{ "counts": { "adjacent": 12, "core": 1, "errors": 0, "negative": 76, "total": 89 }, "date": "2026-08-07", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-07T16:25:33Z", "items": [ { "age_days": 4, "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": 4, "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": "2026-08-04", "url": "https://arxiv.org/abs/2608.01804" }, { "age_days": 1, "arxiv_id": "2608.06261", "authors": [ "Stefan Dziembowski", "Grzegorz Fabiański", "Daniele Micciancio", "Rafał Stefański" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06261", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We present HOPSCOTCH, a Lean 4 framework for mechanizing computationally sound, game-based cryptographic proofs. Security definitions are expressed as indistinguishability between stateful probabilistic oracles, and proofs follow the standard game-hopping paradigm. HOPSCOTCH uses a shallow embedding: oracles and reductions are ordinary Lean definitions, enabling direct integration with the full Lean ecosystem, including general mathematical theories from Mathlib, such as finite-group theory. A game-hopping proof in HOPSCOTCH is represented as an explicit formal object whose constructors correspond to the standard steps of a game-hopping argument, making proofs easier to construct, automate, and inspect. We prove a general computational soundness theorem that interprets these proof objects by constructing reductions against the assumptions they use and deriving a concrete bound on the advantage of any distinguisher. Observational equivalence between oracles is established using a state-abstraction methodology: a simple yet powerful approach that supports transformations such as adding or forgetting state and replacing eager sampling with lazy sampling. We illustrate the framework with formalized proofs of the IND-CCA security of encrypt-then-MAC, the security of ElGamal encryption from DDH, the implication from one-time secrecy to public-key IND-CPA security, and the GGM pseudorandom-function construction. To the best of our knowledge, the last is the first mechanized proof of GGM for non-constant depth.", "title": "Game Hopping in Lean", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06261" }, { "age_days": 1, "arxiv_id": "2608.06315", "authors": [ "Kevin Morio", "Yavor Ivanov", "Robert Künnemann" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06315", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-08-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Tamarin and ProVerif are two prominent tools for the formal verification of security protocols. They share the same high-level goal but differ significantly in their underlying formalisms and verification techniques, making a systematic comparison challenging: Tamarin uses multiset rewrite rules with sound and complete verification, whereas ProVerif employs an extension of the applied-pi calculus that provides fast but potentially incomplete results. We present a sound translation from Tamarin to ProVerif that enables a rigorous comparison of the two tools. It introduces novel techniques for formula rewriting, encoding multiset rewrite semantics, and handling simultaneous events, supporting an extensive subset of Tamarin's features, including multiset rewrite rules, lemmas, and restrictions, while precisely characterizing the cases where faithful translation is not possible. We provide formal proofs: within the faithful fragment, soundness ensures that any property verified in ProVerif also holds in the original Tamarin model, and completeness ensures that exists-trace properties not involving attacker knowledge are preserved. Best-effort encodings, in particular XOR, are reported separately and are outside these guarantees. Finally, we evaluate our translation on 121 Tamarin models. The translation covers 562 of 566 lemma tasks. Among non-XOR tasks with definitive results from both tools, 246 of 247 agree, with the remaining verdict explicitly flagged as using an incomplete model. Among the 362 tasks for which Tamarin returns a Boolean result and ProVerif completes with a logical result, ProVerif is faster in 334 cases (92.3%), with median per-task runtime and peak-memory ratios of 6.74x and 6.24x, respectively.", "title": "A Sound Translation from Tamarin to ProVerif: Enabling Comparative Analysis", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06315" }, { "age_days": 2, "arxiv_id": "2608.04645", "authors": [ "Bruno Rucy Carneiro Alves de Lima", "Victor Henrique Cabral Pinheiro", "Evgenii Dolzhkov", "Joseph Haske" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04645", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Quantum annealers solve problems by finding the lowest-energy (ground) state of a programmable physical system, a 2-local Ising model, whose energy function is the Hamiltonian. We compile recursive Datalog programs into such models so that the ground state projects onto the program's minimal Herbrand model. The compiler has four stages: binarization, grounding, reduction to a Min-Ones SAT formula, and Ising encoding. Each rule becomes an energy penalty on the one assignment that violates it, and a small uniform cost on every true atom selects the minimal model. We contribute both in theory and in practice with per-stage correctness lemmas and a correspondence theorem, verified in Lean 4, establishing that the ground state of the compiled model projects onto the program's minimal Herbrand model. We map the compiled models onto the topologies of commercial annealers and characterize, under classical and simulated-quantum annealing, whether and when that certified ground state is attained.", "title": "Towards Datalog on Quantum Annealers: Compiling Recursive Logic Programs with Bottom-up Semantics to 2-local Ising Models", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04645" }, { "age_days": 2, "arxiv_id": "2608.04992", "authors": [ "Jaume de Dios Pont", "Karlheinz Gröchenig", "Lukas Liehr", "Irina Shafkulovska", "Mitchell A. Taylor" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04992", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the set of time-frequency shifts $\\{e^{2πi βl t} g(t-αk) : k,l \\in \\mathbb{Z}\\}$ with a continuous, integrable totally positive function $g$ and lattice parameters $α,β>0$ generates a frame for $L^2(\\mathbb{R})$ if and only if $αβ<1$. This fully settles the so-called frame set problem for the class of totally positive functions. As a closely related result we prove a sharp Kadets-type theorem for every shift-invariant space generated by a continuous totally positive function. The proofs are based on Fredholm theory and limit-operator theory. A formalization of our main result in Lean 4 is also provided.", "title": "Gabor Frames of Totally Positive Functions: A Complete Characterization", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04992" }, { "age_days": 2, "arxiv_id": "2608.04457", "authors": [ "Hans-Martin Will", "Allen L. Brown", "Matthew Fuchs" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04457", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "As \"AI Scientists\" emerge to drive research via the Model Context Protocol (MCP), systems relying on ephemeral scripts will fail. The sheer scale of stateful, interconnected evidence requires a machine-walkable warranty grounded in a purpose-built database architecture. Eigenius is an open-source, typed knowledge-graph DBMS built on a single premise: answering the audit question (\"what do you know, and what is your warranty?\") requires a unified kernel. By tightly coupling the type system, storage engine, and integration protocol, Eigenius turns data provenance into a structural invariant rather than a property reconstructed across subsystem boundaries. The kernel rests on three pillars: a dependent type theory woven through the core, institutions acting as strongly typed integration boundaries, and a content-addressed immutable storage layer. On this foundation, epistemic status (declared/observed/derived/verified) is enforced as a strict commit-time invariant. Cross-system translations (comorphisms) are checked at commit and materialized directly into the graph as durable, first-class resources. To eliminate O(N^2) polystore bottlenecks, shared on-chain intermediate representations (IRs) collapse multi-system translations to identity. Crucially, this architecture unifies both domains of scientific epistemology: it relies on justification logic for empirical science, while embedding a fast, in-process term checker to safely evaluate formal mathematical proofs (via Lean 4) without IPC overhead. In an end-to-end recomputation of a published Nature study from fragile scripts to a materialized evidence graph, all 52 derived conclusions hold from pinned data, surfacing four machine-checked discrepancies in the original study.", "title": "Eigenius: A Typed Knowledge-Graph DBMS with Epistemic Stratification and Institution-Mediated Reasoning", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04457" }, { "age_days": 2, "arxiv_id": "2608.05420", "authors": [ "Ahmed Ryan", "Md Erfan", "Akond Ashfaque Ur Rahman", "Md Rayhanur Rahman" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05420", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness. A formal proof checker verifies whether each proof step follows established logical rules. Coq bases its rules on the Calculus of Inductive Constructions, a logical framework that defines which proof steps the system may accept. This pilot study evaluated six open-weight LLMs on the same 100 theorems from CoqStoq, a benchmark derived from real Coq projects. Each LLM received one attempt per theorem with the temperature set to 0, and Coq checked every proposed proof in the theorem's original project environment. We counted a proof as successful only if the Coq kernel accepted it. Gemma 4 verified 12 of 100 theorems, Llama 3.3 verified 8, and DeepSeek Coder V2 Lite verified 1. Qwen 3.5, Mistral Small 3.1, and GPT-OSS verified none. The 21 successful model-theorem results covered 15 distinct theorems, 11 of which were not solved by a baseline of standard Coq tactics. All verified theorems had short or medium human-written reference proofs; no model verified a theorem with a long reference proof. Because the proof-length analysis was exploratory, this pattern does not establish that proof length caused the difference. For the three models with at least one success, the total generation cost per verified proof ranged from 741 to 36,193 output tokens, 14.9 to 178.0 seconds, and 0.0167 to 0.2000 aggregate GPU hours. We could not calculate these ratios for models with no verified proofs. Across 600 attempts, the models produced 21 kernel-verified proofs, giving an overall success rate of 3.5%. The study reports descriptive differences among the models but does not statistically test whether one model outperforms another. Therefore, the results do not establish a universal ranking of the six models.", "title": "Can Open-Weight LLMs Produce Kernel-Verified Coq Proofs? A Pilot Study", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05420" }, { "age_days": 3, "arxiv_id": "2608.04228", "authors": [ "Arthur Freitas Ramos", "Ruy J. G. B. de Queiroz", "Anjolina Grisi de Oliveira", "Tiago M. L. de Veras" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.04228", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-04", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Computational paths record equality as explicit finite traces of primitive steps. We give a topological semantics for a scoped rewrite presentation whose steps have continuous geometric realizations and whose named rewrites carry endpoint-fixed homotopies. For every presentation we construct a quotient arrow space with a canonical final-domain groupoid structure: multiplication is continuous on the quotient of explicitly composable representatives. We prove an exact four-way criterion for this final composable topology to agree with the ordinary pullback topology, together with a compact-Hausdorff sufficient condition. Thus the unconditional construction exposes, rather than hides, the product-quotient issue in ordinary topological groupoids. The realization map to geometric homotopy classes is a continuous groupoid morphism and is faithful exactly under a separate geometric-completeness condition. In the universal presentation, a continuous section identifies the coherent-path quotient homeomorphically with the usual quotient-topologized fundamental groupoid. We then give finite-generator circle and genuine torus examples, with winding-based normal forms and classifications by Z and Z^2. A Lean 4.24.0 development checks the theorem package; the mathematical presentation is independent of the implementation.", "title": "Topological Semantics for Scoped Computational Paths", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.04228" }, { "age_days": 5, "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": 3, "arxiv_id": "2608.03327", "authors": [ "Siqi Fan", "Minghao Li", "Xiaoqian Ma", "Wenhui Tan", "Xiusheng Huang", "Juntong Wu", "Liujie Zhang", "Shuo Shang", "Weihang Chen" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.03327", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation", "tool_use_agents" ], "published": "2026-08-04", "score": 3.3, "source": "arxiv-ai4math-core", "summary": "Hybrid computer-use agents can act through screenshots or call text tools. We find that having a tool available does not settle which way the effect goes. Under one identical GUI-MCP harness on the OSWorld-MCP benchmark (309 tasks), the same MCP tools improve a reasoning model by +4.0pp and degrade a non-reasoning model by -5.9pp (5 runs each, both beyond 2 SE). What separates the two is tool-decision behavior. The non-reasoning policy ignores, misnames, or falsely terminates around tools. The reasoning model avoids these failures, yet still calls a tool on only 55/309 tasks, 23.9% of the tool-reachable ones. We call this shortfall the adoption gap. Both levels of the problem share one cause: the model already has a cheaper route and is never trained to take it. Multi-turn RL probes that cause. At the action level, a dense tool bonus raises spreadsheet adoption 0.03 -> 0.33 and carries into greedy decoding, but held-out accuracy does not follow. Behavior is steerable; competence is not. The bottleneck lies in tool-call semantics. At the context level, a successful tool call often makes the next screenshot redundant. Dropping it and halving image history cuts input tokens by about a third, at a small accuracy cost. Retraining under the same observation rule removes that cost. The compressed agent then reaches 37.8% against 33.0% for the uncompressed operating point, at 53% of the input cost, and closes the rich-lean gap on a pre-registered degraded subset to zero. Tools help when the model chooses and integrates them, and current hybrid agents leave many such choices unused. Code and checkpoints: https://github.com/redai-infra/hybrid-routing-agent", "title": "Screenshots or Tools? Eliciting Tool Use and Managing Multimodal Context in Hybrid GUI-MCP Computer-Use Agents", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.03327" }, { "age_days": 1, "arxiv_id": "2608.05480", "authors": [ "Kenny Lau", "Ken Ono" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.05480", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-06", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "For coprime $1` (#42416)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/ac10dc7e9a3d44afd90aaeab0b5246310ac3c787" }, { "age_days": 0, "authors": [ "Rao Xiaojia" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:50a1a3609f97", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Matrix): add echelon form decomposition certificate structure (#42525)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/50a1a3609f97d1a965d8eaba5088d846dab11dce" }, { "age_days": 0, "authors": [ "Yi.Yuan" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:39122a64484c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Complex): generalize harmonic mean value properties to Banach-valued functions (#42328)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/39122a64484ce32b5fdb6f005e5c2da61773e225" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:38c06cd7f351", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: make arguments explicit in `nonempty_of_nonempty_constants` (#42508)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/38c06cd7f3512c1a75917dd29ed435b7bdfa67cf" }, { "age_days": 0, "authors": [ "damiano" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fcdfe229949f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add missing `to_additive` docstrings in MeasureTheory.Group (#41639)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/fcdfe229949f10f534f4627c2c8035d77406f8fa" }, { "age_days": 0, "authors": [ "damiano" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:daa38bd533b3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add missing `to_additive` docstrings in Combinatorics and Dynamics (#41645)", "updated": "2026-08-07", "url": "https://github.com/leanprover-community/mathlib4/commit/daa38bd533b3d7661a1d44f8cc9c904306b335e9" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover/lean4:4a37393b74d1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: add code quality mode to `lake lint` (#14622)", "updated": "2026-08-06", "url": "https://github.com/leanprover/lean4/commit/4a37393b74d177d5e32f06cfd097ff6eb9f507b8" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover/lean4:ddc2f3345704", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: accept match alternatives in an `ensures` clause (#14701)", "updated": "2026-08-06", "url": "https://github.com/leanprover/lean4/commit/ddc2f33457048b96700ac50ac4badf818fc50763" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e506e4611dd4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf(SimpleGraph/Walk/Operations): avoid costly `grind` in `drop_drop` (#42479)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/e506e4611dd4a29e4e045f676a822bd314056e72" }, { "age_days": 1, "authors": [ "Hannah Scholz" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5c483963eff2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: composition lemmas about `mvfderiv` and `mvfderivWithin` (#42478)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/5c483963eff2f5f632b8e5a3f12887ad708b357e" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4a20a0e0d8a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: `Nat.add_div_le_div_add_div_add_one` (#42481)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/f4a20a0e0d8a29d2421fd9d042efe34d920f50c0" }, { "age_days": 1, "authors": [ "Stefan Kebekus" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:92f866971c22", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: API for logarithmic derivatives of meromorphic functions (#41684)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/92f866971c22d14420e745016d5b6e22af9c4279" }, { "age_days": 1, "authors": [ "Gian Sanjaya" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6064d46fbaaa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Nat/ModEq): add a new congruence to divisibility lemma (#42230)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/6064d46fbaaac6e10ba9a3046b1630ce415017ef" }, { "age_days": 1, "authors": [ "Moritz Doll" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:046187e5bbad", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis): the inverse fourier transform from L1 to BCF (#42427)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/046187e5bbad80fe0429eecbe033946fe5b00903" }, { "age_days": 1, "authors": [ "Stefan Kebekus" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1aa85dfb910a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: update docstring in Cartan.lean (#42486)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/1aa85dfb910a0fedb00c60eb8768ee5f781c855d" }, { "age_days": 1, "authors": [ "Kim Morrison" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1f0fbd1ad9ff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: use uniqueDiffOn_uIcc at existing call sites (#41576)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/1f0fbd1ad9ff6e4751ab4564fc70cc4f2a1fadf9" }, { "age_days": 1, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7a1f8433f115", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-08-06 (#42484)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/7a1f8433f11599aee71a0dcb0fc6277c4495f82e" }, { "age_days": 1, "authors": [ "Noah Walker" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bf6473c670ff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename some lemmas containing `not_unit` (#42386)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/bf6473c670ffb5e8c347f90881f0eebbbb3d4ec3" }, { "age_days": 1, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0e98674e03da", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: golf `exists_wellFoundedGT` (#42368)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/0e98674e03da6696b2d8036cf608b2a428bffac4" }, { "age_days": 1, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:944508abf268", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: golf `IsSupClosedCompact.wellFoundedGT` (#42422)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/944508abf2681c73ca4a6618fe3bcea94ad03c98" }, { "age_days": 1, "authors": [ "TJHeeringa" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e900b0260138", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: deprecate apply_eq_iff_eq_symm_apply (#42094)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/e900b02601380aeb32841cbfe68d868bb0c0c59c" }, { "age_days": 1, "authors": [ "damiano" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b7ca352dd16d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add missing `to_additive` docstrings (Normed, TransferInstance) (#41647)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/b7ca352dd16d2d28b9c8f45b0af96f6da5c23106" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f6dc05e369aa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Topology/UniformSpace): rename `complete_univ` to `isComplete_univ` (#42163)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/f6dc05e369aa1c3b6a70f416c4b299cf26e9dd38" }, { "age_days": 1, "authors": [ "Noah Walker" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5edf93c0f3d1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory): fix left/right convention on `Ideal.mul_le_{left,right}` (#42112)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/5edf93c0f3d1f3d509c42c888931b49be5c06816" }, { "age_days": 1, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7bd8067d23d8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/Bounds/Basic): use `to_dual` more (#42362)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/7bd8067d23d893d876aa24274d595be9ba72dfa1" }, { "age_days": 1, "authors": [ "Fabrizio Barroero" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3c2d12d66f72", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(NumberTheory/Ostrowski): simplify and golf proofs (#42183)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/3c2d12d66f728a5a247a127559909d65e8e0988a" }, { "age_days": 1, "authors": [ "damiano" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ce1cc649d9e5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CI): keep the previous Lean declarations diff visible while a new build runs (#40486)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/ce1cc649d9e549333943c5cc18bbf1af5030635c" }, { "age_days": 1, "authors": [ "Moritz Doll" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:df0e56f998cb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Analysis/Seminorm): generalize `smul_le_smul` to arbitrary scalar multiplication (#42294)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/df0e56f998cbd44160a55f013bef8c30755e0885" }, { "age_days": 1, "authors": [ "Kevin Buzzard" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:640b05473b7b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Group/Action/Opposite): fix copy-paste error in +ᵥ> docstring (#42460)", "updated": "2026-08-06", "url": "https://github.com/leanprover-community/mathlib4/commit/640b05473b7bdf75970ec4c175b6915d3d8e60cf" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:e5a38df11cfe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: stack with an allocator in the vcgen separation logic demo (#14685)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/e5a38df11cfe1e806b9f57b65b338117c33ed33e" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:42a1d764b587", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: in-place append with a ramified spec in the vcgen separation logic demo (#14614)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/42a1d764b58761bdda1a175625d4e9dd8e998d9a" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:4c29de6f2cb9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use after free in String.extract for gigantic slices (#14687)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/4c29de6f2cb93ffdabd2838c1eed6f55061bb605" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:c4e6b62c3d95", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: support for assigned mvars at `SymM` discr trees (#14694)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/c4e6b62c3d955ef20da94310797072f7c4c5fa2b" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:16fafca7fe94", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: support for `Expr.mdata` at `SymM` matcher (#14691)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/16fafca7fe94ea23edc0ddab9bb2f98f603df7d5" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:6c50efd414df", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep type ascriptions on contract clause binders (#14686)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/6c50efd414dff04789a802cefc395fadbc549ac8" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:82a131b1d1b2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support a destructuring binder on a `for … invariant` loop (#14682)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/82a131b1d1b283a02177d6854129b17126487a73" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:752b791c31a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: make `bv_decide`'s embedded constraints pass more aggressive (#14683)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/752b791c31a7db7433b2b5bb1b0485ac8a5f10c5" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:3a47eb5d460a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: allow users to supply complex types to `bv_decide` (#14681)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/3a47eb5d460ad54cf95af088042615d3ee8a6dd2" }, { "age_days": 3, "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": 3, "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": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "github:leanprover/lean4:f2bcf2e8660a", "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: one loop-invariant spec for every effect-free `ForIn` container (#14596)", "updated": "2026-08-04", "url": "https://github.com/leanprover/lean4/commit/f2bcf2e8660ab2d16cf3cb50c8e127de0439a337" }, { "age_days": 3, "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": 4, "authors": [ "Henrik Böving" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:a2294bb6deef", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: port bv_decide to SymM (#14215)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/a2294bb6deef5984c971cfcc4f3ef0a38bf3349c" }, { "age_days": 4, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:945e78b86645", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: lake: `builtin-lint` has a `Mode` flag (#14617)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/945e78b86645b179655123cd2fdba83d89d28d07" }, { "age_days": 4, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:41dfb4d1563b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: keep the deletion worklist in a register in `lean_dec_ref_cold` (#14660)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/41dfb4d1563b0df66a8a12dd6047793095239b66" }, { "age_days": 4, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:0bae3215657e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: fold `UInt*.ofNatLT` applied to literals (#14662)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/0bae3215657e2f99e2b7e7bf976fa439e0861b81" }, { "age_days": 4, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:6ce2149e7865", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `mkTheoremFromDecl` from `SymM` (#14664)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/6ce2149e786585ec5ac65b0930c2646702b7c2a3" }, { "age_days": 4, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:58408f99cb2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/58408f99cb2b6cdd72be94b5fbc26881e49502dc" }, { "age_days": 5, "authors": [ "Kim Morrison" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:f1053b60be68", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: replace grind proofs in Vector.Algebra (#14644)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/f1053b60be68ce3149109206989f04eedb5d2239" }, { "age_days": 5, "authors": [ "Jacob Reinhold" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:cdd822aebc52", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: report a missing library root file (#14625)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/cdd822aebc524d97456a21bda1f4724bf9da05e5" }, { "age_days": 5, "authors": [ "Mac Malone" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:0ccd6f74fc3d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: gracefully handle curl and IO errors during transfer (#14651)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/0ccd6f74fc3d6471d7c2c91bbd3cf2a252113590" }, { "age_days": 5, "authors": [ "Sankalp Thakur" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:110db9cb751a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: elide redundant \"Lean exited with code 1\" after diagnostics (#14629)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/110db9cb751afaee8b2ac344887d6c7e632f77b4" }, { "age_days": 6, "authors": [ "Sankalp Thakur" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:05a6ddfb52c0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: error on unknown package names in `lake update` (#14630)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/05a6ddfb52c033f12967c96443a93b0ca7b8a58a" }, { "age_days": 1, "arxiv_id": "2608.05863", "authors": [ "Fanzhe Wei", "Li Liu", "Ziyang Wang", "Chenyu Wang" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.05863", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Modern models no longer keep a plain KV cache: latent caches, learned sparse selectors and recurrent states each carry the model's memory in a different form, and each fails differently under compression. We give a runtime observability contract that covers all four memory classes with three operators, instantiate it on six model configurations across five architecture families, and compose the per-stage bounds into an executable request-level risk ledger. Contracts carry their error metric as a type -- composition is only defined when metrics match, and this check rejected our own first composed chain; the repaired chain crosses metrics through two proved bridges, and whatever no formal system can certify is measured instead, dropping the composed tier to empirical automatically: every claim is certified, partially certified, or empirical, composition inherits the weakest tier, and the tier is decided by the machine. Replayed over $12.4$M entry reads and run under eight-way concurrency with per-request budgets and fail-closed identity attribution, the ledger quantifies the honest trade-off on today's witness and holds its risk budget with zero violations. A fused always-on probe observes a declared one-layer subset under CUDA graphs inside the serving noise floor. Applied to a served DeepSeek-V4 stack with a packed compressed-KV prototype, the same machinery localizes a silent corruption to a precise structural boundary -- exact in the eviction-free, identity-isolated regime, with every observed failure in an eviction or slot-reuse regime -- through a machine-adjudicated discrimination campaign whose calculus rejected two of our own confounded inferences along the way. All artifacts, guards, and the Lean development are released at https://github.com/metask-ai/witprobe-attention-memory; every number in this paper regenerates from the shipped artifacts by one command.", "title": "Runtime Observability for Heterogeneous Attention Memory", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.05863" }, { "age_days": 1, "arxiv_id": "2608.06235", "authors": [ "Zhi Li", "Xiaofei Shi" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06235", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "To probe a bipartite quantum system, one may use arbitrary global operators or restrict to product operators acting separately on the two subsystems. We determine the sharp universal comparison between the resulting norms. For every $z\\in M_n\\otimes M_m$, we prove $\\|z\\|_1\\leq\\sqrt{2}\\min\\{n,m\\}\\|z\\|_\\varepsilon$, where $\\|\\cdot\\|_1$ is the trace norm and $\\|\\cdot\\|_\\varepsilon$ is the injective tensor norm associated with the trace norms on $M_n$ and $M_m$. To prove the upper bound, we establish an $L_1$ noncommutative Khintchine inequality whose random coefficients are the entries of a Haar unitary. We also show that the coefficient $\\sqrt{2}$ is sharp. As applications, we show that the same sharp constant governs the gap between bipartite correlation measured in trace norm and that measured by a correlation function, and obtain an improved universal upper bound for quantum data hiding. The upper bound has also been formalized and machine-checked in Lean.", "title": "Global vs. Product Observables in Bipartite Quantum Systems: The Sharp Bound", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06235" }, { "age_days": 2, "arxiv_id": "2608.05451", "authors": [ "Zhengyao Lin", "Yi Cai", "Milijana Surbatovich" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05451", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Dataflow architectures have gained renewed interest due to their balance between power efficiency and performance. In (spatial) dataflow architectures, a program is represented as a set of entirely distributed and dynamically scheduled dataflow operators that communicate through asynchronous channels, which greatly improves data locality and parallelism. However, compiling to dataflow architectures remains an error-prone process, in order to maintain determinacy while enabling pipelining. Determinacy means that the result of a dataflow program is deterministic and independent of the schedule of operator execution, and pipelining is an important optimization in spatial dataflow that enables parallelism across loop iterations. In this work, we present Wavelet, the first effort to formally verify a compiler for asynchronous dataflow. We use a mix of techniques to achieve this goal. Our frontend uses a novel capability type system with fences to synchronize conflicting memory accesses and enable pipelining. We then verify a Lean formalization of two core passes of our compiler that translates elaborated programs from the type checker to dataflow graphs, proving important properties of forward simulation and determinacy. Notably, our formalization semantically propagates the soundness guarantees of the frontend type system, ensuring modularity between simulation and determinacy proofs. In evaluation, we show that dataflow graphs compiled by Wavelet have comparable sizes to those produced by an unverified optimizing compiler for the RipTide spatial dataflow architecture.", "title": "Let it Flow: A Formally Verified Compilation Framework for Asynchronous Dataflow", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05451" }, { "age_days": 2, "arxiv_id": "2608.05075", "authors": [ "Peer Saleth", "Segun T. Aroyehun", "Fabio Carrella", "Christoph M. Abels", "Stephan Lewandowsky", "David Garcia" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05075", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The spread of misinformation is widely perceived as a threat to democratic deliberation, yet how political elites' rhetorical commitments to truth shift alongside the rise of populist actors remains poorly understood. Analysing 4.5 million tweets and 59,170 parliamentary speeches by German political elites between 2015 and 2025, we measure evidence-based and intuition-based rhetoric using a validated distributed dictionary representation. Across both arenas, intuition-based language has become more prominent, and right-leaning actors consistently exhibit the lowest Evidence Minus Intuition (EMI) scores. The parliamentary entry of the extreme-right Alternative for Germany (AfD) in 2017 coincides with sharp downward shifts in EMI across the broader chamber, while a more gradual decline is observed on Twitter. These findings document an association between far-right visibility and a changing approach to truth in elite discourse in a multiparty European democracy.", "title": "German parties shifted towards intuition-based rhetoric after the far right's parliamentary breakthrough", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05075" }, { "age_days": 2, "arxiv_id": "2608.04516", "authors": [ "David Victor Feldman" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04516", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Given finitely many compact convex bodies in $\\R^n$, one seeks translates maximizing the volume of their common intersection. A lazy solver merely translates each body so as to place its centroid at the origin. We prove that the lazy strategy always captures strictly more than $\\left(\\tfrac{2}{n+1}\\right)^n$ of the optimal volume, and that this constant is sharp: families of cones over tangent disks, indexed by finite nets on the sphere, approach it. The infimum is not attained. For two convex bodies in the plane the resulting sharp constant $4/9$ closes a gap open since 1996, when de Berg, Cheong, Devillers, van Kreveld and Teillaud proved that centroid alignment of two convex polygons captures at least $9/25$ of the maximum overlap and exhibited examples capturing only $4/9$. The proof rests on the following identity: for a convex body $K$ with centroid at the origin, the intersection of all centroid-recentered compact convex supersets of $K$ equals $\\tfrac{1}{n+1}(K-K)$. We close with a promise-problem variant in which the lazy strategy captures at least $\\left(\\tfrac{n}{n+1}\\right)^n > \\tfrac1e$ of the optimum, uniformly in the dimension. All results below have been checked in Lean~4; the one classical input quoted rather than proved is the equality case of the Brunn--Minkowski inequality, which enters only for $n\\ge2$.", "title": "Arranging convex bodies for maximum intersection volume: the sharp efficiency of centroid alignment", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04516" }, { "age_days": 2, "arxiv_id": "2608.05142", "authors": [ "Michal Mogielnicki", "Ken Ono", "Niels Voss", "Jujian Zhang" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05142", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In 2016, Berkovich and Uncu proved that, for all nonnegative integers $i$, $j$, and $n$, the number of strict partitions of $n$ with $i$ odd-indexed odd parts and $j$ even-indexed odd parts equals the number of strict partitions of $n$ with $i$ parts congruent to $1$ modulo $4$ and $j$ parts congruent to $3$ modulo $4$. Their proof used generating functions, and they asked for a combinatorial proof. We answer their question with an explicit bijection, assembled from three classical ingredients: $2$-modular diagrams, an insertion algorithm of Chen, Gao, Ji, and Li, and Glaisher's bijection. AxiomProver autonomously formalized and verified the proof of the main theorem in Lean.", "title": "A bijective proof of a partition theorem of Berkovich and Uncu", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05142" }, { "age_days": 3, "arxiv_id": "2608.03803", "authors": [ "Tomáš Burkert", "Angelika Peljak-Łapińska", "David Zelený" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.03803", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Multilingual language models are deployed across a hundred or more languages, yet most benchmarks test whether a model can perform a task _in_ a language rather than whether it commands the language itself, conflating fluency with proficiency. We introduce M-GATE (Multilingual Grammar, Accuracy in Translation, and Efficiency), a benchmark of linguistic proficiency spanning 30 typologically diverse languages from high- to low-resource. M-GATE comprises three tasks: grammatical error detection on linguist-crafted, adversarially selected sentences that turn on hard, language-specific phenomena; round-trip translation of shared English sources across 29 target languages, scored by a three-provider LLM judge panel validated against professional annotators; and a supplementary tokenizer-efficiency measure. We evaluate over 50 models in more than 80 configurations. Fluency and proficiency come apart sharply: models that translate competently sit near chance on the adversarial grammar items, the best reaching a Matthews correlation coefficient (MCC) of only 0.36, and their errors lean systematically toward under-flagging, accepting ungrammatical text rather than raising false alarms. Translation quality closely tracks a language's share of pretraining data (r = 0.86 against log Common Crawl share), producing a steep low-resource penalty that is nonetheless narrowing with successive model releases. Enabling reasoning reliably improves translation, while its effect on error detection is smaller and for some models negative, so the best configuration is task-dependent. To resist contamination, test items are kept private behind a continuously updated public leaderboard, with illustrative examples released (https://m-gate.ai).", "title": "M-GATE: Multilingual Grammar, Accuracy in Translation, and Efficiency Benchmark for Large Language Models", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.03803" }, { "age_days": 3, "arxiv_id": "2608.02970", "authors": [ "Richie Sater" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.02970", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove that every finite group that is the product of every pair of its non-conjugate maximal subgroups is soluble, answering Problem 10.34 of the Kourovka Notebook (V. S. Monakhov, 1986) in the negative. Tikhonenko and Tyutyanov settled the almost simple case in 2010. What remains is the possibility of a minimal counterexample whose unique minimal normal subgroup is S^k, with S non-abelian simple and k >= 2. Because k is unbounded, no bound depending on a fixed ratio of subgroup orders can handle all such groups. We rule out this possibility with a divisibility criterion: a single pair of automorphism-stable conjugacy classes of subgroups of S, satisfying a valuation inequality, excludes the configuration for every k >= 2 and every admissible embedding. Such pairs are constructed uniformly for every infinite family of finite simple groups, with Zsigmondy primes as the arithmetic obstruction. The sporadic groups and the finitely many exceptional cases are handled by independently checkable GAP certificates.", "title": "Finite groups that are the product of every pair of non-conjugate maximal subgroups are soluble", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.02970" }, { "age_days": 3, "arxiv_id": "2608.04061", "authors": [ "Carl Dickinson", "Gaetano Di Caterina" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.04061", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Utility poles are an essential part of the infrastructure used to support power distribution systems and other critical public services. Their regular inspection is crucial to ensure the stability and safety of the electrical grid. A deep learning framework is presented for the automated detection, segmentation and lean angle estimation of wooden utility poles, and classification of attached electrical warning signs, using ground-level imagery. The system is trained on a custom dataset of 4,570 annotated images extracted from Google Street View, featuring challenging real-world scenes with visually ambiguous wooden poles lacking distinctive features. The proposed model is based on the Detection Transformer (DETR), suitably modified and trained on the custom dataset. The model outperforms standard object detectors (RetinaNet, Faster R-CNN, YOLOv3-Tiny), achieving a mean average precision of 90.43% for pole detection and 88.26% for sign detection. Extending this model with a segmentation head enables per-instance mask generation, which is then used to estimate pole lean angle. The model accurately estimates lean for 1,367 out of 1,433 test-set poles, with a mean absolute error of 1.01 degrees. Moreover, the custom dataset created in this work is also made publicly available to be used as a benchmark.", "title": "Advancing Utility Pole and Sign Detection Through Deep Learning", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.04061" }, { "age_days": 4, "arxiv_id": "2608.01671", "authors": [ "Eric Li" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "arxiv:2608.01671", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-03", "score": 0.5, "source": "arxiv-ai4math-core", "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": 4, "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": 4, "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": 4, "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": 5, "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": "2026-08-05", "url": "https://arxiv.org/abs/2608.01393" }, { "age_days": 5, "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": 5, "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": 5, "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" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }