{
  "counts": {
    "adjacent": 9,
    "core": 2,
    "errors": 0,
    "negative": 78,
    "total": 89
  },
  "date": "2026-08-04",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-04T17:13:56Z",
  "items": [
    {
      "age_days": 1,
      "arxiv_id": "2608.02295",
      "authors": [
        "Hao Shen",
        "Junyu Guo",
        "Tian Cui",
        "Yuxuan Xiao",
        "Lihong Zhi"
      ],
      "content_date": "2026-08-03",
      "freshness": "fresh",
      "id": "arxiv:2608.02295",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "general_ai_math_reasoning",
        "lean_formal_proving_agents",
        "tool_use_agents"
      ],
      "published": "2026-08-03",
      "score": 9.3,
      "source": "arxiv-ai4math-core",
      "summary": "We present MechGeo, a Mathlib native agentic framework that jointly addresses faithful autoformalization and certified proof construction for Euclidean geometry. In this framework, GeoFormalizer represents informal problems in GeoIR, deterministically translates them into Lean 4, and iteratively repairs candidate statements using structural diagnostics and semantic evaluation. GeoProver constructs geometric proof plans, derives intermediate lemmas, and selectively algebraizes suitable subgoals through a library verified in Lean. Singular or SymPy may generate algebraic certificates, but all resulting proofs and counterexamples are checked by Lean's kernel. Experiments across seven LLM backbones show substantial improvements in autoformalization, particularly for models with weaker direct translation performance. On 43 historical IMO geometry problems, GeoFormalizer generates formal statements that GeoProver proves in 29 cases; for the remaining 14, it constructs counterexamples verified in Lean and proves all repaired statements after expert correction. Together with IMO 2026 Problem 2, this yields, to the best of our knowledge, the largest reported collection of automated, kernel-checked Lean proofs for IMO geometry problems. On the 14 geometry statements in LEAP's Lean-IMO-Bench, MechGeo proves 12 for the first time, formally refutes the remaining two, and proves both repaired statements. These results establish counterexample guided diagnosis, geometric reasoning, and certified symbolic computation as a practical foundation for trustworthy formal geometry.",
      "title": "MechGeo: Autoformalizing and Proving Euclidean Geometry in Lean 4",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.02295"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28877",
      "authors": [
        "Ha Trung Tran"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28877",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-30",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Verification consumes the majority of modern chip design effort, yet the formal verification tools that provide mathematical guarantees of correctness remain expensive and restrictively licensed. While large language models (LLMs) have shown promise for hardware design, existing approaches to RTL repair validate their results through simulation - which exercises only a subset of inputs - or rely on commercial tools, and few combine formal proof with an entirely open-source toolchain. In this paper, we present a multi-agent pipeline that couples an LLM with an open-source formal backend (Yosys, SymbiYosys, and Z3) to repair RTL through counterexample-guided iteration: the framework generates formal properties, verifies the design, and feeds counterexamples back to the LLM until the design is proved correct by k-induction or an iteration budget is exhausted. Through an ALU case study, we show that the pipeline can detect and repair a real functional bug with a formal proof of correctness. Across a six-benchmark suite, one design is repaired reliably, and we characterize four distinct failure modes: bounded-cover vacuity, specification ambiguity, temporal-logic bugs, and multi-property pressure. We frame this work as a feasibility study with a detailed failure analysis, and additionally report a practical limitation of the Yosys bind directive relevant to the open-source formal verification community.",
      "title": "Open-Source LLM-Driven Formal Verification: A Multi-Agent Pipeline for RTL Repair",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28877"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.01804",
      "authors": [
        "Tankun Li",
        "Zhi Chen",
        "Yaohua Tang"
      ],
      "content_date": "2026-08-03",
      "freshness": "fresh",
      "id": "arxiv:2608.01804",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "reasoning_rl_distillation",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-03",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "Post-training large language models (LLMs) via reinforcement learning (RL) has significantly advanced code generation capabilities. To bypass the heavy memory footprint of critic networks, current state-of-the-art frameworks leverage critic-free paradigms like Group Relative Policy Optimization (GRPO) tied to rule-based verification sandboxes. However, applying these frameworks to low-level systems programming, such as CUDA kernel generation-presents severe challenges: binary pass/fail rewards introduce severe signal sparsity, while multi-turn environmental feedback loops suffer from prohibitive compilation latencies and reward dilution across trajectories. In this work, we introduce LEAP (Lean Environment-Feedback via Adaptive Pruning), a scalable and computationally efficient multi-turn RL framework optimized for low-level hardware accelerator alignment. LEAP features Difficulty-Conditioned Pruning (DCP), a dynamic gating mechanism that adaptively cuts off simple and overly catastrophic tasks from multi-turn expansion, focusing resource-heavy compilation and hardware exploration exclusively on high-value, complex tasks. To fully operationalize these paths without manual hyperparameter engineering, we propose a Rank-Based Reward formulation. By deriving scale-free relative advantages from pairwise tournament outcomes within the GRPO rollout group, our method inherently penalizes token inefficiency on simple prompts while maximizing learning gradients on challenging distributions. Empirical evaluations show that LEAP achieves superior first-turn proficiency and robust multi-turn debugging resilience while converging faster than unpruned multi-turn baselines, establishing a practical paradigm for low-level code RL.",
      "title": "LEAP: Lean Environment-Feedback via Adaptive Pruning for Code RL in GPU Kernel Generation",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.01804"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01396",
      "authors": [
        "Alper Ferudun"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01396",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-02",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "For a finite simple graph $G$, let $t(G)$ be the largest order of an induced tree and let $g(G)$ be the girth. We prove three consecutive conjectures of DeLaViña's Graffiti.pc program. First, writing $\\ell(v)$ for the independence number of the subgraph induced by the neighbourhood of $v$, we prove $t(G) \\ge \\lfloor g(G)/2 \\rfloor - 1 + \\max_{v \\in V(G)} \\ell(v)$. Second, if $\\mathrm{Per}(G)$ is the periphery and $f(G) = \\max_x d(x, \\mathrm{Per}(G))$, we prove $t(G) \\ge \\frac{2}{3} g(G) + f(G)$, and establish the stronger integral bound $t(G) \\ge f(G) + \\lceil 2g(G)/3 \\rceil$ when $G$ contains a cycle. Third, if $δ'(G)$ is the second-smallest degree, counted with multiplicity, then every connected non-tree graph satisfies $t(G) δ'(G) \\ge g(G) + 1$. These are Conjectures 141, 142, and 143 of Written on the Wall II. Complete, machine-checked Lean 4 proofs of all three formal statements accompany the manuscript.",
      "title": "Three Graffiti.pc Conjectures on Largest Induced Trees: Proofs of Conjectures 141, 142, and 143",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01396"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.29349",
      "authors": [
        "Jonathan Washburn",
        "Milan Zlatanović"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2607.29349",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-31",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Let $δ$ denote the primitive act of distinction, formally realized as the one-step extension $r \\mapsto Sr$ of a finite record. We study the inductively generated $δ$-orbit and its first-order arithmetic presentation $\\mathbb{N}_δ$. The corresponding $δ$-calculus is an intuitionistic first-order proof system over the signature $\\{0,S,+,\\cdot\\}$. Every derivation carries a ledger recording the use of the law of excluded middle, the limited principle of omniscience, Markov's principle, and induction on quantified formulas. The last entry does not affect whether a derivation is forced. If a closed formula is derivable in the forced fragment, then it is true in the standard model. Starting from $δ$, we construct a choice-free number tower $δ\\leadsto \\mathbb{N}_δ\\hookrightarrow \\mathbb{Z}_δ\\hookrightarrow \\mathbb{Q}_δ$. The metatheoretic number systems $\\mathbb{N}$, $\\mathbb{Z}$, and $\\mathbb{Q}$ each admit an explicit injection into $\\mathbb{N}_δ$. We also classify the recognition quotients of the additive monoid $(\\mathbb{N}_δ,+,0)$. Assuming the law of excluded middle, every recognizer is either injective or has a kernel congruence $\\equiv_{i,p}$, with index $i$ and period $p$, for a unique pair $i\\ge 0$, $p\\ge 1$. In the noninjective case the quotient is isomorphic to the finite monogenic monoid $M(i,p)$. We price this classification with the ledger, determining which nonconstructive principles each form requires. If the congruence is decidable and an explicit pair of distinct related elements is given, the classification is forced. If the congruence is decidable and different from equality, Markov's principle is needed. For an arbitrary congruence, the dichotomy requires the law of excluded middle. The reverse implications show that the last two prices cannot be lowered. The main results are formalized in Lean 4.",
      "title": "The $δ$-calculus: from distinction to arithmetic",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2607.29349"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28110",
      "authors": [
        "Ruslan Khrulev"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28110",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-30",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operation names the node it edits, so the target theorem cannot be changed. Lean checks every applied change, and an accepted repair must declare every blueprint lemma its proof uses. We also construct BlueprintTrace, a benchmark of 142 controlled failures with complete accepted and rejected repair trajectories. We compare typed edits, exact source patches, and complete module rewrites under matched source, feedback, model, and budget, one episode per state and interface. With DeepSeek-V4-Flash, the three interfaces solve almost the same number of the benchmark's localized failures. Typed repair is the cheapest per solved state (patching is 1.30x as expensive, rewriting 2.06x), and within 10,000 completion tokens per task it reaches almost all of its final coverage, while both free-form interfaces are well behind. A second model, Qwen3.6-Flash, solves fewer states but keeps typed repair cheapest, puts it ahead on the proof-authoring states, and repeats the localized pattern.",
      "title": "BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprints",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28110"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01515",
      "authors": [
        "Michael Greinecker",
        "Patrick Lahr",
        "Christoph Schwerdtfeger"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01515",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-02",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Aumann (1974) showed that an atomless public randomization device makes the feasible- and equilibrium-payoff sets of a game with a fixed information structure convex, and asked whether they are closed. We show that, in every case the question leaves open, they need not be. One information structure drives all the examples: two sequences of fair signs whose coordinate correlations increase to a ceiling $ρ<1$ that no pair of separately measurable square-integrable rules attains. For every $0<ρ<1$ it yields a three-player game with a public randomization device whose equilibrium-payoff set is exactly the open interval $\\{(0,0,t):-ρ<t<ρ\\}$; a two-player game with a public randomization device whose equilibrium-payoff set is convex, full dimensional, and not closed; and, without any public device, nonclosed feasible- and equilibrium-payoff sets, the latter along equilibria with unique best replies modulo null events whose payoffs approach a vector that is not even feasible. With distinct but mutually absolutely continuous subjective priors, even the feasible-payoff set can fail to be closed in the presence of an objective public randomization device, together with every $\\varepsilon$-equilibrium payoff set and the set of induced law tuples. Our construction also allows us to resolve a conjecture of Stinchcombe (2011). The main results and the lemmas supporting them are formalized in the Lean proof assistant; an appendix records the exact coverage of each statement, including the clauses for which only a paper proof is given.",
      "title": "The Set of Correlated Equilibrium Payoffs for a Fixed Information Structure Need Not Be Closed",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01515"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.00885",
      "authors": [
        "Lucas Rabechini Amaral"
      ],
      "content_date": "2026-08-01",
      "freshness": "fresh",
      "id": "arxiv:2608.00885",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-01",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "At the scale of seconds the observed mid carries a stationary, mean-reverting error around a latent efficient price. We build an order book whose own flow produces that error and solve for the trading rule that maximises the long-run average profit rate net of the bid-ask spread. In a liquid large-tick asset the spread is one tick or two, and it is exactly the parity of the mid on the half-tick grid: tight at a half-integer, open at an integer. One coordinate therefore carries the problem: the gap $G$ between the mid and the efficient price; the price is an exogenous Brownian martingale, and $G$ is observable. The mid is a pure jump process whose move intensities lean toward the efficient price. Under one balanced-response condition, which equalises the book's corrective drift across parities, mean reversion of $G$ is a theorem: its conditional mean and stationary covariance are exactly those of an Ornstein-Uhlenbeck process with reversion rate $α$ and stationary standard deviation $s_G$. Its paths are not: the mid jumps. Passage times are therefore evaluated on the Gaussian diffusion those two moments define, at an error we bound on the reward side and leave heuristic on the timing side. A symmetric band of half-width $θ$ buys when the gap reaches $-θ$, sells at $+θ$, and holds inside; on the surrogate it is optimal among all admissible strategies, on the jump process itself that reduction remains a conjecture. With $φ$ the tight-book half-spread, the optimal half-width and its profit rate are $θ^*(θ^*-φ)=s_G^2$ and $R^*=αs_G\\sqrt{2/π}\\,e^{-θ^{*2}/2s_G^2}$. Threshold times margin equals the stationary variance of the gap. Trading as soon as the gap covers the spread earns zero: all profit is the option value of waiting.",
      "title": "Optimal Trading of Microstructure Mean Reversion",
      "updated": "2026-08-01",
      "url": "https://arxiv.org/abs/2608.00885"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.00323",
      "authors": [
        "Ken Ono"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2608.00323",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-07-31",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Han and Xiong recently extended the Gaussian binomial coefficient $\\genfrac{[}{]}{0pt}{}{r+k}{k}_{q}$ to positive rational $r$ and conjectured that its integer trace, the integer-exponent part of the resulting power series, is coefficientwise largest at $r=1/2$. We prove a support-dominance theorem comparing rational parameters under an explicit divisibility condition. It settles the conjecture for every $r\\geq 1/2$ and reduces the full conjecture to the unit fractions $r=\\frac{1}{2m}$, only finitely many of which are nontrivial for each fixed $k$. A computer computation then verifies the conjecture for every positive rational $r$ and every $k\\leq 200$. The theoretical results were autonomously produced and verified in Lean by AxiomProver.",
      "title": "On a conjecture of Han and Xiong for fractional Gaussian binomial coefficients",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2608.00323"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.29191",
      "authors": [
        "Jinhui Li",
        "Beibei Xiong",
        "Zhengfeng Yang"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2607.29191",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-07-31",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "The Dittert conjecture states that the Dittert functional on nonnegative $n\\times n$ matrices whose entries sum to $n$ is uniquely maximized by the uniform matrix. We prove the conjecture in dimension $4$. More precisely, let $K_4$ be the simplex of nonnegative $4\\times4$ real matrices whose entries sum to $4$, let $U_4$ be the uniform matrix, and let $φ$ denote the Dittert functional. We establish $\\frac{61}{32}-φ(A)\\geq \\frac{1}{52}\\lVert A-U_4\\rVert_F^2$ for every $A\\in K_4$. Consequently, $U_4$ is the unique maximizer of $φ$ on $K_4$. The proof reduces to certifying the nonnegativity of a structured quartic polynomial in sixteen variables on a simplex. We construct an exact rational constrained sum-of-squares certificate using an agent-guided symbolic-numeric procedure that combines template selection with sequential rational recovery. The main SOS consists of $152$ positively weighted rational squares, while each of the $136$ smaller SOS blocks consists of $16$ such squares. Exact $LDL^{\\mathsf{T}}$ decompositions certify positivity, and exact coefficient comparison over $\\mathbb{Q}$ verifies the complete polynomial identity. The resulting exact certificate is formally verified using the Lean proof assistant.",
      "title": "A Proof of the Dittert Conjecture in Dimension 4 via an Agent-Guided Exact Sum-of-Squares Certificate",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2607.29191"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28225",
      "authors": [
        "Haoqing Wang",
        "Xingrun Xing",
        "Wei Xia",
        "Ziheng Li",
        "Yehui Tang"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28225",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "negative:vision_world_models",
        "tool_use_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-30",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Agentic vision-language models (VLMs), which interleave textual reasoning with explicit tool calls such as cropping and code-based image manipulation, have emerged as a compelling paradigm for reliable and interpretable multimodal reasoning. However, recent studies have revealed that such models often use tools unfaithfully. Many process images are irrelevant to the question (e.g., the tool crops the wrong region or misses the queried target), yet the call still receives full credit and the model still answers correctly. Such decorative or misaligned tool calls waste computation and reveal that the model leans on prior knowledge or the original image rather than the evidence it retrieves. This may stem from two limitations of prevailing methods: the tool reward fails to distinguish useful from useless calls, and tool feedback carries no signal of usefulness. To this end, we introduce FaithEyes, a multi-agent self-judging framework. Concretely, we use a VLM to judge whether each process image helps answer the question. The judgement is injected into the reasoning context as part of the tool observation to help subsequent reasoning, and meanwhile is used to scale the tool reward by the helpful-tool ratio to suppress reward hacking. To keep judgement available at evaluation and thus ensure train-test consistency, we further design a multi-agent framework where the model itself serves as a subagent to judge the tool calls from main agent, eliminating any dependence on an external model at inference. Training via a two-stage SFT + RL pipeline on adapted open-source data, FaithEyes attains competitive or superior accuracy across visual perception and reasoning benchmarks, while markedly improving tool faithfulness. The homepage is at https://github.com/Mosi-AI/FaithEyes.",
      "title": "FaithEyes: Towards Faithful Tool Use via Multi-Agent Process-Image Verification",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28225"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:8c72ff8f5b13",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: decouple loop state and element universes in `Std.Internal.Do` specs (#14675)",
      "updated": "2026-08-04",
      "url": "https://github.com/leanprover/lean4/commit/8c72ff8f5b13625c7add73b69139e8ca68edc1c1"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:6eaa2f8af3cb",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: try the next `@[spec]` candidate when a spec rule does not apply (#14669)",
      "updated": "2026-08-04",
      "url": "https://github.com/leanprover/lean4/commit/6eaa2f8af3cb3b114a46de33822b3ef80eec07be"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:1da536882671",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: make `bv_decide` available in `sym` mode (#14672)",
      "updated": "2026-08-04",
      "url": "https://github.com/leanprover/lean4/commit/1da5368826718eb874ca74a9c3e7c50e61826266"
    },
    {
      "age_days": 0,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:98d2c1d1cfc8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(SimpleGraph/Walk/Operations): more operations API (#41460)",
      "updated": "2026-08-04",
      "url": "https://github.com/leanprover-community/mathlib4/commit/98d2c1d1cfc83510faf337915e038395fe11d55b"
    },
    {
      "age_days": 0,
      "authors": [
        "Felix Pernegger"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:a4b006456e26",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Analysis): open half planes are open (#42325)",
      "updated": "2026-08-04",
      "url": "https://github.com/leanprover-community/mathlib4/commit/a4b006456e26f4d2de94fc8aa21f20c357a83f04"
    },
    {
      "age_days": 0,
      "authors": [
        "Yi.Yuan"
      ],
      "content_date": "2026-08-04",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1c3257b287ab",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-04",
      "repo": "leanprover-community/mathlib4",
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      "summary": "Erdős Problem 725 asks for an asymptotic formula for the number $L_{k,n}$ of ordered, labelled $k\\times n$ Latin rectangles. Godsil and McKay proved that $L_{k,n}\\sim (n!)^k((n)_k/n^k)^n(1-k/n)^{-n/2}e^{-k/2}$ for $k=o(n^{6/7})$. We provide a partial solution to Erdős Problem 725 by proving this asymptotic for every $k=o(n)$. More precisely, set $\\widetilde A_{k,n}=(n!)^k((n)_k/n^k)^n\\exp\\{[n(H_n-H_{n-k})-k]/2\\}$. For every $K(n)=o(n)$, uniformly for $0\\leq k\\leq K(n)$, we prove $\\log(L_{k,n}/\\widetilde A_{k,n})=O(k^2/n^2)$, with an absolute implied constant. The results of this paper have been formally verified in Lean.",
      "title": "The Godsil--McKay Asymptotic for Latin Rectangles in the Sublinear Range of Erdős Problem 725",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.01671"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.02292",
      "authors": [
        "Mark T. Mac Lean"
      ],
      "content_date": "2026-08-03",
      "freshness": "fresh",
      "id": "arxiv:2608.02292",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-03",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove a new Carnot-scale $n$-step nilpotent $π_1$-de Rham theorem: along every convergent scale sequence, the asymptotic homotopy class of a long trajectory is identified with the nilpotent development of its macroscopic horizontal path. The key analytic mechanism is an asymptotic-development theorem showing that uniform convergence of rescaled horizontal paths, together with a uniform bound on variation, forces uniform, layer-by-layer convergence of their full Carnot-rescaled nilpotent developments. The theorem recovers Schwartzman's theory of asymptotic cycles in step one and the 2-step asymptotic homotopy theory of Benardete and Mitchell in step two, while extending the correspondence to arbitrary nilpotent step.",
      "title": "The Asymptotic Development of Paths on Nilmanifolds",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.02292"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.02530",
      "authors": [
        "Arthur H. D. Nunes",
        "Vinicius M. Gonçalves",
        "Guilherme V. Raffo",
        "Leonardo A. B. Torres",
        "Luciano C. A. Pimenta"
      ],
      "content_date": "2026-08-03",
      "freshness": "fresh",
      "id": "arxiv:2608.02530",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-03",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "In this paper, we propose a new robust navigation framework for path following tasks in robots operating within unknown, cluttered environments. Our approach ensures reactive safety through obstacle avoidance and guaranteed convergence to a target path, while simultaneously mitigating the impact of unknown-but-bounded disturbances using a tube-based control strategy. The methodology integrates key aspects in the robot navigation: (i) a nominal Integrated Guidance and Control scheme for path-following employing Artificial Vector Fields guidance and Backstepping control; (ii) a smooth distance function that enables a continuous control law formulation for seamless obstacle avoidance; (iii) a unified control objective that balances collision avoidance with path-following; and (iv) an adaptive control component to provide robustness against external disturbances. We provide formal proofs of safety and stability using barrier functions and Lyapunov stability theory. The effectiveness of the proposed framework is validated through extensive numerical simulations.",
      "title": "Safe and robust tube-based path-following for robot navigation",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.02530"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.02066",
      "authors": [
        "Akira Toyohara",
        "Ye Tao",
        "Siqiong Yao"
      ],
      "content_date": "2026-08-03",
      "freshness": "fresh",
      "id": "arxiv:2608.02066",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-03",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "No quasiperfect number ($σ(n) = 2n + 1$) is known, and its number of distinct prime factors is bounded below; the bound $ω\\ge 7$ of Hagis--Cohen has stood since 1982, obstructed by a family of ``deep leaves'' on which pure enumeration cannot terminate (the scan bound for the intermediate prime reaches $8 \\times 10^8$, and the exponent dimension is unbounded). This paper clears that obstruction with three lemmas at the level of secondary-school algebra --- a discriminant criterion, a quadratic-residue sieve, and a multilinear resolver --- which eliminate the last prime $q$, the intermediate prime $p$, and the exponent dimension respectively, turning a non-terminating search into a finite decision. On this basis all 381 stems of ``$3 \\mid n$ and $ω= 7$'' and their $79{,}751{,}212$ deep leaves are eliminated, with the ledger closing exactly and zero solutions throughout; the complementary case ``$3 \\nmid n$ and $ω= 7$'' collapses to a single stem, which is eliminated directly, so that the proof does not rest on any theorem whose published record we could not independently re-verify. Together with the machine elimination of $ω\\le 6$ (Theorem B4), this yields the main theorem: \\emph{any quasiperfect number, if one exists, satisfies $ω(n) \\ge 8$} --- the first advance of this bound since Hagis--Cohen 1982. The full computation has been reproduced by seven separately closed ledgers across three algorithmic architectures (CPU and GPU), all with zero solutions and exact ledger closure, and the lemma layer is formalized in Lean (259 theorems, zero \\texttt{sorry}). A 2023 preprint of Zemann reported the same bound by a different computation; our audit of its public code found a coverage gap of 35 feasible exponents, so the elimination given here is, to our knowledge, the first complete proof. Code, ledgers, and Lean sources are available from the authors.",
      "title": "Every quasiperfect number has at least eight distinct prime factors",
      "updated": "2026-08-03",
      "url": "https://arxiv.org/abs/2608.02066"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01393",
      "authors": [
        "Zhipeng Deng"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01393",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "In this paper, we present a general formulation to address the problems of covering curves and polygonal chains with triangle, and fitting these curves into triangle. These problems can be formulated as special cases of Bellman's lost-in-a-forest problem (escaping triangular forest) and Moser's worm problem (covered by triangle). We model and reformulate the problem by keeping the curve stationary while allowing the triangle to translate and rotate. Subsequently, we derive the functional minimization formulation with support function constraints to solve. We also prove the equivalence and convergence of the formulas. Finally, we employ numerical methods and present results for covering curves with arbitrary triangles of various angles. We also present some corollaries and variant results, including closed curves and closed polygonal chains.",
      "title": "Universal Triangle Covering Curve and Polygonal Chain: Escaping Forest and Fitting Worm",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01393"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01514",
      "authors": [
        "Taegyoon Kim",
        "Alexander Furnas",
        "Dashun Wang"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01514",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Policymaking relies on institutions that translate expertise into politically actionable knowledge. Yet little is known about how such knowledge is created, structured, and politically polarized, or how science shapes these processes. Using 2 million U.S. policy documents and nearly 1 million scientific citations from more than 200 think tanks and 100 government organizations, we analyze the supply side of science in policymaking: the production of policy knowledge. We find that think tanks are the dominant suppliers of science-based policy knowledge to government, but that this production has become increasingly politically polarized, driven primarily by growing insularity among left-leaning institutions. We further find that science is linked to lower polarization, as policy documents grounded in scientific evidence, especially those citing high-impact science, are less ideologically segregated and occupy more central positions in policy knowledge networks. These results reveal the potential of scientific expertise to shape and, at times, bridge the ideological landscape of policy knowledge production. Amid rising political polarization and the growing role of science in policymaking, understanding how policy knowledge is produced and how scientific expertise relates to its ideological structure is essential to strengthening the informational foundations of democratic governance.",
      "title": "The Production of Policy Knowledge in the United States",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01514"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.00983",
      "authors": [
        "David Victor Feldman"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.00983",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "An $n$-dimensional subspace of $\\ell^p$ has Plücker coordinates indexed by the $n$-element subsets of $\\N$. We show these coordinates lie in $\\ell^p\\In{n}$ --- the exponent is preserved --- with multilinear norm exactly $1$ for $0<p\\le 2$; for $p>2$ the sharp constant exceeds $1$ and its determination contains the Hadamard maximal determinant problem. A reconstruction lemma shows every nonzero solution of the quadratic Plücker relations in $\\ell^p\\In{n}$ is decomposable with frame in $\\ell^p$; consequently $\\Gr_n(\\ell^p)$ is a closed Banach-analytic submanifold of $\\mathbb{P}\\big(\\ell^p\\In{n}\\big)$ cut out by the Plücker relations alone, with no auxiliary summability condition and no polarization. For mixed sums $\\bigoplus \\ell^{p_i}$ the exterior power is graded by compositions of $n$; the support of the grading is the lattice-point set of a generalized permutohedron determined by the intersection pattern of the subspace with partial sums, this stratification is canonical for the isometry group though not for $\\GL$, and each stratum admits a tubular neighborhood whose normal coordinates are precisely the Plücker blocks vanishing on it. We record what is proved and what is conjectured; the finitary and single-space core of the theory, including full proofs of Cauchy--Binet and Hadamard's inequality, has been formally verified in Lean~4.",
      "title": "Plücker coordinates of finite-dimensional subspaces of $\\ell^p$ and its direct sums: summability, reconstruction, stratification",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.00983"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01277",
      "authors": [
        "Alexander Kolpakov",
        "Igor Rivin"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01277",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "How many knot types can be built from a fixed budget of straight sticks? We prove that the answer has factorial-scale growth, settling its order for the first time. No previously published general upper bound improves on the exponential-in-the-square estimate obtained from crossing-number enumeration; we replace it with a factorial-scale upper bound, which is optimal at the level of growth order. The proof turns polygonal self-intersection into a sparse real-algebraic chamber problem in only linearly many dimensions, while a complementary braid construction supplies factorially many distinct knots. The result creates a direct bridge between knot topology, real algebraic geometry, fewnomial structure, and permutation combinatorics.",
      "title": "Discriminant Varieties for Stick Knots and Links",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01277"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01512",
      "authors": [
        "Orthy Toor",
        "Khandaker Mashiat Rahman",
        "Tonoya Mustafa",
        "Abdullah Bin Shams"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01512",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Prolonged sitting with poor posture results in musculoskeletal injury. Early intervention and prevention methods to monitor posture rely on cameras, wearable devices, and dense pressure arrays. Although effective, these approaches introduce privacy concerns, calibration needs, higher cost, etc. In this paper, we explore the spatial pattern of body contact as a binary posture feature vector for a distinct contact-based sitting posture recognition system without the need for analog signal conditioning and calibration. Our sensing principle uses 10 mechanical contact switches arranged in a 5 x 2 array on the backrest. Each switch encodes local body contact into 10-bit binary posture signatures for four postures: normal sitting, leaning back, leaning left, and leaning right. Decision tree and logistic regression classifiers achieved highest accuracy of 96%. Low correlation amongst the switches indicates that every switch captures complimentary information for successful posture classification. SHAP analysis identified the central contacts as the most informative and significant region for posture discrimination. Our results show that binary contact patterns can capture sufficient spatial information for reliable posture recognition. This sensing strategy offers a simple & low-cost alternative to pressure-based systems to monitor posture without the need for mapping the biomechanical pressure distribution.",
      "title": "Binary Contact Sensing for Sitting Posture Recognition Without Pressure Sensors",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01512"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.01317",
      "authors": [
        "Lin Zhu",
        "Ranyiliu Chen",
        "Xin Wang"
      ],
      "content_date": "2026-08-02",
      "freshness": "fresh",
      "id": "arxiv:2608.01317",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-02",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional with rational coefficients that separates the two measurement models at local dimension two. An explicit three-outcome qubit positive-operator-valued measure with rational matrix entries attains $2\\sqrt2+1/100$. On the other hand, all qubit-projective strategies are bounded by $2\\sqrt2+\\sqrt5/250+\\sqrt2/32400$, giving a fully analytic certified gap greater than $1/1000$. To our knowledge, this is the first fully analytic Bell-functional separation between qubit POVMs and qubit projective measurements over arbitrary shared two-qubit states. Lean certificate for the separation theorem is provided for completeness. Separately, an exact level-3 noncommutative sum-of-squares certificate proves that the explicit qubit strategy attains the unrestricted finite-dimensional tensor-product quantum optimum.",
      "title": "Analytic Qubit Separation between POVMs and Projective Measurements",
      "updated": "2026-08-02",
      "url": "https://arxiv.org/abs/2608.01317"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.00851",
      "authors": [
        "Alexander Meiburg"
      ],
      "content_date": "2026-08-01",
      "freshness": "fresh",
      "id": "arxiv:2608.00851",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-01",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The spectral sensitivity $λ(f)$ of a Boolean function is the largest eigenvalue of the adjacency matrix of its sensitivity graph. It lower-bounds every standard measure of query complexity, and Aaronson, Ben-David, Kothari, Rao and Tal, who introduced it, asked whether block sensitivity is at most quadratic in it: is $bs(f)=O(λ(f)^{2})$? We show that it is not. We construct a total Boolean function on $2017584$ variables with $bs(f)\\ge 14011$ and $λ(f)\\le 89.0162$, so that $bs(f)\\geλ(f)^{2.127}$, and hence by composition a family with $λ(f_n)\\to\\infty$ and $bs(f_n)=Ω(λ(f_n)^{2.127})$. The function is the indicator of a union of $k$ subcubes indexed by the vertices of a doubly regular tournament, and the freedom left in the construction is fixed by the Lovász local lemma. The main result has been formally verified in Lean. We also give numerical evidence that a member of the same family on $1255$ variables reaches an exponent near $2.20$, and exhibit a member on $30$ variables whose exponent already exceeds $2$ and whose spectral sensitivity can be computed exactly.",
      "title": "Block Sensitivity can exceed Spectral Sensitivity Squared",
      "updated": "2026-08-01",
      "url": "https://arxiv.org/abs/2608.00851"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.29681",
      "authors": [
        "Pjotr Buys",
        "Sven Polak",
        "Jeroen Zuiddam"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2607.29681",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-31",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We give new lower bounds for the Shannon capacities of small odd cycles: $Θ(C_7)\\geq3.258805369885\\ldots$, $Θ(C_{11})\\geq5.294502522149\\ldots$, $Θ(C_{13})\\geq6.302455083464\\ldots$, $Θ(C_{15})\\geq7.301600534487\\ldots$, $Θ(C_{19})\\geq9.357192705918\\ldots$, $Θ(C_{21})\\geq10.342455853338\\ldots$, and $Θ(C_{23})\\geq11.328224257774\\ldots$. The bounds are obtained by an iterative procedure due to Gao (2026) which is based on a method by Itty, Rosin, Carstensen and Reichman (2026). The bounds are fully formalised in Lean.",
      "title": "Lean-verified lower bounds for the Shannon capacity of odd cycles",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2607.29681"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.29602",
      "authors": [
        "Jeffrey M. Girard",
        "Jason Z. Zheng",
        "Jacqueline R. Vertino",
        "Antony D'Avirro",
        "Benjamin Peloquin"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2607.29602",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-31",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Reading a social situation often depends on behavior, not words alone. We introduce FriendBench, a benchmark for inferring whether two people are already familiar or are meeting as strangers, from a 20-second clip of a dyadic ice-breaker conversation. Every pair answers the same type of prompt, so only the manner of interaction can reveal the answer. Across text, audio, and video, we compare 26 models from seven companies against matched human panels over 96 balanced dyads. The best model and the human crowd are statistically indistinguishable on accuracy in every modality, but reach it differently: humans stay balanced across the two answers, while the strongest models lean toward \"stranger\"---a difference in effective prior, not discrimination. Richer channels help both unequally, and only humans gain from visible behavior on top of speech. We release the stimuli, human ratings, and model predictions.",
      "title": "FriendBench: Benchmarking Dyadic Familiarity Inference in Humans and Multimodal Large Language Models",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2607.29602"
    },
    {
      "age_days": 4,
      "arxiv_id": "2607.29111",
      "authors": [
        "Damiano Testa"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2607.29111",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-31",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We define a non-unital, generally non-associative, commutative semiring structure on the collection of normal subgroups of a group $G$. This viewpoint allows us to recast in ring-theoretic terms Fitting's classical theorem that the join of two nilpotent normal subgroups is nilpotent. From this perspective, the two key inputs are a binomial expansion in a non-associative setting and the fact that the commutator subgroup of two normal subgroups lies in each factor. The development is formalized in Lean, making essential use of Mathlib for the core definitions and results.",
      "title": "Fitting's Theorem and Semirings of Normal Subgroups",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2607.29111"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.00219",
      "authors": [
        "Louis Davis",
        "Guenther Walther"
      ],
      "content_date": "2026-07-31",
      "freshness": "fresh",
      "id": "arxiv:2608.00219",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-31",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We consider the problem of detecting and localizing a growing number of changepoints in a sequence of independent observations. We propose a new method, Lean Bonferroni Detection - False Discovery Rate (LBD-FDR), which produces a set of localized regions in the data sequence where, in expectation, a high proportion of them contain a changepoint. LBD-FDR guarantees control of the false discovery rate in a wide range of distributional settings, including the challenging case of independent non-parametric and heavy-tailed data. For independent Gaussian sequences, we derive conditions on changepoint arrangements where the method consistently detects all changepoints with a large enough signal while simultaneously being unaffected by those that are undetectable, and we show that LBD-FDR obtains the optimal detection constant in certain regimes. Moreover, we derive the settings where our method is more powerful than the minimax optimal Type I error controlling method. We finally develop a computationally feasible algorithm for the LBD-FDR and compare it in simulation to five existing procedures.",
      "title": "An Optimal False Discovery Rate Controlling Procedure for Changepoint Detection",
      "updated": "2026-07-31",
      "url": "https://arxiv.org/abs/2608.00219"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28332",
      "authors": [
        "Haewoon Kwak"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28332",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "When AI systems surpass elite human performance and settle into everyday expert practice, the question that follows is how machine judgment is made publicly intelligible and attributable. We study Korean Go commentary on YouTube, where AI systems such as KataGo became standard analytic tools after AlphaGo. Our corpus spans a decade (2016--2025) and approximately $1{,}900$ hours of footage across institutional broadcasters and creator-led channels, in four phases of AI availability. We document a widening asymmetry between visual and verbal AI presence: AI winrate graphs are visible for about $98\\%$ of late-period institutional broadcast time, yet AI-salient talk accounts for only $2.63\\%$ of sentences. What recedes is the source label, not the metric: winrate and point-gap talk persists while ``AI'' itself goes unsaid. We read this recession as the communicative signature of domestication. Our strongest evidence is a compositional shift in verbal mediation: explicit naming gives way to interface rendering, and creator-led commentary leans further toward it than institutional commentary. We develop a typology distinguishing source-foregrounding from source-receding mediation, and argue that the two preserve different hooks of contestability: discursive anchors through which audiences can recognize and question the machine source. The stakes of that difference rise in domains where AI is less reliable than in Go.",
      "title": "When AI Becomes Routine: A Decade of Public AI Mediation in Korean Go Commentary",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28332"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28778",
      "authors": [
        "Nils Küchenmeister",
        "Alex Ivliev",
        "Dörthe Arndt",
        "Markus Krötzsch"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28778",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging. Existing methods to stratify negation often fail for RDF rules, since individual triples do not carry enough information to meaningfully restrict potential dependencies. Blank nodes in rule heads further complicate the matter, since the order of rule applications may determine whether new values are created, which in turn can change the applicability of rules with negation. To solve these open problems, we propose chain stratification as a robust new condition that guarantees a well-behaved semantics for RDF rules with negation, and existential rules in general. Our condition combines an elaborate analysis of potential multistep derivations with a mechanism for using integrity constraints to discard impossible cases. Applying rules in any order that respects chain stratification is guaranteed to derive an RDF graph that is unique, lean, and justified under the usual negation-as-failure semantics. To show the practicality, we also provide a prototype implementation.",
      "title": "Stratified Negation in RDF Rules: A Correct Approach (Extended Version)",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28778"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28459",
      "authors": [
        "Pablo Manrique",
        "Stefan Szeider"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28459",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Constraint programming is a core technology for solving complex combinatorial problems in scheduling, planning, configuration, and verification. Trusting its results therefore demands guarantees at two levels: that reformulations applied beforehand are semantics-preserving, and that solvers produce correct answers. In this work, we introduce a framework that addresses both verification levels in the Lean theorem prover: it can be used to prove formulation-level properties, such as equivalence, equisatisfiability, and the correctness of symmetry-breaking constraints, parametrically for entire problem families; and to check solver-produced certificates for individual instances via translation backends to external formats such as MiniZinc, SMT-LIB, and OPB. Combining both levels yields an end-to-end workflow that establishes the satisfiability or unsatisfiability of a constraint problem without trusting the external solver. Experimental results show that our framework's verified symmetry breaking also pays off in practice: a single parametric proof per problem family, reused across all instance sizes, reduces solver search effort by a factor of up to 2x10^7, while the entire in-Lean certification stays affordable, taking at most a few minutes for our largest instances.",
      "title": "LeanCSP: A Framework for Certifying Constraint Reformulation and Solving in Lean",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28459"
    },
    {
      "age_days": 5,
      "arxiv_id": "2607.28133",
      "authors": [
        "John Conlon",
        "Peter Schwardmann"
      ],
      "content_date": "2026-07-30",
      "freshness": "fresh",
      "id": "arxiv:2607.28133",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-30",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We examine whether sycophantic AI advice distorts decisions. Our experiment involves 1,500 participants in 30 decision environments spanning core domains in economics and the social sciences. Contrary to the vast majority of predictions in an expert survey we conduct, we find that AI advice depolarizes choices on average, moving participants away from their initial leanings. This depolarization arises despite the LLM being measurably sycophantic: it disproportionately offers considerations that support users' initial leanings and uses agreeable and flattering language. Depolarization occurs across moral and non-moral, objective and subjective, strategic and non-strategic, and complex and simple tasks. Increasing sycophancy weakens depolarization, showing that sycophancy is behaviorally relevant, even if it is generally outweighed by the informativeness of AI advice. Finally, several results mitigate the concern that market forces will generate greater polarizing effects outside the experiment or in the future. On the supply side, our baseline AI's level of sycophancy is typical of leading models, and these models are not becoming more sycophantic over time. On the demand side, participants do not prefer greater sycophancy, do not select into AI advice in tasks where it is more polarizing, and exhibit greater depolarizing effects when they are more frequent AI users outside the experiment.",
      "title": "AI Sycophancy and Decisions",
      "updated": "2026-07-30",
      "url": "https://arxiv.org/abs/2607.28133"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}