{
  "counts": {
    "adjacent": 14,
    "core": 4,
    "errors": 0,
    "negative": 70,
    "total": 88
  },
  "date": "2026-08-19",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-19T15:59:03Z",
  "items": [
    {
      "age_days": 4,
      "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": 5,
      "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": 6,
      "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": 4,
      "arxiv_id": "2608.16947",
      "authors": [
        "Ian D'Ambrosio"
      ],
      "content_date": "2026-08-15",
      "freshness": "fresh",
      "id": "arxiv:2608.16947",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-15",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Huang, Lou, and Xiao introduced Dynamic Mixture-of-Experts Serving and gave an O(sqrt(log k))-competitive randomized algorithm for its integral primal problem, where k is the number of replica GPUs beyond the mandatory copy of each expert. Their matching lower barrier applies to an auxiliary dual and leaves the primal order open. We prove that the randomized primal competitive ratio is in fact Theta(1) for arbitrary numbers of experts. The upper bound reduces reciprocal-max service costs to chasing positive bodies with covering row sparsity two. A finite tangent envelope approximates each reciprocal epigraph within a constant factor, summable positive resets convert accumulated service into movement, and a nonexpansive balanced projection removes the positive-body algorithm's resource augmentation. Combining the resulting fractional path with Lazy Threshold Rounding gives E[ALG] <= 10 C_PB OPT + (5 C_PB + 2) k + 16, where C_PB is the absolute constant from Chasing Positive Bodies at resource augmentation one and covering sparsity two. The full reduction, rounding composition, and quantified main theorem are machine-checked in Lean 4 relative to exact formal interfaces for the two cited source theorems. Deterministic rational controls and a fresh independent replay accompany the formal proof.",
      "title": "A Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving",
      "updated": "2026-08-15",
      "url": "https://arxiv.org/abs/2608.16947"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.17274",
      "authors": [
        "Hongru Zhao"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.17274",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-18",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We study the von Neumann entanglement entropy generated by a Haar distributed passive interferometer acting on $n$ equally squeezed input modes with fixed nonzero squeezing strength $s$. Previous work established proportional weak typicality for integer R'enyi orders $α\\geq 2$ and stated a sublinear von Neumann result, while the proportional von Neumann case remained open. For a subsystem of $k_n$ modes satisfying $k_n/n\\to r\\in(0,1)$, we prove that, for every $\\varepsilon>0$ and all sufficiently large $n$, $\\mathbb{P}\\left(\\left|\\frac{S_{1,n}}{\\mathbb{E}S_{1,n}}-1\\right|\\geq\\varepsilon\\right)\\leq2\\exp\\left[-\\frac{c_{s,r}\\varepsilon^2n^2}{\\log^2(en)}\\right].$ The proof represents the entropy as a singular value statistic of a principal block of $UU^{\\mathsf T}$, where $U$ denotes the unitary interferometer. It regularizes the logarithmic singularity at the endpoint corresponding to a pure Gaussian mode and applies concentration on the unitary group. The result establishes proportional von Neumann weak typicality and further implies almost sure convergence of $S_{1,n}/\\mathbb{E}S_{1,n}$ to $1$, a typical volume law, and the variance bound $\\mathrm{Var}(S_{1,n})=O_s(\\log^2 n)$. An accompanying Lean 4 development verifies the proof chain.",
      "title": "Weak Typicality of von Neumann Entanglement Entropy in Gaussian Boson Sampling",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.17274"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.17741",
      "authors": [
        "Olga Mashkova",
        "Asaad Mohammedsaleh",
        "Fernando Zhapa-Camacho",
        "Robert Hoehndorf"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.17741",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-18",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "OWL 2 DL ontologies, grounded in the description logic $\\mathcal{SROIQ}$, express large knowledge bases in biomedicine and the Semantic Web. Neuro-symbolic (NeSy) learners over description logics either embed the ontology in a continuous space, abandoning classical entailment, or restrict to the Horn fragment $\\mathcal{EL}^{++}$, which has a single canonical model. We present Baobab, which compiles a $\\mathcal{SROIQ}$ ontology with a finite ABox into a Sentential Decision Diagram (SDD): it saturates a propositional core under a consequence-based calculus and instantiates the remaining $\\mathcal{SROIQ}$ features (nominals, number restrictions, and the role axioms) over the active domain. The SDD's evidence-conditioned weighted model count then trains a perception network to recognize real images under partial ABox supervision: on an ontology that exercises every distinctive $\\mathcal{SROIQ}$ feature, a CNN learns to read MNIST digits coupled by a successor relation and recovers latent ontology concepts that an independent perception leaves at chance. When the supervision admits several ontology-consistent completions, an independent perception collapses onto one, a reasoning shortcut: we show that a mixture indexed by the query's justifications can represent the calibrated posterior no independent perception can, and that seeding it from the circuit's enumerated completions attains the Bayes-optimal posterior on a real-image MNIST task where single-WMC and learned mixtures (the BEARS-ensemble hypothesis class) do not: to our knowledge the first to characterize and mitigate reasoning shortcuts in a non-Horn description logic. Soundness of the compiler and the representation result are machine-checked in Lean 4. Code is available at https://github.com/bio-ontology-research-group/baobab.",
      "title": "Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.17741"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.17880",
      "authors": [
        "Ibrahim Mian",
        "Shayaan Siddique"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.17880",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-18",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Erdős problem 647 asks whether any $n > 24$ satisfies $\\max_{m<n}(m + τ(m)) \\le n + 2$, where $τ$ is the divisor-count function. Computational searches have excluded solutions up to $10^{12}$ by direct sieve and up to roughly $9.17 \\times 10^{18}$ within a modular reduction whose Lean component relies on native_decide; those computations sit outside any proof kernel. We give the first exclusion checked end to end by one: no solution exists with $24 < n \\le 10^9$, proved in Lean 4 with axiom closure exactly {propext, Classical.choice, Quot.sound} -- no sorry, no native_decide, no problem-specific axiom. The proof replays a chain of 6,685,922 factorization witnesses whose excluded intervals concatenate across $(24, 10^9]$; it needs no primality facts beyond primes below 1024, and it is the finite, fully proved form of a domination-interval argument whose asymptotic step was the identified gap in a withdrawn January 2026 claim on this problem. The generation pipeline is cross-checked by two further independent implementations, the compiled development replays through the standalone lean4checker, and two from-source verification legs -- Lean toolchains compiled from source by gcc and by clang, mathlib rebuilt with no cache -- reproduce the committed certificates byte for byte, with olean digests identical across three builds on two architectures. Our range is three to ten orders of magnitude below the computational frontiers we cite; the contribution is the trust base, not the range.",
      "title": "A Kernel-Checked Exclusion Certificate for Erdős Problem 647",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.17880"
    },
    {
      "age_days": 2,
      "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": 3,
      "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": 3,
      "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": 4,
      "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": 5,
      "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": "2608.16944",
      "authors": [
        "Ian D'Ambrosio"
      ],
      "content_date": "2026-08-14",
      "freshness": "fresh",
      "id": "arxiv:2608.16944",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-14",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Jaillet et al. introduced a fully online model for batching nonpreemptive LLM requests under a growing KV-cache memory constraint. For total end-to-end latency they proved that every deterministic algorithm has competitive ratio Omega(sqrt(n)), while the elementary sequential upper bound is n. We close this gap. Let R_det(n,M) be the optimal deterministic ratio for exactly n requests at memory M, and let R_det(n)=sup_M R_det(n,M). For every n >= 2 we prove (n-1)/12 <= R_det(n) <= n, so R_det(n)=Theta(n). The lower bound releases one memory-filling long request, observes its deterministic start time, and then releases n-1 wide one-token requests halfway through the long run. No short request can overlap the long one, whereas a hindsight schedule runs the two groups in the opposite order when useful. The hard instance uses the explicit fixed memory M=2(n-1)n. The upper bound is achieved by a uniform causal serial policy. The exact model, causality argument, both comparator branches, and quantifier order are machine-checked in Lean 4. Exact finite controls and replay commands accompany the proof.",
      "title": "A Tight Linear Deterministic Competitive Ratio for Fully Online KV-Cache Scheduling",
      "updated": "2026-08-14",
      "url": "https://arxiv.org/abs/2608.16944"
    },
    {
      "age_days": 6,
      "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": 6,
      "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": 1,
      "arxiv_id": "2608.18024",
      "authors": [
        "Haruhisa Enomoto"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.18024",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-18",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules. We propose the quotient--submodule equidistribution conjecture: over a representation-finite algebra, the number of quotient-closed subcategories of size $i$ is equal to that of submodule-closed subcategories of size $i$ for every $i$, where size is the number of indecomposable modules in the subcategory. We prove the following cases of the conjecture: (1) the five smallest and five largest values of $i$, hence all algebras with at most nine indecomposable modules; (2) Nakayama algebras; (3) algebras with radical square zero; and (4) representation-directed algebras. In the last case, we classify quotient-closed subcategories by a lower Bruhat interval in a Coxeter group constructed from the Auslander--Reiten quiver, extending the classification of Oppermann--Reiten--Thomas for Dynkin quivers. We also prove that quotient closure defines a finitary convex geometry and classify the functorially finite quotient-closed subcategories by Gen-minimal modules.",
      "title": "An equidistribution conjecture for quotient-closed and submodule-closed subcategories",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.18024"
    },
    {
      "age_days": 4,
      "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": 5,
      "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"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:a25f21e4e9c3",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: test: clean up tests writing to tracked files, prevent future violations (#14772)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/a25f21e4e9c32ea7db61afff1279f0e08a4b3251"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:af46668adab4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: mark simp specs conjunctive in their precondition (#14837)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/af46668adab413eed68e9921ad19996fc7312924"
    },
    {
      "age_days": 0,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2623bb67ef4a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: record code quality metrics from linters (#14748)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/2623bb67ef4adfb367c713108f87e4bef2a7df6a"
    },
    {
      "age_days": 0,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d6e84ed4be96",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: lake: support package code quality checks in `lake lint` (#14716)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/d6e84ed4be96d0c428594d435492c7d3da903229"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0b71f584f9c2",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add a `given` clause to `def` contracts (#14825)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/0b71f584f9c281f9e50716669c7ba5bd2274b426"
    },
    {
      "age_days": 0,
      "authors": [
        "Lean stage0 autoupdater"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:091d23740bb6",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: update stage0",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover/lean4/commit/091d23740bb634b8b45f262ca6c873b5de7aeb29"
    },
    {
      "age_days": 0,
      "authors": [
        "Francesco Chotuck"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:d5ddea8adf86",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: refactor(Topology/Compactness): use `𝓝ˢ` in `exists_subset_nhds_of_isCompact'` (#42550)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/d5ddea8adf86ab12b130218ed5ab7cc9315de2e8"
    },
    {
      "age_days": 0,
      "authors": [
        "Michael Rothgang"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:26c01238f55d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix: outdated link in new contributor welcome comment (#42900)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/26c01238f55db7b43d0e8baaf70281d65b60250b"
    },
    {
      "age_days": 0,
      "authors": [
        "Justin Palumbo"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:10b83106951a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix(Topology/Metrizable/CompletelyMetrizable): make instances anonymous to avoid name collisions (#42896)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/10b83106951a3c31069a5c640b40a4559f0aaff7"
    },
    {
      "age_days": 0,
      "authors": [
        "Noah Walker"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:35b2c4c19604",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix(RingTheory/PowerSeries): rename `order_zero_of_unit` to `order_zero_of_isUnit` (#42930)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/35b2c4c196043d5d5a4ef58793fd1d299efe1608"
    },
    {
      "age_days": 0,
      "authors": [
        "Xavier Généreux"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:abec2f7ba4f5",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Valuation/ValuationSubring): add ofSubring_toSubring (#42701)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/abec2f7ba4f54e234e6421b9e959770f7d827bf2"
    },
    {
      "age_days": 0,
      "authors": [
        "Kevin Wilson"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ffbfefaec67d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Topology/Semicontinuity/Michael): michael's selection theorem (#39116)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ffbfefaec67d01d561affd800125a281db8bb7f3"
    },
    {
      "age_days": 0,
      "authors": [
        "Noah Walker"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:19f1e5bd94c1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal/Maps): add lemma `Ideal.map_eq_image_of_surjective` (#42928)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/19f1e5bd94c1c7ef5a785243a036d9653f7b4256"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:fd891ee98c2a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Order/SupClosed): a lower directed set is sup-closed (#42838)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/fd891ee98c2a2188e2d19011d304e0db23a1759f"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:abec794dccc8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Order/Preorder/Chain): `IsMaxChain` is `Maximal IsChain` (#42555)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/abec794dccc82583e8ac6f31968adf01c264d2da"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:aead6374acbd",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Order/Interval/Set/Disjoint): a union of `Ioi` is the `Ioi` of the least element (#42826)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/aead6374acbd2c152d881c5980cc24a3e478b95f"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:b799d482b012",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Order/Directed): the empty set is directed (#42837)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/b799d482b012780247643ffb5d88689d926d4137"
    },
    {
      "age_days": 0,
      "authors": [
        "Nailin Guan"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:2be5027d86b1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(LinearAlgebra): lemmas for vanishing of exteriorPower (#40927)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/2be5027d86b1a51d28a2b51ca497ecab192ecf22"
    },
    {
      "age_days": 0,
      "authors": [
        "Noah Walker"
      ],
      "content_date": "2026-08-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:b09a5ef0e381",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Data/Finset/Card): add `Finset.card_le_card_of_surjective` (#41597)",
      "updated": "2026-08-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/b09a5ef0e3813973f6a95a195943b218dcf13f36"
    },
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      "title": "leanprover/lean4: feat: head-reduce a verification condition before emitting it (#14823)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/6310719d79f7f549c205b332d153f7ec4367f30e"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:a8ec7f8ed86b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: conjunctive Hoare triple lemmas, and two `Std.WP` cleanups (#14813)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/a8ec7f8ed86b4343e4080c05ed5af1fb5ff902cd"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2d268e9cae8b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: complete the `PredTrans` simp framework, and collapse the identity instances (#14824)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/2d268e9cae8bb7ca20d4f3ab1f0efb5c3fca2a82"
    },
    {
      "age_days": 1,
      "authors": [
        "Wojciech Różowski"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:3e7776671e8f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add a warning to transitive deprecations (#14816)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover/lean4/commit/3e7776671e8fefa35f88fd48aaa877db3a228a3e"
    },
    {
      "age_days": 1,
      "authors": [
        "Gaëtan Serré"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3a8b009373bf",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: a measurable space structure on matrices (#42621)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3a8b009373bf77127c6f272c92de2e0e4944f96b"
    },
    {
      "age_days": 1,
      "authors": [
        "Sebastien Gouezel"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:513523c2a2f6",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: Fubini theorem for vector measures (#41891)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/513523c2a2f66dd3dfe8fb27a4c4a5992f141983"
    },
    {
      "age_days": 1,
      "authors": [
        "Stefan Kebekus"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ab146e52f9af",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: API for (co)discrete sets (#42227)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ab146e52f9af71ce45b32f57af37d3fd47808c22"
    },
    {
      "age_days": 1,
      "authors": [
        "Attila Gáspár"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ebf6107dc188",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Topology/Algebra): topology on `ContinuousAffineMap` (#41774)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ebf6107dc188dbfdd6106baf35dd8b03bf933e8f"
    },
    {
      "age_days": 1,
      "authors": [
        "Weiyi Wang"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:b4d363202ee1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Analysis/Meromorphic): a non-zero meromorphic function has multiplicative inverse (#39843)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/b4d363202ee1550d8b31c595a87e27f03165a3b1"
    },
    {
      "age_days": 1,
      "authors": [
        "Attila Vajda"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:4ac22c7efcf2",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Algebra/BigOperators/NatAntidiagonal): remove unused variable (#42907)",
      "updated": "2026-08-18",
      "url": "https://github.com/leanprover-community/mathlib4/commit/4ac22c7efcf253ec41e1b469f381b4ab68ca2646"
    },
    {
      "age_days": 2,
      "authors": [
        "Robin Arnez"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:5594178cba78",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-17",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: perf: improve proof-over-applied cases in `ToLCNF` (#12814)",
      "updated": "2026-08-17",
      "url": "https://github.com/leanprover/lean4/commit/5594178cba78098b6b42b5a13c3506234b64f7a5"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:a7dfd2e2875a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-17",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `let_to_have` tactic to `sym =>` mode (#14802)",
      "updated": "2026-08-17",
      "url": "https://github.com/leanprover/lean4/commit/a7dfd2e2875ac37c43162c9b0166bbdf7a316fca"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.17317",
      "authors": [
        "Juliane Trianon Fraga",
        "Vinicius de Oliveira Rodrigues"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.17317",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove in ZFC that every torsion-free Abelian group of cardinality $\\mathfrak c$ admits a Hausdorff countably compact group topology without nontrivial convergent sequences. In particular, this applies to the free Abelian group $\\mathbb{Z}^{(\\mathfrak c)}$, the Baer-Specker group $\\mathbb{Z}^ω$ and $\\mathbb{Q}^{(\\mathfrak c)}$. For the topology constructed on $\\mathbb{Z}^{(\\mathfrak c)}$, the coordinatewise nonnegative cone is countably compact in the subspace topology. Consequently, there exists in ZFC a commutative Tychonoff countably compact topological semigroup which has two-sided cancellation but is not a group, giving a negative answer to Wallace's question. Combined with earlier results, the main theorem also yields in ZFC a Tychonoff countably compact topological semigroup containing a copy of the bicyclic semigroup and a functionally Hausdorff countably compact paratopological group that is not a topological group.",
      "title": "The Wallace problem and countably compact torsion-free Abelian groups in ZFC",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.17317"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.17758",
      "authors": [
        "Nalin A. G. Arachchilage",
        "Asangi Jayatilaka",
        "Senuri Wijenayake",
        "David Herbert",
        "Kaie Maennel",
        "Nicole Herbert",
        "Claudia Szabo",
        "Gabrielle Murray",
        "Gary Thomas"
      ],
      "content_date": "2026-08-18",
      "freshness": "fresh",
      "id": "arxiv:2608.17758",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-18",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Australian women, gender-diverse individuals, and culturally and linguistically diverse (CALD) communities are often more susceptible to phishing and other forms of cybercrimes due to factors such as language barriers, limited access to cybersecurity education, and social isolation. These communities encounter substantial obstacles both entering and progressing in the cybersecurity field. In Australia, the Higher Education sector still leans heavily on a largely uniform cybersecurity curriculum, focusing heavily on technical proficiency, overlooking the vital impact of intersectionality and user-centered thinking for boosting student engagement and learning. Without gender inclusivity and proper consideration of intersectionality forms such as CALD, the workforce is deprived of the varied perspectives necessary to tackle today's intricate cybersecurity issues. In this study, we conducted semi-structured interviews with 15 experienced academics teaching and coordinating cyber security programs from a diverse range of Australian universities, covering all states, to explore their perspectives on: i) current strategies for addressing the women, gender-diverse and CALD perspective in cyber security education in the Australian HE sector; ii) barriers to incorporate women, gender-diverse and CALD perspective in cybersecurity curriculums in higher education; iii) future work and support that is needed. Our research highlights a lack of systematic methods for integrating intersectional perspectives into cybersecurity curriculums. In particular, we identified four key barriers and four areas where support and future efforts are needed to address this issue. Our findings offer vital insights that can substantially guide curriculum development in cybersecurity education.",
      "title": "Advancing Inclusivity in Cybersecurity Education: Integrating Intersectionality to Enhance Student Engagement in Australian Higher Education Curriculums Strategies, Barriers, and Future Directions",
      "updated": "2026-08-18",
      "url": "https://arxiv.org/abs/2608.17758"
    },
    {
      "age_days": 2,
      "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": 2,
      "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": "2608.17065",
      "authors": [
        "Hongru Zhao"
      ],
      "content_date": "2026-08-17",
      "freshness": "fresh",
      "id": "arxiv:2608.17065",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-17",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Anticoncentration is central to hardness arguments for approximate sampling. In the independent Gaussian surrogate for collision free Gaussian boson sampling, the moment ratio studied here also determines the averaged ideal linear cross entropy reference value. Let $H_{k,n}=\\mathrm{haf}(X^{\\mathsf T}X)$, where $X\\in\\mathbb{C}^{k\\times 2n}$ has independent standard circular complex Gaussian entries. We evaluate $\\mathbb{E}|H_{k,n}|^2$ and $\\mathbb{E}|H_{k,n}|^4$ exactly by reducing four hafnian copies to a rank two Gaussian integral. For $R_{k,n}=(\\mathbb{E}|H_{k,n}|^2)^2/\\mathbb{E}|H_{k,n}|^4$, we obtain $R_{k,n}=4^{-n}\\binom{2n}{n}/F_{k,n}$, where $F_{k,n}={}3F_2(-n,-n,1/2;1,k/2;1)$ is a terminating generalized hypergeometric polynomial. If $k/n^2\\to c>0$, then $F{k,n}\\to e^{1/c}I_0(1/c)$, where $I_0$ is the modified Bessel function of the first kind of order zero, and consequently $R_{k,n}\\sqrt{πn}\\to[e^{1/c}I_0(1/c)]^{-1}$. Thus $k\\asymp n^2$ is a smooth Bessel crossover, whereas the scaling order boundary for inverse polynomial weak anticoncentration is $k\\asymp n^2/\\log n$. These conclusions concern the Gaussian surrogate moment criterion; finite dimensional Haar moment transfer and high probability small ball anticoncentration remain separate problems.",
      "title": "Exact Moments of Gaussian Gram Hafnians Reveal an $n^2/\\log n$ Threshold for Weak Anticoncentration",
      "updated": "2026-08-17",
      "url": "https://arxiv.org/abs/2608.17065"
    },
    {
      "age_days": 3,
      "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": 4,
      "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": 4,
      "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": 5,
      "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": 5,
      "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": 6,
      "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": 6,
      "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"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}