{ "counts": { "adjacent": 17, "core": 2, "errors": 0, "negative": 71, "total": 90 }, "date": "2026-07-23", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-23T16:59:42Z", "items": [ { "age_days": 5, "arxiv_id": "2607.16855", "authors": [ "Hongqin Lyu", "Junxing Dong", "Yonghao Wang", "Zhiteng Chao", "Tiancheng Wang", "Huawei Li" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "arxiv:2607.16855", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-18", "score": 9.5, "source": "arxiv-ai4math-core", "summary": "Formal verification with interactive theorem provers can provide strong correctness guarantees for register transfer level designs, but applying it to existing SystemVerilog code requires substantial manual effort in semantic modeling and proof construction. This paper presents Rtl2lean, a framework that automatically translates RTL designs into executable Lean 4 models and builds a hierarchical theorem library for subsequent verification. The generated model represents hardware execution as a pure state transition function, while a four layer theorem framework captures combinational semantics, sequential updates, single cycle behavior, and reachability and invariants. When a high level property cannot be discharged by the existing theorem base, an LLM based proving loop proposes intermediate lemmas from the current proof context and Lean feedback. Only lemmas accepted by the Lean kernel are added to the reusable lemma pool. Experiments on six SystemVerilog designs generate 403 theorems, all of which are successfully checked by Lean. Among 358 foundational lemmas, 287 are available for automatic reuse, yielding a reusable lemma ratio of 80.2 percent. The results demonstrate that Rtl2lean can construct machine checked RTL proof libraries with low checking overhead and substantial cross property lemma reuse.", "title": "Rtl2lean: Automated RTL-to-Lean Translation with Hierarchical Theorem Generation and Lemma Reuse", "updated": "2026-07-18", "url": "https://arxiv.org/abs/2607.16855" }, { "age_days": 4, "arxiv_id": "2607.17352", "authors": [ "Yuqing Li", "Zeguan Wu", "Yu Gan", "Junyu Liu" ], "content_date": "2026-07-19", "freshness": "fresh", "id": "arxiv:2607.17352", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-07-19", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Designing effective Lean proof agents is a central challenge in formal mathematical reasoning. Beyond building stronger provers, recent work emphasizes the workflow around Lean: how an agent decomposes proof obligations, uses tools and compiler feedback, diagnoses failures, repairs proofs, and maintains structured proof context. Motivated by code-level self-evolving agents, we study whether such workflows can be evolved rather than hand-designed. We present a self-evolving Lean proof agent in which a small fixed, trusted runtime wraps a fully mutable workspace: the proof workflow, prompts, and tools. Unlike most self-evolving systems, which optimize against a fixed external benchmark, our system coevolves the agent and its benchmark. Between generations, the highest-scoring agent (the champion) revises the active task distribution through a mastery-throttled curriculum update that introduces harder proof obligations only after the current level is mastered, and a single-anchor recalibration re-runs the champion on the updated benchmark to keep scores comparable as difficulty rises. All evolution stays inside a Lean-grounded verification loop: however the agent rewrites itself, a success counts only when its behavior yields Lean-verified proofs under a trusted snapshot, and each attempt must emit a machine-readable, Lean-grounded proof context whose representation may evolve but whose groundedness is enforced. We run the coevolving trajectory and a fixed-benchmark baseline for 15 active generations and compare them on a held-out miniF2F test split. The best coevolving agent reaches a 45.1% held-out solve rate, versus 12.7% for the seed and 32.0% for the best fixed-benchmark agent, showing that verifier-grounded self-evolution can improve Lean proof workflows under a coevolving benchmark.", "title": "Self-Modifying Lean Proof Agents with Verifier-Grounded Benchmark Coevolution", "updated": "2026-07-19", "url": "https://arxiv.org/abs/2607.17352" }, { "age_days": 2, "arxiv_id": "2607.19129", "authors": [ "Sara Giordano", "Miguel A. Martin-Delgado" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.19129", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-21", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We present a rigorous perturbative analysis of the Szegedy quantum walk search algorithm on the complete graph with marked nodes, when a specific anomaly is present in the graph. This is motivated by the problem of monitoring the integrity of dense trusted communication networks with a quantum-assisted procedure. The topology of these networks is modeled as a complete graph, and the anomaly of interest is the disappearance of a single communication link which represents the minimal and spectrally hardest structural defect to detect. Building on the graph-completeness testing algorithm framework, we quantify how the removal of a single unmarked-unmarked edge propagates through the relevant spectral quantities of the Szegedy quantum walk. Denoting by $n$ the total number of nodes of the graph and by $m$ the number of marked nodes, we prove that the perturbation to the transition matrix has spectral norm $Θ(1/n)$, and that the gap eigenvalue undergoes a strictly negative first-order shift for every $n$ and every number of marked nodes $m$, providing a formal proof of a conjecture from our completeness testing algorithm work; in the regime $m = Θ(n)$ relevant for the search algorithm, this shift has magnitude $Θ(1/n^2)$. The corresponding eigenphase shift satisfies $Δθ_\\star = Θ(1/n^2)$ in the same regime. We establish that the rotation angle of the effective subspace under this perturbation is $O(1/n)$ for $m = Θ(n)$. Finally, we bound the change in success probability to $O(1/\\sqrt{n})$ in this same regime of marked nodes, and show that this bound is dominated by the geometric misalignment of the effective subspace rather than by the spectral shift of the eigenphase. These results provide both the theoretical foundations and the fundamental scaling limits of quantum walk-based topology integrity monitoring under minimal structural perturbations.", "title": "Single Link Removal Perturbation in Szegedy Quantum Walk: from Graph Completeness Testing to Integrity Monitoring", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.19129" }, { "age_days": 6, "arxiv_id": "2607.16171", "authors": [ "Jun Liu", "Maxwell Fitzsimmons" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.16171", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-17", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a planar homogeneous cubic polynomial vector field with integer coefficients. It admits no positive definite homogeneous polynomial with nonpositive Lie derivative and, more strongly, no real-analytic Lyapunov function even locally. Nevertheless, it has an explicit degree-two homogeneous Lyapunov function that is radially unbounded, continuously differentiable everywhere, and smooth away from the origin. We also provide a machine-checked Lean 4 formalization of the main result.", "title": "A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.16171" }, { "age_days": 1, "arxiv_id": "2607.20418", "authors": [ "Jack Fitzsimons" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20418", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Nikolov and Ullman asked whether k statistical queries on a universe of size T can be released under pure differential privacy with expected worst-coordinate error at the square-root rate suggested by known lower bounds. We prove their conjectured upper bound. For every database size n and privacy parameter $\\varepsilon>0$, there is an $\\varepsilon$-differentially private mechanism with expected error $O(\\min\\{1,\\sqrt{\\log(2T)\\log(2k)/(\\varepsilon n)}\\})$. This matches the lower-bound dependence in the standard high-dimensional regimes where those bounds apply; the shifted logarithms and outer minimum make the upper bound valid without additional parameter assumptions. The construction starts from a selection-only private multiplicative weights transcript, then replaces its probability mass function by a distance-penalized likelihood envelope. To prove that the modification preserves accuracy, a likelihood-level Maurey argument upper-bounds each Hamming-ball maximum by a small family of auxiliary PMW laws. Renyi moment bounds control nearby balls, a direct mixture bound controls distant balls, and grouping radii at the privacy scale prevents an additional $1/\\varepsilon$ factor in the error. The mechanism is information-theoretic. A companion Lean 4 development machine-checks the finite construction, pure privacy after deterministic decoding, and the displayed all-regimes upper bound.", "title": "Pure-DP Statistical Query Release at the Conjectured Square-Root Rate", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20418" }, { "age_days": 1, "arxiv_id": "2607.20186", "authors": [ "Lorenzo Saraiva", "Edward Hermann Haeusler" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20186", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In this article, we present a method for encoding Dag-Like Derivability Structures (DLDS), obtained via horizontal compression of Natural Deduction proofs in purely implicational minimal logic, as Boolean circuits. These DLDS compress Natural Deduction tree-like proofs into directed acyclic graphs, preserving logical correctness while reducing redundancy. We formally define the circuit construction process and establish its pointwise correctness, showing that, for any fixed path assignment, the resulting Boolean circuit agrees with the intended dependency-propagation semantics. A Lean formalization establishes machine-checked guarantees for the circuit evaluator and includes a restricted bridge for the uncompressed simple-tree fragment, connecting valid DLDS instances in that fragment to genuine circuit acceptance of their extracted paths under the route and discharge conditions formalized in Lean. This approach opens new perspectives for automated theorem proving and formal certification.", "title": "From Dag-Like Proofs to Boolean Circuits in Lean", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20186" }, { "age_days": 1, "arxiv_id": "2607.20188", "authors": [ "Sebastián Urciuoli" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20188", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In this paper we continue assessing the feasibility of the approach to the mechanization of type theory by using classical syntax and Stoughton's multiple substitutions and report some substantial progress. We present formal proofs of confluence for beta-reduction and by using Takahashi's revision of Tait and Martin-Löf's proof, subject reduction for the entire family of the Pure Type Systems and consistency for some impredicative subclass, assuming normalization. As to the proof of confluence, we also develop a theory of alpha-commutative relations which, in our view, entails a clearer presentation and treatment of the problem than in similar developments. Finally, we assess general merits and drawbacks of the approach. The whole development has been machine-checked using Agda.", "title": "A Machine-checked Proof of Consistency for Impredicative Pure Type Systems", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20188" }, { "age_days": 2, "arxiv_id": "2607.19263", "authors": [ "Cameron Khanpour", "Samuel Talkington" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.19263", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-21", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth, making recent empirical observations rigorous. The bounds also hold with overwhelming probability for arbitrary bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified with accompanying Lean 4 source code.", "title": "The Limits of Quantum Computers for Power Flow", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.19263" }, { "age_days": 3, "arxiv_id": "2607.18139", "authors": [ "Christoph Schwerdtfeger" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "arxiv:2607.18139", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-20", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For four agents with nonnegative additive valuations, a complete 1-out-of-5 maximin-share allocation always exists, improving the previous 1-out-of-6 guarantee. Together with known exact-MMS counterexamples, this completely characterizes the four-agent case: the guarantee holds exactly for $d\\geq5$. The main technical contribution is a balanced-residual partition lemma: removing rejected bundles with one of the four highest-ranked goods apiece leaves a remainder that still admits the required number of unit-valued balanced bundles. In its central $2+2$ case, three unit bundles repair two pairs of colliding high-valued goods. The theorem is machine-checked in Lean 4.", "title": "1-out-of-5 Maximin-Share Allocations Always Exist for Four Agents", "updated": "2026-07-20", "url": "https://arxiv.org/abs/2607.18139" }, { "age_days": 5, "arxiv_id": "2607.16721", "authors": [ "Anik Jha" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "arxiv:2607.16721", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-18", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The strongest open-weight coding models are mixture-of-experts (MoE) networks: most of their size comes from large pools of \"expert\" subnetworks, of which only a few act on any token. That pool is why these models do not fit on the machines most developers own, yet for a user who only wants coding help, most experts encode abilities that will never be invoked. We ask how many experts can be removed, and which, by pruning two recent open-weight MoE models from different families (Qwen3.6-35B-A3B and Gemma-4-26B-A4B) under five selection strategies, judged the way a user would: by whether the model still writes correct code. Half the experts can be removed from either model with no statistically detectable loss on the primary code benchmark, and the damage lands almost entirely on abilities outside coding, the intended trade. But the winning strategy flips between the two models, so a recipe validated on one family cannot be assumed to work on another. We further show that perplexity, the metric much of the pruning literature leans on, can rate a broken model above an intact one; that a lightweight fine-tune recovers about half of what aggressive pruning loses; and that against quantizing the full model to the same memory, pruning wins only where quantization would have to drop below 3 bits per weight. Five attempts to overturn that crossover, with failure criteria fixed in advance (better calibration, guarded selection, causal expert importance, failure attribution, and an agentic evaluation letting each model repair its failures from execution feedback), all leave it standing; the last shows single-shot benchmarks overstate compression penalties broadly, as one repair turn erases the 2-bit quantization penalty entirely. Expert pruning works, but it demands per-model validation on the task the model will actually serve.", "title": "Half the Experts, All the Code: One-Shot Domain Pruning of Mixture-of-Experts LLMs for Coding", "updated": "2026-07-18", "url": "https://arxiv.org/abs/2607.16721" }, { "age_days": 6, "arxiv_id": "2607.16533", "authors": [ "Hanxi Chen", "Noam Zilberstein", "Andrew C. Myers", "Alexandra Silva" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.16533", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-17", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In the context of probabilistic programs, an oblivious adversary resolves nondeterminism without seeing the outcomes of random draws. Obliviousness is a common assumption in online algorithms and distributed protocols, but the complex interaction between random draws and adversarial choices makes it challenging to reason about correctness. While there has been significant progress toward reasoning about programs that combine randomization with nondeterminism, most of the work has focused on the adaptive model, whose omniscient view of program state is too powerful to establish correctness for certain classes of programs. We introduce Oblivious Probabilistic Outcome Logic (opOL), a new logic for reasoning about probabilistic programs with nondeterminism controlled by an oblivious adversary. Building on Outcome Logic and Probabilistic Separation Logic, opOL models adversarial choice as a resource and uses probabilistic independence to ensure that random outcomes are hidden from the adversary. The opOL proof system provides expressive and compositional rules for case analysis on both random and nondeterministic outcomes, and for proving almost-sure termination. Expressivity is tested through several case studies, including a paging algorithm and a leader election protocol. The opOL metatheory and case studies are mechanized in Lean 4.", "title": "Oblivious Probabilistic Outcome Logic: Verifying Probabilistic Programs with an Oblivious Adversary", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.16533" }, { "age_days": 6, "arxiv_id": "2607.15647", "authors": [ "Aritro De", "Juliana Felkner" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.15647", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-17", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "LEED v4.1 BD+C certification remains a document-intensive process that requires reviewers to read hundreds of pages of project evidence and apply credit-specific threshold logic by hand. This paper investigates whether small, locally deployed language models can perform meaningful screening of LEED documentation and how deterministic symbolic components should share that work. A neuro-symbolic pipeline is introduced that aligns project PDFs to LEED credit sections, retrieves evidence with credit-aware keyword signatures, verifies compliance with a locally hosted 4-billion-parameter language model, and applies a LEED-specific numeric checker to quantitative thresholds. Experiments on four university buildings (484 PDFs, 153 credit-level decisions) show that a 4-billion-parameter model (gemma3:4b) is the strongest text-only core verifier, achieving 67.3% accuracy and outperforming a larger 8-billion-parameter model (llama3.1:8b) in this task. The deterministic numeric checker corrects arithmetic errors on key quantitative credits, moving EA-p2 from 50% to 100% accuracy and improving several other credits when required values are reliably extracted. At the same time, the full neuro-symbolic configuration achieves 61.6% overall accuracy, trailing the best text-only baseline due to extraction failures and conservative behavior on qualitative categories. Systematic ablations show that adding low-resolution drawing images (150-300 dpi) consistently reduces accuracy, and that prompt effectiveness depends on the building's ground-truth PASS rate: rubric prompts perform best on documentation-rich projects, while chain-of-thought prompts perform best on documentation-lean projects. Within the specific scope of LEED v4.1 BD+C compliance verification over raw project documentation, this pipeline and its baselines provide an initial reproducible reference point for both accuracy and failure modes.", "title": "Neuro-Symbolic AI for LEED compliance: Document-Centric Benchmarking, Deterministic Numeric Checking, and When Multimodal Hurts", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.15647" }, { "age_days": 6, "arxiv_id": "2607.16524", "authors": [ "Tasha Pais", "Richard Higgins" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.16524", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-17", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution. We ask whether this leaves a measurable signature, geometric or behavioral, on learned representations. We propose EffRank/$n$ (effective rank normalized by agent count) and $D_\\text{act}$ (mean pairwise KL divergence between agents' action distributions) as low-overhead diagnostics for reward-attribution effects, then test them on competent MAPPO agents in SMACv2 \\texttt{protoss\\_5\\_vs\\_5}, where unit type is encoded in the observation. In an observation $\\times$ reward-attribution comparison (unit type observed vs.\\ masked; individual damage-contribution reward vs.\\ shared team reward), geometry follows observation rather than reward. With unit type observed, shared and individual rewards have similar EffRank/$n$ ($0.31{\\pm}0.03$ vs.\\ $0.29{\\pm}0.02$) and probe accuracy ($0.75{\\pm}0.05$ vs.\\ $0.73{\\pm}0.05$, both $\\gg 1/3$ chance), while $D_\\text{act}$ leans higher under individual rewards ($1.23{\\pm}0.06$ vs.\\ $1.07{\\pm}0.20$). Masking unit type cuts the above-chance probe signal by more than half, to $0.49$ in both reward arms. In short: individually rewarded agents are competent and separable by role, but on SMACv2 the observation explains the geometry and reward attribution shows up mainly in behavior. Thus geometric diagnostics must control for observed role information and test persistent roles that are not directly observed. EffRank/$n$ and $D_\\text{act}$ add $<$5\\% overhead.", "title": "Feedback Attribution and Representation Geometry: Metrics for Comparing Individual and Shared Rewards in MARL", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.16524" }, { "age_days": 7, "arxiv_id": "2607.15174", "authors": [ "Xueying Qin", "Marco Peressotti", "Fabrizio Montesi" ], "content_date": "2026-07-16", "freshness": "fresh", "id": "arxiv:2607.15174", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-16", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Choreographic programming (CP) is a programming paradigm for the correct-by-construction development of concurrent and distributed systems: programmers write the intended overall behaviour of a system from a global perspective in a choreography, which is then automatically compiled into communicating endpoint programs by a procedure known as endpoint projection (EPP). The central promise is that the projected endpoint programs, when executed together, are behaviourally equivalent to the source choreography. Fulfilling this promise becomes delicate for expressive CP languages. Existing mechanisations of CP treat only restricted fragments, while textbook and general purpose language implementations with rich features leave crucial interactions informal. In particular, general branching in knowledge of choice, general recursion, and nondeterministic choice in choreographies have not yet been integrated in a machine-checked theory. We present Mech, a new mechanisation of CP in Lean 4 that captures these features. There are two central technical challenges in our development of Mech. First, the sketched semantics from the literature does not correctly capture how nondeterministic choice interacts with concurrency. We therefore formulate new semantics that align nondeterministic choreographic executions with the behaviours of projected endpoint programs. Second, managing all these features in proofs is complex. We address this by uncovering new algebraic laws for choreographies, the operators used in their semantics, EPP, and their combinations. Using our development, we prove completeness and soundness of EPP and derive communication safety and deadlock-freedom for projected networks, yielding the most extensive mechanised theory of CP to date.", "title": "Mech: Mechanised Choreographic Programming", "updated": "2026-07-16", "url": "https://arxiv.org/abs/2607.15174" }, { "age_days": 7, "arxiv_id": "2607.14582", "authors": [ "Junjie Zhang", "Jiayu Liu", "Wenbin Liu", "Zhenya Huang", "Doudou Wang", "Yan Jiang", "Leiye Xu", "Tao Xiong", "Wen Huang", "Qi Liu", "Guoping Hu", "Enhong Chen", "Mengping Zhang", "Xiangdong Ye" ], "content_date": "2026-07-16", "freshness": "fresh", "id": "arxiv:2607.14582", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-07-16", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.", "title": "MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research", "updated": "2026-07-16", "url": "https://arxiv.org/abs/2607.14582" }, { "age_days": 7, "arxiv_id": "2607.14699", "authors": [ "Serhii Zabolotnii" ], "content_date": "2026-07-16", "freshness": "fresh", "id": "arxiv:2607.14699", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-16", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Wiener-Hermite cross-correlation identification represents a polynomial response in the Hermite basis. Under Gaussian excitation the basis is orthogonal and a diagonal rule recovers it exactly; under non-Gaussian excitation the same basis is kept, but its Gram matrix gains off-diagonal terms and the diagonal rule is no longer the population projection. We give the exact finite-order excess $L^2(P)$ risk of this mismatch: a moment quadratic form from two Hankel-Cholesky factorizations and one diagonal solve, at $O(s^3)$ cost from moments to order $2s$. Closed cumulant forms at orders three and four expose which non-Gaussian features drive it; symmetry protects the Gaussian basis only through order two. A bootstrap decides, from data, whether a matched basis is worth building; on a Wiener-Hammerstein benchmark it separates a near-Gaussian channel (penalty $\\approx 10^{-4}$) from a skewed output (penalty $0.05$). The computation is a weighted-$L^2$ projection whose core normal-system correspondence is machine-checked in Lean 4.", "title": "Exact Computation of Non-Gaussian Mismatch Penalties in Wiener-Hermite Cross-Correlation Identification", "updated": "2026-07-16", "url": "https://arxiv.org/abs/2607.14699" }, { "age_days": 2, "arxiv_id": "2607.18921", "authors": [ "Yang Sheng", "Jie Fu" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.18921", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-07-21", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Circuit extraction identifies a small set of model components whose presence preserves a target behavior under ablation, and the resulting circuit is often read as the mechanism behind that behavior. We argue that this reading is under-determined: preserving behavior does not single out one circuit, because the claim it supports depends on which circuit is reported and how two circuits are compared. We make this concrete in a synthetic Lean tactic-prediction benchmark -- predicting the next step of a proof -- where fixed proof rules with randomized surface form let differences between extracted circuits be attributed to these choices rather than to the task. Across dense and weight-sparse checkpoints (most weights constrained to zero) of the same transformer, evaluated on atomic (single-rule) and compositional (multi-rule) proofs, we vary which extracted object is reported (a compact prediction-preserving circuit, a broader graph that also keeps surrounding read, write, and routing structure, or the smallest subgraph meeting a post-ablation loss threshold), and whether each attention head's query and key are represented jointly or separately. Exact component-to-component edge overlap is low and sensitive to these choices, at times dropping to a random baseline, while two coarser summaries stay stable: the set of selected attention heads, and the circuit-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL). The largest accuracy gains from RL on compositional proofs come with the most structure beyond the atomic circuits. A circuit-level claim is therefore well defined only once one states which circuit is reported, the pruning threshold used to extract it, and the level at which circuits are compared. We distill these requirements into a reporting practice for circuit-extraction studies.", "title": "Circuit Claims Depend on What Is Extracted and How It Is Compared", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.18921" }, { "age_days": 2, "arxiv_id": "2607.19281", "authors": [ "Philip John", "Eloghosa Ikponmwoba", "Pinaki Pal", "Opeoluwa Owoyele" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.19281", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-07-21", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "This study introduces a reinforcement learning (RL) framework for generating optimal liquid-fueled reactors to improve lean blowout (LBO) predictions in gas turbine combustors. Existing approaches for determining cluster boundaries rely on manual heuristics or distance-based metrics in the input space. In contrast, the proposed method is goal-oriented, explicitly accounting for the target metric (e.g., LBO prediction accuracy) during cluster formation. The framework employs a multi-stage clustering--classification strategy: an initial clustering step (e.g., $k$-means clustering) generates a large set of homogeneous micro-clusters, followed by an actor-critic RL agent that merges them into optimal reactor zones. The validation study, performed using a Jet-A mechanism (119 species, 841 reactions), shows the RL framework offers improved predictive fidelity compared to $k$-means and captures the correct LBO trends, while achieving substantial speedups relative to the high-fidelity computational model. Overall, the RL-driven approach demonstrates strong potential as a computationally efficient reduced-order modeling technique that can complement high-fidelity simulations for rapid design-space exploration.", "title": "A Reinforcement-Learning-Augmented Liquid-Fueled Reactor Network Model for Predicting Lean Blowout in Gas Turbine Combustors", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.19281" }, { "age_days": 6, "arxiv_id": "2607.18313", "authors": [ "Ahaan Kallat" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.18313", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-17", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let $a(n)$ be the sequence A028342 in the On-Line Encyclopedia of Integer Sequences (OEIS), defined by the exponential generating function $\\sum_{n\\ge0} a(n)x^n/n! = \\prod_{i\\ge1}(1-x^i)^{-1/i}$. Equivalently, $a(n)$ counts permutations of an $n$-element labeled set in which every cycle is assigned one divisor of its length, where a cycle of length $m$ has $d(m)$ choices, $d(m)$ being the number of positive divisors of $m$. We prove a family of congruences for $a$, conjectured by Peter Bala. They state that $k \\mid a(n+k)+a(n)$ for odd $k$, that $k \\mid a(n+k)-a(n)$ for $k\\equiv 0,2,6 \\pmod 8$, and that $k \\mid 2(a(n+k)-a(n))$ for $k\\equiv 4\\pmod 8$. The proof first establishes a product congruence $a(n+k)\\equiv a(n)a(k)\\pmod k$, and then computes $a(p^r)\\bmod p^r$ for each prime power by counting the colored permutations fixed by a subgroup of order $p$.", "title": "A Proof of Bala's Congruence Conjecture for A028342", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.18313" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:7db3fc26f141", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use pi_congr instead of forall_congr; deprecate the latter (#7577)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/7db3fc26f141a71a450a07823448e099129ed73a" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:debc2dadf281", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: prefer explicitly supplied specs over ambient local specs in vcgen (#14492)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/debc2dadf281808e3724d9fce4a0e7ab1a1c21f1" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:2b3c28aea1c9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: add missing space before `do` in `for` loop pretty-printing (#14512)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/2b3c28aea1c923c94b08f194d61616ad8eedc428" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:ec525bbb5fe7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: deprecate options via deprecated tag (#14478)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/ec525bbb5fe7e864bf9d114bdd74e8e015deef1e" }, { "age_days": 0, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:202c7914a6c4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `RedirectPlan` for validating and following redirects (#13901)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/202c7914a6c494e82d6efce4aa7a576e8ea204fa" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:421c0229f3fd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add ThreadSanitizer support (#14161)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/421c0229f3fdc87ca19c42f8edf8e4048ba9ec6b" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:77a5093d9b75", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: use lld for sanitize preset (#14513)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/77a5093d9b7537ef23fba2fea07cddc9a2cafa8f" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:7f03b505c689", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: revert \"fix: use pi_congr instead of forall_congr; deprecate the latter (#7577)\" (#14515)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/7f03b505c689e8c88e54845eab1fe1f9f11f4a0a" }, { "age_days": 0, "authors": [ "Mac Malone" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:46e7a11028e1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: initialize Lake plugin using `Lake.All` in core build (#14511)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/46e7a11028e13dc0cf67368535d6762aa1699475" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:212cf2db8b3e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: clarify `stdlib_flags.h` comments (#14474)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/212cf2db8b3e59ca36744a293b4ff59e397df541" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover/lean4:749f580c3b7a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: create adaptation PRs regardless of PR target (#14518)", "updated": "2026-07-23", "url": "https://github.com/leanprover/lean4/commit/749f580c3b7aec0908a057a51a89b304ecbd8151" }, { "age_days": 0, "authors": [ "Etienne Marion" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3e8105934319", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor: change the definition of the stopped sigma-algebra (#42021)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/3e8105934319cb416a3536919a7d84bf7d72cd0c" }, { "age_days": 0, "authors": [ "Nailin Guan" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b5d557f7df25", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(LinearAlgebra): semilinearize `Submodule.Quotient.equiv` (#42001)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/b5d557f7df250b0a7476c30778a3b17a1e448a26" }, { "age_days": 0, "authors": [ "Riccardo Brasca" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8e45b0548034", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add Ideal.IsPrincipal.of_isPrincipal_pow_of_coprime (#39982)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/8e45b0548034eeda677a64e1e0b07837390835b6" }, { "age_days": 0, "authors": [ "ajirving" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e780b56e9235", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Algebra): inv and div for infinite products over groups with zero (#40591)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/e780b56e9235c747285043b5cd5f2ebba300daad" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bd913bfd965f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Order/ConditionallyCompleteLattice/Indexed): `iSup_iSup_eq_{left/right}` for `ConditionallyCompleteLinearOrderBot` (#38856)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/bd913bfd965f710f91b813f79e2f8186f0d5346b" }, { "age_days": 0, "authors": [ "Jun Kwon" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bbc4475e9e8f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/Graph): `Simple` typeclass for `Graph` (#37870)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/bbc4475e9e8fd25fbc8e26d636dd8b37be8f105a" }, { "age_days": 0, "authors": [ "Nailin Guan" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8f560a221155", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/ModuleCat): injective dimension in linear equiv (#41885)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/8f560a221155625bff8f33163ec62b33cd9f81a2" }, { "age_days": 0, "authors": [ "François G. Dorais" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1b92f9f34136", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: adaptations for batteries#1921 (#42013)", "updated": "2026-07-23", "url": "https://github.com/leanprover-community/mathlib4/commit/1b92f9f3413674899dbec743da67a884ffd76a21" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:cd25632fced6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: split `∀` and `iInf` on the RHS of `vcgen` entailments (#14497)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/cd25632fced6a5eaac45706952cb721c4013de17" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:0008e2a34693", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: let sanitizers instrument non-runtime code as well (#14499)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/0008e2a3469353614e11eedf114ebda89eb3570a" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:ee1184c94f6a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake cache misses in CI (#14485)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/ee1184c94f6a87325eee55e08808c95c55a8107c" }, { "age_days": 1, "authors": [ "Joachim Breitner" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:734621996795", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: kernel to check opaque values for fvars (#14498)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/7346219967957ca3dd4302a75a849b67eed1b3cd" }, { "age_days": 1, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:8b83b84ad941", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: handle errors in `Selectable.one` and simplify `Selectable` helpers (#14253)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/8b83b84ad941edfacf4506041e9e2db820b9e780" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:7d4da399657a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: clean missing-spec error when a selected `vcgen` spec fails to apply (#14490)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/7d4da399657ab27e4385908291680328c4d855aa" }, { "age_days": 1, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:e51752cf2f9a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: avoid the non-thread-safe `strerror` in `lean_deode_io_error` (#14479)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/e51752cf2f9a8b305e67ea90c5aa631b210056ce" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:f82e306cbf0f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: activate CompleteLattice→CCPO under open Std.Internal.Do (#14502)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/f82e306cbf0fec7b635e2c5e86dd33c7a693a47e" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:2065c9006289", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `vcgen [f]` unfolding of definitions by root `match` (#14429)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/2065c90062893508ded6433d2e2d81c33af4e761" }, { "age_days": 1, "authors": [ "Wrenna Robson" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:0264578bc2ca", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: remove unnecessary dependency of pairwise characterisation lemmas and improve `List.Nodup` API (#12166)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/0264578bc2cafdc7139147bf231419a75e036f01" }, { "age_days": 1, "authors": [ "Robin Arnez" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:1545cc8d57ef", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: logical model for `Float` / `Float32` <-> `IntN` / `ISize` conversions (#14495)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/1545cc8d57ef25a450e9baef4d689eb63df1f8e0" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:0de561c0608e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: accept term arguments in `vcgen [...]` (#14487)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/0de561c0608eb86dc8d67c56dedceed7c9c23d3f" }, { "age_days": 1, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:9e44042a4208", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/9e44042a4208e8bbb06dc3a43a0ada0d933170b9" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:1b75922bf5e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: lake: import all Lake modules in `Lake.All` (#14510)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/1b75922bf5e4b019926bdaa773b4c4f37949f468" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:00f9caf44935", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: inline `LintVerbosity.medium` in builtin lint (#14503)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/00f9caf44935b96cbeee36082c3abea67ab06792" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:15adc1ca5b08", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: correct vcgen bench toolchain and move IMP test to elab (#14504)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/15adc1ca5b081b58ae8d13f10130c0e0e45a63c0" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover/lean4:7ecf5dc83f4b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: add debug info to all the debug-like cmake configurations (#14500)", "updated": "2026-07-22", "url": "https://github.com/leanprover/lean4/commit/7ecf5dc83f4bdb92630676f486443352d63d670f" }, { "age_days": 1, "authors": [ "ajirving" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cba869277b7f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: style: fix by on newline (#41794)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/cba869277b7f3c09f96ece2a118ed4c1c8115b89" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:03b2a04be172", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf: lower priority for `IsSimpleRing.instNontrivial` and `UnitalShelf.toOne` (#40304)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/03b2a04be172c9ef9c9b9d25cdbf4ffd2064a326" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b1de3b7b0763", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf(Positivity): filter with `isProp` in `compareHyp` (#42014)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b1de3b7b0763def682d9f6f6877eb395629cce45" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0c60917e5824", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(GroupTheory/Coprod): fix recursor argument name (#41930)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/0c60917e582430c2052c4d5ccd7ca1176ad9a6cc" }, { "age_days": 1, "authors": [ "Eric Wieser" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8c507ffc7609", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: connect BinaryTree and Ordnode (#40370)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/8c507ffc76096945923128217ca4c9e6180b7282" }, { "age_days": 1, "authors": [ "Bhavik Mehta" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3a41afdb6a1e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/MetricSpace): add separatesPoints_lipschitzWith_one (#41436)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/3a41afdb6a1ea6f2d01d07ef13cef1d56273b72c" }, { "age_days": 1, "authors": [ "Tian Chen" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2e27cde44566", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology): generalize Dieudonné's theorem to R1 spaces (#41968)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/2e27cde445666f05d31d420598bba4c78b3251b2" }, { "age_days": 1, "authors": [ "Bhavik Mehta" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b050d8ed0371", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Logic/Function): add Set.separatesPoints_mono (#41434)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b050d8ed03718019165da9e14302cf3a69272476" }, { "age_days": 1, "authors": [ "Thomas Browning" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3d8d5c0359d5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/LinearIndependent/Basic): linear independence along faithful algebra maps (#41682)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/3d8d5c0359d52cc45e9a5283d8328e5385201f22" }, { "age_days": 1, "authors": [ "Junyan Xu" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ef7aa707423d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(EllipticCurve/Affine/Point): easy instances (#41264)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/ef7aa707423d6835bc485b7c128842c0ebe0e5f4" }, { "age_days": 1, "authors": [ "Louis (Yiyang) Liu" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7779d601f710", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/SpecialFunctions/ImproperIntegrals): Frullani integral (#34815)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/7779d601f7103882175b3125539d5d1232911f5e" }, { "age_days": 1, "authors": [ "Judson" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bcaf924143a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/CStarAlgebra/Matrix): add CStarAlgebra instance for matrices (#41518)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/bcaf924143a7c24b55a6ce214d4c327670de8f4c" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0b6c1c0146ff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/FreeMonoid): `FreeMonoid.length` is surjective (#41928)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/0b6c1c0146ff30103803371f12a16c8d515c8c97" }, { "age_days": 1, "authors": [ "Justus Springer" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b7d0290f4efa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(RingTheory/MvPowerSeries/Order): improve docstrings of `order` and `weightedOrder` (#41959)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b7d0290f4efa01090ea4141df3a07a02f29016c2" }, { "age_days": 1, "authors": [ "Marcelo Lynch" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:713a1f62a8c8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci: publish the cache for off-master release tags (#42009)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/713a1f62a8c880cf66692d93e0bc3b2bf416d082" }, { "age_days": 1, "authors": [ "Oliver Nash" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b8a692e177dd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: split file `Algebra.Lie.Algebra.Basis` (#41985)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b8a692e177dda10fde4d351f9b00c81ae9f76a20" }, { "age_days": 1, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6ff9d2aabb8c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: replace some redundant `simpa only using h` (#41931)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/6ff9d2aabb8ca3a2d2b70ad0f239b49830e01a5b" }, { "age_days": 1, "authors": [ "Junye" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:280cbb137e26", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove flexible linter suppressions (#40033)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/280cbb137e2622964c6bc46be3678b50d05b0d22" }, { "age_days": 1, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:dfda59dbfd3b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: no `public def` inside `public section` etc (#41787)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/dfda59dbfd3b5f54f214d40d9f7aff1f6ad41085" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9b53612f8d8d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: golf proofs of `mdifferentiableAt_atlas{_symm}` (#42011)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/9b53612f8d8de79c06e752024f9b087e9ea5d0fa" }, { "age_days": 1, "authors": [ "Oliver Nash" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:69ac67288807", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: add deprecation for file move `Mathlib.Algebra.Lie.Basis` (#42004)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/69ac67288807cdc1d809a91e1f9c6a520c423bbb" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:17b4b96c4eb8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Geometry/Manifold/MFDeriv/Atlas): remove backcompat option (#41843)", "updated": "2026-07-22", "url": "https://github.com/leanprover-community/mathlib4/commit/17b4b96c4eb874624e9cab005e966a25fd68ab14" }, { "age_days": 2, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "github:leanprover/lean4:943e616509e2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add type class for replayable body types (#13900)", "updated": "2026-07-21", "url": "https://github.com/leanprover/lean4/commit/943e616509e287b7055c0571e11dba6cbb8c9b3b" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "github:leanprover/lean4:d5790c1f0882", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: more bv_decide benchmarks (#14482)", "updated": "2026-07-21", "url": "https://github.com/leanprover/lean4/commit/d5790c1f088236fe67b52500ff87bce2c848b0bb" }, { "age_days": 1, "arxiv_id": "2607.19811", "authors": [ "Xudong Ouyang", "Wenlun Zhang", "Yimin Xu", "Huazhong Liu", "Yunshan Zhong" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.19811", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The Segment Anything Model 2 (SAM2) has advanced temporal promptable segmentation, yet its deployment remains hindered by heavy memory cross-attention overhead and redundant full-frame visual feature extraction. While recent methods explore efficiency via heuristic memory pruning and window-based sparse routing, they typically suffer from catastrophic performance degradation in complex segmentation scenarios replete with occlusions and distractors. To resolve these limitations, we propose \\textbf{Lean-SAM2}, a holistic lightweight framework designed to address the above vulnerabilities while systematically eliminating computational redundancies. Specifically, Lean-SAM2 integrates three collaborative mechanisms: (1) Target-Anchored Memory Pruning (TAMP) safeguards target tokens against deceptive attention by modulating raw attention significance with semantic consistency against prompt-derived foreground anchors; (2) Temporal Condensation with Insurance Memory (TCIM) condenses historical context via a visibility-gated fusion while conditionally archiving high-confidence entries in a parallel insurance bank; and (3) Target-Anchored Risk-Aware Routing (TARR) selectively activates the heavy image encoder for target-related windows based on anchor similarity, utilizing a risk-aware fallback policy to trigger full-frame refreshes during volatile transitions. Extensive evaluations across multiple challenging benchmarks demonstrate that Lean-SAM2 establishes a superior balance between accuracy and efficiency. For example, on the LVOSv2 validation dataset, Lean-SAM2 achieves overall inference speedups of $1.412\\times$ and $1.417\\times$ on the SAM2.1-Large and SAM2.1-Base+, respectively, significantly outperforming Efficient-SAM2 while boosting the corresponding $\\mathcal{J}\\&\\mathcal{F}$ scores by $5.0\\%$ and $3.6\\%$. Code is available at https://github.com/DeawhaleQwQ/Lean-SAM2.", "title": "Lean-SAM2: Target-Anchored Memory and Encoder Acceleration for SAM2", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.19811" }, { "age_days": 1, "arxiv_id": "2607.19727", "authors": [ "Moritz Doll", "Iman Shames" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.19727", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We introduce an open-source library for machine-checked control theory in the interactive proof assistant Lean to lay foundations for the verification of cyber-physical systems. To this end, as representative theorems, we present formalizations of Lyapunov stability theory and the small-gain theorem. First, the machinery employed for formalizing Lyapunov stability, i.e., neighborhood filters, allows stating a Lyapunov theorem that covers both points and sets and applies to continuous, discrete, and hybrid systems. Second, the small-gain theorem is proved via stating input-output systems as relations without the usual well-posedness assumption. The Lean formalization of each of these theorems is then presented. We conclude by discussing the library architecture and mentioning some of the other system theoretic results that are formalized in the library along with future plans.", "title": "Foundations of Machine-Checked Control Theory in Lean", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.19727" }, { "age_days": 1, "arxiv_id": "2607.20382", "authors": [ "Eva McCord", "Ernest Pedapati", "Zag ElSayed" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20382", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Clinical biomarker workflows in translational research settings often rely on spreadsheet-driven tracking, manual quality control (QC) reconciliation, and loosely integrated systems, resulting in limited state visibility, delayed reporting, and increased operational risk. These challenges are particularly pronounced in multi-day assays such as Luminex-based quantification of Fragile X Messenger Ribonucleoprotein (FMRP), where HIPAA-compliant data governance, deterministic workflow progression, and coordinated communication across laboratory and clinical teams are required. This paper presents FMRP-LEAN, a HIPAA-compliant, AI-augmented Laboratory Information Management System (LIMS) architecture that formalizes biospecimen lifecycle management through a finite-state workflow model with explicit transition guards and dwell-time observability. The system integrates a self-hosted Supabase/PostgreSQL stack deployed within hospital-controlled infrastructure, hybrid edge-internal isolation with encrypted tunneling and loopback-only services, and bi-directional REDCap synchronization. A unified MRN-UUIDv7 identifier framework with QR-based tracking ensures traceable clinical-research linkage under PHI residency constraints. FMRP-LEAN incorporates automated statistical QC pre-screening and a governance-constrained AI operations module that operates exclusively on aggregate projections, with deterministic fallback guarantees. Deployment demonstrates improved workflow observability, reduced QC latency, and enhanced cross-role transparency between laboratory technicians, research coordinators, and patient-facing teams. The architecture provides a reproducible model for secure, state-explicit, and AI-augmented clinical research workflows in regulated healthcare environments.", "title": "FMRP-LEAN: A HIPAA-Compliant AI-Augmented LIMS Architecture for End-to-End Clinical Assay Workflow Optimization", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20382" }, { "age_days": 2, "arxiv_id": "2607.18993", "authors": [ "Alex M. Garcia", "Emiliano M. Fortes", "Eduardo J. Pérez-Sánchez", "Daniel Mira", "Marco Vivenzo", "Michael Gauding", "Heinz Pitsch", "Nico Schmitz", "Christian Wuppermann" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.18993", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-21", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Lean hydrogen flames are prone to thermo-diffusive instabilities due to preferential and differential diffusion effects, posing significant challenges for their modeling in computational fluid dynamics simulations. This work extends a tabulated-chemistry (TC) model that includes preferential and differential diffusion effects to a Reynolds-averaged Navier-Stokes (RANS) framework and assesses its performance for a lean premixed $\\mathrm{H_2}$-air slot burner at two Reynolds numbers ($\\mathrm{Re}=5500$ and $11000$) using direct numerical simulation (DNS) as a reference. The approach is based on transport equations for the progress variable and mixture fraction derived from the species mass transport equations considering mixture-averaged diffusion and Soret effect, and incorporates turbulence--chemistry interaction via a presumed probability density function (PDF) approach. RANS simulations including preferential-differential diffusion are able to correctly reproduce the DNS flame length, heat-release distribution, and the characteristic equivalence-ratio and super-adiabatic temperature branches of the slot flame. Comparisons with (i) a unity-Lewis-number variant and (ii) a model including thermo-diffusive effects only in the flamelet table show the impact of preferential and differential diffusion on the TC model at both the thermochemical and transport levels. Finally, the impact of the turbulence closures for turbulent diffusion, scalar dissipation rate, and Reynolds stresses is assessed. The results presented in this paper demonstrate the capability of the model to include preferential and differential diffusion effects in cost-effective RANS simulations of lean hydrogen flames.", "title": "Preferential and differential diffusion in RANS simulation of lean hydrogen flames with tabulated chemistry", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.18993" }, { "age_days": 3, "arxiv_id": "2607.17477", "authors": [ "Wouter van Doorn", "Elias Judin", "Pietro Monticone", "Daniel Morrison" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "arxiv:2607.17477", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The Kourovka Notebook is a long-running collection of open problems in group theory. In this paper we present solutions to eight of its problems. We construct a group with exactly two maximal locally soluble normal subgroups and show that, for every $1 \\le k\\le n!$, there is a group containing $n$ distinct elements whose $n!$ ordered products take exactly $k$ distinct values. We also give examples showing that group order together with the statistic $\\sum_g\\varphi(\\lvert g\\rvert)$ does not determine simplicity, and we construct a surjective non-injective Rota-Baxter operator on a non-abelian group. Further, we determine the group generated by the class transpositions of moduli at most $k$, prove that every power graph of a finite group that is a cograph is chordal, show that the right-relatively convex subgroups of a right-orderable group need not form a sublattice of its subgroup lattice, and disprove a proposed rank inequality for certain $p$-group extensions. All of these solutions were autonomously discovered and formally verified in Lean by Aristotle, a formal reasoning agent developed by Harmonic.", "title": "On Some Problems from the Kourovka Notebook", "updated": "2026-07-20", "url": "https://arxiv.org/abs/2607.17477" }, { "age_days": 3, "arxiv_id": "2607.18401", "authors": [ "Zijue Luo", "Jae Eu", "Tianyi Wang", "Boerge Hemmerling" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "arxiv:2607.18401", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Qubits encoded in the spin of trapped electrons have been proposed as a promising novel platform for quantum information processing. While trapping of electrons has been largely carried out in Penning traps for precision measurement purposes, it is desirable to use linear Paul traps instead, leaning on the successes of trapped ion quantum processors. Here we present a Paul trap for electrons made of a single printed circuit board. Our approach requires no assembly and the rigid design minimizes manufacturing intolerances. We characterize the trap performance and observe trapped electron lifetimes of 2.13 ms and secular frequencies of up to 90 MHz.", "title": "Monolithic printed-circuit board RF-trap for electrons", "updated": "2026-07-20", "url": "https://arxiv.org/abs/2607.18401" }, { "age_days": 3, "arxiv_id": "2607.18032", "authors": [ "Hong-Bin Chen" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "arxiv:2607.18032", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove full replica symmetry breaking for the zero-field Sherrington-Kirkpatrick model at zero temperature: the Parisi minimizer is absolutely continuous, has a smooth density, and has support $[0,1)$. At inverse temperature $β>1$, [arxiv.org/abs/2607.11756v3] recently proved that the Parisi measure has support $[0,q_β]$. Here, we show $q_β$ converges to $1$ as $β\\to\\infty$.", "title": "FRSB in the SK spin glass: convergence to full-interval support at zero temperature", "updated": "2026-07-20", "url": "https://arxiv.org/abs/2607.18032" }, { "age_days": 3, "arxiv_id": "2607.18455", "authors": [ "David Richter", "Timon Böhler" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "arxiv:2607.18455", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We revisit the role of higher-order unification in dependently typed languages and identify a fundamental limitation of existing pattern-based fragments: their inability to synthesize functions defined by case analysis. Even simple and ubiquitous constraints arising from type inference, particularly from use of induction principles, fall outside the expressive power of Miller patterns and their modern extensions. We observe that such constraints naturally correspond to definitions by dependent pattern matching. Motivated by this correspondence, we propose integrating dependent pattern matching into the unification process. We present a prototype implementation of a small dependently typed language that collects delayed unification constraints and resolves them via a pattern matching compiler. Our approach successfully infers solutions that are rejected by current systems such as Rocq and Lean, suggesting a new direction for unification that unifies type inference and pattern matching compilation.", "title": "Extended Abstract: From Pattern Unification Towards Pattern Matching Unification", "updated": "2026-07-20", "url": "https://arxiv.org/abs/2607.18455" }, { "age_days": 5, "arxiv_id": "2607.16997", "authors": [ "Neel Somani" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "arxiv:2607.16997", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-18", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Mathematicians distinguish proofs that explain, simplify, or introduce a nonstandard route, but these judgments are difficult to operationalize. We study a deliberately narrower construct: time-relative proof-route nonstandardness in formal mathematics. For a Lean theorem, PriorProof extracts the dependency footprint of its elaborated proof term and scores the weighted surprisal of that footprint under a retrieval-conditioned, hierarchically smoothed prior built only from an earlier quarterly snapshot of Mathlib. The method requires no hand-built technique ontology and no human labels: statement retrieval is learned from proof-derived contrastive pairs, while the scored object is read mechanically from proof terms. In a blinded topology study, 100 presentations collapse to 76 distinct underlying pairs: 12 canonical contrasts shown three times for consistency screening and 64 distinct stratified pairs. Against the majority of three retained domain raters, PriorProof agrees on 53/76 pairs (69.7%, Wilson 95% CI 58.7-78.9%), including 11/12 canonical pairs (91.7%, 64.6-98.5%) and 42/64 stratified pairs (65.6%, 53.4-76.1%). Score-gap quartiles are nonmonotone after repeat collapse; the endpoints are 12/19 (63.2%, 41.0-80.9%) in the smallest-gap bin and 16/19 (84.2%, 62.4-94.5%) in the largest, supporting an endpoint-calibration tendency rather than a resolved staircase. The best language-model condition agrees on 60/76 pairs (78.9%, 68.5-86.6%); on paired outcomes, PriorProof alone is correct on 8 pairs and the model alone on 15 (exact two-sided McNemar p = 0.210), so the difference is not established at this sample size. We therefore present PriorProof not as a replacement for expert or model judgment, but as a decomposable, time-anchored signal whose score gap provides an interpretable reliability indicator.", "title": "PriorProof: A Point-in-Time Measure of Technique Novelty for Formal Proofs", "updated": "2026-07-18", "url": "https://arxiv.org/abs/2607.16997" }, { "age_days": 6, "arxiv_id": "2607.16451", "authors": [ "Heejin Jo" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "arxiv:2607.16451", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-17", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Chat models sometimes commit to an answer and then produce reasoning that justifies it rather than deriving it -- even when the answer contradicts a task premise. We study a minimal probe: \"I want to wash my car. The car wash is 100 meters away. Should I walk or drive?\" Only drive works (the car must be at the car wash), yet models overwhelmingly recommend walking. (1) Behavioral reproduction: on Qwen3-8B across five system-prompt conditions (210 rollouts), the wrong commitment occurs in 85-100% of sampled rollouts per condition and 100% of greedy rollouts, in both thinking and non-thinking modes; a 4,096-token thinking budget does not repair it. (2) Preliminary activation-level evidence: probing hidden states with a pretrained, training-free activation oracle (no task-specific probe training) at positions before the answer text is emitted, \"walk\" read-outs exceed a neutral-context baseline (68% vs. 17%; walk-committing rollouts p=.005, drive-committing rollouts p=.005, Fisher exact) -- notably, rollouts that eventually answer drive also read as walk-leaning before commitment (5/6). The oracle's default on unrelated content is \"drive\" (83%), so the read-outs are not lexical bias; stratifying by literal walk/drive occurrence shows they are not text recovery either (spans containing \"drive\" still read out walk; in balanced lexical fields, per-rollout walk-majorities beat a per-prompt neutral baseline 15/22 vs. 1/8, p=.01; drive-committing rollouts 6/6, p=.002). Samples are small and the within-rollout positional gradient is not significant (p=.34); we frame these results as preliminary. (3) Methodological: with fixed oracle, activations, and positions, question wording alone moves a positive control from 2/16 (open question) to 11/16 (closed); negative oracle results are uninterpretable without per-wording positive controls.", "title": "Committed Before Reasoning: Behavioral Reproduction and Preliminary Activation-Level Evidence of Answer Pre-Commitment in an Open-Weight LLM", "updated": "2026-07-17", "url": "https://arxiv.org/abs/2607.16451" }, { "age_days": 7, "arxiv_id": "2607.14888", "authors": [ "Robert Graham", "Edward Stevinson", "Yariv Barsheshat" ], "content_date": "2026-07-16", "freshness": "fresh", "id": "arxiv:2607.14888", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-16", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Finetuning language models on small, curated datasets is standard practice for adapting them to specific policies or domains. We show that finetuning on narrow, factually-defensible, moderation-passing data can cause broad ideological shifts across unrelated domains, while preserving general capabilities. Training GPT-4.1 on right- or left-leaning economics Q&A yields matched ideological shifts on topics such as criminal justice, the environment, and cultural taste. The same effect appears with plausibly-deployed datasets such as workplace HR policy and practical finance queries, as well as on a science-pseudoscience axis where food-safety finetuning increases sycophantic agreement with users expressing false health beliefs. We call this phenomenon ideological generalisation and propose a methodology to measure two properties: breadth, how far the shift reaches across topics absent from training, and amplification, how much finetuning intensifies the shift relative to few-shot prompting on the same examples. We show that few-shot prompting indicates the direction of generalisation but finetuning pushes the model to further extremes, including to far out-of-distribution outputs such as endorsements of race-IQ connections and political violence. The effect replicates on Gemma-3, holds under judge-free evaluations and external benchmarks, survives mixing with generic data, and leaves GSM8K accuracy within $\\pm 1$pp of the baseline.", "title": "Innocuous-Seeming Data, Latent Ideology: Ideological Generalisation in Finetuned LLMs", "updated": "2026-07-16", "url": "https://arxiv.org/abs/2607.14888" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }