberto Pagaria"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.14836",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-14",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Recent major breakthroughs in $q,t$-combinatorics include the introduction of the Dyck path algebra $\\mathbb{A}_{q,t}$ by Carlsson and Mellit and of the Catalanimals by Blasiak et al., both of which led, among other things, to independent proofs of different extensions of the rational shuffle conjecture of Bergeron et al. The first main contribution of this paper is a simple, explicit formula inside the algebra $\\mathbb{A}_{q,t}$ for the Neguţ operators, yielding a direct, elementary connection between the original operators of the rational shuffle conjecture and the corresponding Catalanimals. Our formula bypasses the elliptic Hall algebra, turning these operators into transparent, workable tools whose action we can compute exactly and efficiently on any symmetric function, not just constants. Our second main contribution consists of a series of explicit formulas relating the Neguţ operators to the Theta operators introduced by D'Adderio et al. To prove these formulas, we provide an extension of the aforementioned Theta operators to the entire algebra $\\mathbb{A}_{q,t}$, allowing us to obtain a series of new combinatorial results. The algebraic computations underlying this extension have been formalized in Lean. To showcase the power of our results, we give a proof, also partially formalized in Lean, of the Theta conjecture of D'Adderio et al., first stated in 2019.",
      "title": "Leaving the Hall: explicit formulas for Neguţ operators",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.14836"
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        "Sebastian Graf"
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      "summary": "Recent commit on leanprover/lean4.",
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      "summary": "Recent commit on leanprover/lean4.",
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      "summary": "Recent commit on leanprover/lean4.",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: remove iff True from array lemmas (#12330)",
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      "summary": "Recent commit on leanprover/lean4.",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: make kernel `is_def_eq` caching order-independent (#14806)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: infer `do←` binder types from the wrapper (#14821)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/25dacd72958b3a4dc480ee2e41c611d8b5dff277"
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: classify spec preconditions through `binderNameHint` (#14819)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/0bdfa796ef6e1c94fa3c57a4fe0e5f728abb176e"
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      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: type-check generated recursors in the kernel (#14808)",
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      "title": "leanprover/lean4: feat: support unfolding definitions in `Sym.simp` parameters (#14820)",
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      "summary": "Recent commit on leanprover/lean4.",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: kernel-friendly `Bool` operations (#14788)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: conjunctive Hoare triple lemmas, and two `Std.WP` cleanups (#14813)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: name the assertion library constants directly again (#14784)",
      "updated": "2026-08-14",
      "url": "https://github.com/leanprover/lean4/commit/3797afed42c4f27738de2d81104b634b6c8b73f4"
    },
    {
      "age_days": 4,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:12392058ad1e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-14",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: split `cond` programs in `mvcgen` and `vcgen` (#14787)",
      "updated": "2026-08-14",
      "url": "https://github.com/leanprover/lean4/commit/12392058ad1e8a6da2d76abe60640a4f3bc5f7fd"
    },
    {
      "age_days": 4,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:639065aa1e42",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-14",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: cost metrics for the grind e-matching graph (#14118)",
      "updated": "2026-08-14",
      "url": "https://github.com/leanprover/lean4/commit/639065aa1e42edd83d8f4f9857981d172d95beda"
    },
    {
      "age_days": 4,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d97bd7be9a8c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-14",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add hint to `deprecated` linter (#14705)",
      "updated": "2026-08-14",
      "url": "https://github.com/leanprover/lean4/commit/d97bd7be9a8c0cb33e21367c88db9cd9326011b1"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.16688",
      "authors": [
        "Ethan M. Alt",
        "Miheer Dewaskar",
        "Jacob M. Maronge",
        "Yuelin Lu",
        "Matthew A. Psioda"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "arxiv:2608.16688",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-17",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Bayesian dynamic borrowing (BDB) methods leverage historical data to reduce treatment effect uncertainty, yet existing approaches rely on parametric outcome models susceptible to misspecification. We propose the nonparametric latent exchangeability prior (NP-LEAP), an outcome-agnostic, assumption-lean framework to borrow information from historical data. The NP-LEAP performs individual-level exchangeability assessment, inducing Bayesian model averaging over all possible partitions of the historical data into exchangeable and nonexchangeable subsets. Although applicable to a variety of data types with choice of appropriate kernel, the NP-LEAP is particularly well-suited for studies with time-to-event outcomes, where parametric BDB is potentially triply misspecified - imposing a parametric baseline hazard, the proportional hazards structure, and blanket exchangeability. We establish posterior consistency under mild regularity conditions. Simulation studies demonstrate favorable operating characteristics relative to parametric borrowing methods and nonborrowing semiparametric frequentist methods. We illustrate the method by augmenting the control arm in a randomized trial of patients with non-small cell lung cancer.",
      "title": "NP-LEAP: Nonparametric Latent Exchangeability Prior for Model-Lean Borrowing from Historical Data",
      "updated": "2026-08-17",
      "url": "https://arxiv.org/abs/2608.16688"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.16346",
      "authors": [
        "Timon Böhler",
        "Simon Daniel",
        "David Richter",
        "Pascal Weisenburger",
        "Mira Mezini"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "arxiv:2608.16346",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-17",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Choreographic programming is a programming model for developing distributed applications where an entire communication protocol is written as a single program, which a compiler then projects to one process per participant. Choreographic programming abstracts over low-level network communication primitives such as sockets, and provides a high degree of safety guarantees with deadlock freedom ensured by construction. Mechanizing choreographies necessarily deals with both operations specific to distributed programming and standard (local) operations that also occur in non-distributed programs, as well as the typical issues of binding and substitution. We aim to sidestep the latter issues, thereby obtaining a more concise mechanization that focuses on the essential distributed aspects of choreographies. To this end, we use a method recently proposed by Thiemann to elegantly model deadlock-free processes in a dependently typed language: Using state transformers to represent the computations performed by each process. We bring the state transformer model to choreographies, allowing us to reduce the usual mechanization effort around binding and substitution, and to abstract over the details of the \"local\" aspects of the language. We mechanize in Lean a choreographic language that supports point-to-point communication, broadcasting, recursive procedures, and local stateful methods, allowing each participant to be assigned a different set of methods. We prove soundness and completeness of endpoint projection, establish deadlock freedom for the projected processes, prove confluence, and verify a Hoare logic for choreographies.",
      "title": "Mechanizing Choreographic Programs and Hoare Logic with State Transformers",
      "updated": "2026-08-17",
      "url": "https://arxiv.org/abs/2608.16346"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.15900",
      "authors": [
        "Dinh-Khiet Le",
        "Minh-Quyet Ha",
        "Hong-Phuc Vu-Dinh",
        "Takashi Miyake",
        "Hiori Kino",
        "Hieu-Chi Dam"
      ],
      "content_date": "2026-08-16",
      "freshness": "fresh",
      "id": "arxiv:2608.15900",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-16",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Data-driven materials discovery interpolates more reliably than it extrapolates and seldom reaches new structure types. We present MatEvolve, an agentic-AI framework designing crystals, proposing each candidate with a stated rationale and testing it. The agent reasons in an interpretable \\emph{language of motifs}, writing each crystal as a \\emph{motif profile} that describes the recurring geometric patterns---the \\emph{motifs}---composing it. The motif profile serves not merely as a description of a material but as the medium for material design: the agent edits the profile and constructs a crystal from the modified one, and the most promising candidates are validated by first-principles calculation. Applied to the design of rare-earth-lean permanent magnets, MatEvolve---built on the state-of-the-art language model Claude Fable~5 without fine-tuning---reaches new structural prototypes more than three times as often as generative models under an equal validation budget, at a comparable on-target-magnet rate. Beyond design, analysing the discovered crystals' human-readable profiles reveals structure--property relationships.",
      "title": "Crystal-structure design by agentic AI in a language of motifs",
      "updated": "2026-08-16",
      "url": "https://arxiv.org/abs/2608.15900"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.15182",
      "authors": [
        "Vignon Oussa"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.15182",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We establish an abstract storage theorem for projectively $C_0$ unitary representations admitting a pair of one-parameter subgroups with conjugation escape. It produces, for every $0<\\varepsilon<1$, a single orbit whose sampling set is relatively separated modulo the projective kernel and whose frame bounds are $(1-\\varepsilon)^2$ and $(1+\\varepsilon)^2$. Two applications are obtained from the same mechanism. First, every nonabelian exponential Lie group admits a near-Parseval frame of left translates for its left regular representation. Consequently, a positive-dimensional exponential Lie group is an FT group if and only if it is nonabelian; in particular, the three-dimensional Heisenberg group admits such a frame. Second, every infinite-dimensional irreducible unitary representation of an exponential Lie group admits a near-Parseval discrete orbit frame. When the effective projective quotient is abelian, the orbit may be chosen to be an orthonormal basis arising from a transported Weyl lattice.",
      "title": "Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.15182"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.15318",
      "authors": [
        "Sanjit Singh Mehat"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.15318",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "An Euler magic matrix is an integer matrix M with MM^t = gamma I for some gamma != 0, whose squared entries sum to gamma along both main diagonals; it is proper if its squared entries are pairwise distinct. Euler gave a proper example of order 4; Müller settled orders 3 (none exists) and 8; and Kominers settled order 5. We give an order-6 construction, a case not addressed by Müller or Kominers, exhibiting a proper Euler magic matrix of order 6 with gamma = 18500 together with a second, independent one with gamma = 43290. The proof is the explicit matrix and a finite exact verification. We also record an elementary counting bound gamma >= 2485 for proper order-6 examples.",
      "title": "A proper Euler magic matrix of order 6",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.15318"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.14896",
      "authors": [
        "Florian Braun"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.14896",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-14",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Large language models work well on English and behave in poorly understood ways on languages typologically far from it. Japanese is a clean example, where evaluation still leans on translation quality and JGLUE-style benchmarks, which roll lexical, syntactic and pragmatic competence into a single score. The phenomena on which general-purpose models fail Japanese users are pragmatic: honorifics, in-group and out-group reference, context-sensitive politeness, zero anaphora. I introduce J-PragEval-v0, a minimal-pair benchmark isolating four such phenomena from surface fluency, and combine it with linear probes and teacher-forced log-probability evaluation to ask where inside TinySwallow-1.5B (28 layers, hidden size 1536) the corresponding contrasts live. The four features split three ways. Honorific register sits cleanly in the residual stream: 0.96 balanced accuracy at layer 15, and the model flips its preferred continuation with the scenario on 93 percent of items. Implicit subject and in-group reference are not linearly decodable at the final prompt token (0.48 and 0.38), yet flip rates are 0.77 and 0.79, so the contrast is worked out during generation rather than stored at the prompt. Indirect refusal is the negative case: 0.95 probe accuracy collapsing to a 0.43 flip rate under length-normalised teacher forcing, because the current minimal pairs conflate politeness with continuation length. I also specify Pragmatic Representation Steering, a parameter-free inference-time method that edits residual-stream activations along the class-mean-difference directions probing identifies. Feasibility is argued indirectly rather than demonstrated: the contrastive activation addition baseline, the same geometry the method would inject, recovers probe accuracy within one to two points of logistic regression wherever a linear signal exists. Scaling to Llama-3.1-Swallow-8B is the next step.",
      "title": "Interpretable Cross-Lingual Alignment in Small Language Models: Probing Cultural and Pragmatic Reasoning in Japanese-English Bilingual LLMs",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.14896"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.14209",
      "authors": [
        "Hengzhe Zhang",
        "Qi Chen",
        "Bing Xue",
        "Lean Yu",
        "Wolfgang Banzhaf",
        "Mengjie Zhang"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.14209",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-14",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Evolutionary feature construction has shown strong promise in symbolic regression by automatically discovering informative transformations of input features that enhance a simple base learner. However, existing approaches often lack explicit mechanisms to preserve important constructed features discovered during evolution, and valuable genetic material can be lost when genetic operators disrupt effective features. This paper introduces an adaptive protection mechanism that leverages feature importance metrics to selectively preserve constructed features during evolution. The mechanism provides stronger protection for more important constructed features while still allowing less important features to be modified and to incorporate useful building blocks from more important features. We evaluate the approach using multiple feature importance calculation methods and demonstrate its robustness across different base learners. Experimental results on 98 regression benchmark datasets show that the proposed mechanism consistently improves solution quality over baseline approaches, and experiments on two credit classification datasets demonstrate that the method also extends effectively to improve search effectiveness beyond symbolic regression.",
      "title": "Adaptive Protection for Evolutionary Feature Construction in Symbolic Regression with Application to Credit Classification",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.14209"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.12961",
      "authors": [
        "Olga Mashkova",
        "Asaad Mohammedsaleh",
        "Fernando Zhapa-Camacho",
        "Robert Hoehndorf"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.12961",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-13",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The OWL 2 EL profile is used in some of the largest production ontologies, including the Gene Ontology and SNOMED CT. Existing neuro-symbolic (NeSy) learning methods accept propositional theories or Datalog, and reasoning-shortcut (RS) awareness has not been investigated in ontology settings. We present Moose, a method that compiles an $\\mathcal{EL}^{++}$ TBox and finite ABox to a Sentential Decision Diagram (SDD). The SDD acts as a differentiable weighted-model-counting layer, and we add closure clauses outside the $\\mathcal{EL}^{++}$ profile on declared exhaustive families to overcome the limited expressivity of $\\mathcal{EL}^{++}$ under partial supervision. We show termination, soundness, completeness, and polynomial intermediate sizes, and validate the proofs in Lean. We then define the first formal partial-supervision latent-concept-learning task over an OWL EL ontology, i.e., learning per-individual classifiers for latent concepts from observed ABox literals, and evaluate Moose on MNIST-with-ontology and Pizzaïolo. Moose improves over propositional-NeSy, fuzzy-logic, and ontology embedding baselines, and presents the first reasoning-shortcut analysis in an OWL EL setting.",
      "title": "Moose: Latent concept learning with reasoning-shortcut awareness in $\\mathcal{EL}^{++}$",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.12961"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.13320",
      "authors": [
        "David V. Feldman",
        "Alexander Wilce"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.13320",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-13",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Say that a topological space $X$ has finite, respectively bounded, cliques iff every closed, irreflexive binary relation --- equivalently, every closed, loop-free directed graph --- on $X$ has cliques of finite, respectively bounded finite, size. Every compact space has bounded cliques. Having finite cliques implies limit-point compactness, and is implied by $ω$-limit point compactness (equivalently, countable compactness). Thus, for $T_1$ spaces, having finite cliques is equivalent to countable compactness. Having bounded cliques is strictly weaker than compactness. Indeed, any space $X$ such that $X^ω$ is countably compact has bounded cliques. However, we have found no example of a countably compact space having finite but unbounded cliques. The existence of such a space is the major open problem raised in this note.",
      "title": "A Note on Compactness and Clique Size",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.13320"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.13757",
      "authors": [
        "Chungha Sung",
        "Nikil V. Shyamsunder",
        "Hanliang Zhang",
        "Daniel Kroening",
        "Joonwon Choi"
      ],
      "content_date": "2026-08-13",
      "freshness": "fresh",
      "id": "arxiv:2608.13757",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-13",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Multi-engine AI accelerators such as AWS Trainium comprise specialized compute engines that execute in parallel, and the compiler must synchronize the data dependencies between them. For straight-line code this is simple: each dependency reduces to waiting for a threshold count of instruction completions, which the compiler computes statically. Loops admit no such static threshold; a simple solution inserts all-engine barriers at iteration boundaries, resetting synchronization state so each loop body can be treated as straight-line, at the cost of parallelism. We present a barrier-free synchronization algorithm that instead enforces each dependency precisely across structured control flow with arbitrarily nested, dynamically bounded loops. The key idea is to compute dynamic thresholds at runtime from tracked loop iteration counts. We implemented it as a compiler backend pass at the AWS Neuron ISA level. On a suite of ML kernels, it reduces latency 10-45% relative to the barrier-based baseline, achieves a 3.3x speedup on a synchronization-bound microbenchmark, and often matches or exceeds hand-tuned manual allocation. Issuing a consumer too early violates its dependency, while issuing too late unnecessarily stalls execution. We formally characterize the minimum synchronization required for correctness and verify in the Lean proof assistant, via bisimulation, that our algorithm meets this criterion.",
      "title": "A Barrier-Free Synchronization Algorithm for Multi-Engine AI Accelerators",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.13757"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12633",
      "authors": [
        "Yibo Yan",
        "Seo Jin Park"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12633",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-12",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Serverless platforms commonly colocate many diverse workloads, each in a fast-booting, memory-lean virtual machine (VM), to improve deployment density. Overprovisioning each VM for its peak protects tail latency during traffic bursts but hurts density; maintaining high density while effectively protecting tail latency requires the infrastructure to be able to shift physical cores, at a microsecond timescale, to whichever latency-sensitive VM is bursting and reclaim them as the burst subsides. No VM substrate delivers this: conventional VMs resize a guest's cores only through a millisecond-scale vCPU hot-plug path, Firecracker fixes a VM's core count at boot, and the ultralight VMs that boot fastest drop multicore execution entirely. We present HyperFlux, a commodity-KVM ultralight VM substrate that makes a VM's parallelism width (the number of physical cores backing it) elastic at runtime. We show that HyperFlux can move a core across VMs in merely 13$μ$s, even when forcibly reclaiming it from a busy donor, orders of magnitude faster than vCPU hot-plug. A HyperFlux VM incurs only a 3.2MB memory footprint and can cold-boot in 1.37ms, on par with the fastest-booting ultralight VMs, while uniquely supporting multicore parallelism. Under colocation, it can reduce high-priority VMs' tail latency by up to 10x under high load compared to static core-sharing with Firecracker and Cloud Hypervisor, and deliver a lower and more stable tail latency compared to using cgroup and vCPU hot-plug under changing load bursts.",
      "title": "Offering Microsecond-Scale Cross-VM Core Elasticity on Colocated Lightweight Virtual Machines",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12633"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.11941",
      "authors": [
        "Tom Adamczewski"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.11941",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-12",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al. Whereas these conjectures had previously been attempted only with a bespoke agent, our open-source evaluation code runs any generic language model (LM) against them, and is secure against LM cheating attempts. We find that LMs equipped with a minimal set of tools resolve 147 of these conjectures with a budget of \\$50 per attempt, scoring 30% on OEIS Open. OEIS Open Lite is a random subset of 100 conjectures for cheaper evaluation. When evaluated with a budget of \\$200 per attempt, the best current LM scores 44% on OEIS Open Lite. Giving LMs access to the mathematics literature via 476,000 papers from arXiv did not increase performance on OEIS Open Lite, and nor did using more sophisticated agent loops. The conjectures covered in this work are of uncertain mathematical significance, and most have likely received little previous attention. Nevertheless, our results show that LMs can resolve open research conjectures autonomously and at modest cost.",
      "title": "OEIS Open: How many conjectures can language models turn into theorems?",
      "updated": "2026-08-13",
      "url": "https://arxiv.org/abs/2608.11941"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12223",
      "authors": [
        "Ivan S. Yakovenko",
        "Alexey D. Kiverin"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12223",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-12",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Ultra-lean hydrogen flames under terrestrial gravity are governed by a coupled interaction among preferential diffusion, thermal diffusion, heat loss, and self-induced convection. This study numerically examines combustion in a quiescent 6~vol.\\% H$_2$--air mixture using detailed chemistry and a low-Mach-number formulation. A complete calculations set was considered, with Soret diffusion and optically thin radiative heat loss independently enabled and disabled. One-dimensional spherical calculations were used to isolate the initial post-ignition flame kernel growth, while two-dimensional planar and axisymmetric simulations described its subsequent buoyant rise, deformation, and breakup. Over the analyzed interval, the spherical flame-front radius followed $R_f^2\\approx Kt$ rather than constant-speed expansion. Soret diffusion increased the effective growth coefficient $K$, whereas radiation reduced it. The axisymmetric calculations reproduced the experimentally measured leading-point trajectory substantially better than the planar formulation. Soret diffusion produced larger, faster-rising kernels and maintained a more nearly circular upper cap, whereas radiation had a weaker effect on trajectory but increased relative lateral flattening. In all cases, a toroidal vortex stretched the flame segment and caused local extinction and fragmentation. Soret diffusion delayed breakup, while radiation advanced it; their combined effect on breakup time was nearly compensating. The results show that Soret transport and radiation primarily alter kernel growth and resistance to vortex-induced extinction, while the qualitative breakup pathway remains hydrodynamically controlled.",
      "title": "Effects of Soret Diffusion and Radiative Heat Loss on the Evolution of Buoyant Flame Kernels in Ultra-Lean Hydrogen-Air Mixture",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12223"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12570",
      "authors": [
        "Najmeh Forouzandehmehr",
        "Topojoy Biswas",
        "Evren Korpeoglu",
        "Kannan Achan"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12570",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-12",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Fashion retrieval often requires satisfying multiple attributes at once, such as category, color, pattern, and demographic. Monolithic embeddings mix these signals into a single vector, making attribute-specific control difficult at retrieval time. Many existing semantic-ID methods provide discrete item codes, but these codes are typically optimized as item-level or residual addresses and do not expose named, independently controllable attribute slots. We introduce MM-slotgate, a multimodal slot encoder that factorizes Fashion-CLIP text and image embeddings into four named attribute slots. Each slot learns its own text-image gate, so visually grounded attributes such as color and pattern can rely more on image evidence, while taxonomy-oriented attributes such as category and demographic can remain more text-driven. On H&M, using a combined slot-similarity and slot-logit retrieval score, MM-slotgate achieves 0.7566 macro ConstraintSatisfied@10, outperforming equal-weight multimodal fusion (0.7142) and fCLIP text-only retrieval (0.4755). The largest gain is on color, which improves from 0.321 to 0.889 (+0.568 absolute), as the learned color gate assigns 57.4% weight to image evidence. The learned gates are interpretable without modality supervision: color is image-leaning, category is text-leaning, and pattern and demographic lie near the middle. The resulting slots also remain controllable: linear probes show no measured excess leakage beyond the label-correlation baseline, and quantized slot codes support targeted intervention, including a 15.3x lift for color. These results suggest that controllable fashion retrieval benefits from typed, attribute-conditioned multimodal slots rather than either a single global embedding or opaque item-level semantic IDs.",
      "title": "Attribute-Conditioned Multimodal Slot Factorization for Controllable Fashion Retrieval",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12570"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.11792",
      "authors": [
        "Lin Mai",
        "Yaobo Zhang"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.11792",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-12",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We study whether a tree-level MHV gravity numerator is determined by its degree and by vanishing on $\\langle ij\\rangle=[ij]=0$ for every pair. A flag-variety standard-monomial basis and an $S_n$-resolved restriction map reduce the problem to exact finite-dimensional calculations. At seven points we find $W_{7,\\mathbb{Q}}\\simeq S^{(2,1^5)}\\oplus S^{(1^7)}$. The Hodges numerator spans the sign summand, while the six-dimensional hook gives additional algebraic solutions. The pair-ideal conditions therefore do not determine a unique algebraic solution, but Bose symmetry selects the Hodges line. At eight points, pair-ideal conditions and Bose symmetry leave a two-dimensional alternating space. Same-helicity BCFW scaling, normalized collinear factorization, and the leading soft coefficient impose the same linear condition and select the Hodges line. We also prove that, at arbitrary multiplicity, an alternating fixed-degree numerator is determined by its full value on one collinear boundary with the marked legs and their spinor ratio fixed. Together with standard factorization, this determines the numerator up to normalization within the fixed-common-denominator ansatz. All rank and ideal-membership calculations use exact integer or rational arithmetic, and their finite-dimensional consequences are checked separately in Lean.",
      "title": "Algebraic versus physical uniqueness of MHV gravity numerators",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.11792"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.12179",
      "authors": [
        "Yung-Hsu Yang",
        "Luigi Piccinelli",
        "Samuel Rota Bulò",
        "Sunghwan Hong",
        "Denis Rozumny",
        "Johannes Schönberger",
        "Zuria Bauer",
        "Hermann Blum",
        "Peter Kontschieder",
        "Marc Pollefeys"
      ],
      "content_date": "2026-08-12",
      "freshness": "fresh",
      "id": "arxiv:2608.12179",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [
        "negative:vision_world_models"
      ],
      "published": "2026-08-12",
      "score": -2.5,
      "source": "arxiv-ai4math-core",
      "summary": "Metric 3D object detection is a core capability for embodied agents, yet most reliable systems lean on depth sensors, trading away cost, power, and integration simplicity. This motivates monocular 3D detection, which avoids additional constraints, yet it faces a major obstacle: from a single image, depth, and especially absolute scale, are underconstrained. As a result, the prevailing pattern of detecting in 2D and then predicting 3D attributes is often brittle, since modest range errors can dominate 3D localization, and the learned scale prior can fail when cameras, motion, or environments undergo domain shifts. To address this, we propose Map-Det3D, an online multi-view 3D object detection model that brings detection directly into a 3D space reconstructed from RGB. We map a short temporal window into multiple views and repurpose a feed-forward metric 3D reconstruction model as our geometric backbone while tuning its object-aware capabilities. Building on this representation, Map-Det3D directly predicts boxes in metric 3D space, without the widely used 2D-to-3D lifting. Experiments across different benchmarks show that this design supports strong online performance and robust transfer without adaptation, suggesting that training reconstruction priors for detection is a practical route to stable metric 3D detection from monocular video. Code and models are available at https://royyang0714.github.io/Map-Det3D.",
      "title": "Map-Det3D: Metric Feed-Forward 3D Reconstruction Prior for Multi-view 3D Object Detection from Streaming Inputs",
      "updated": "2026-08-12",
      "url": "https://arxiv.org/abs/2608.12179"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}