{
  "counts": {
    "adjacent": 17,
    "core": 2,
    "errors": 0,
    "negative": 66,
    "total": 85
  },
  "date": "2026-07-21",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-07-21T16:56:54Z",
  "items": [
    {
      "age_days": 3,
      "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": 2,
      "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": 4,
      "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": 6,
      "arxiv_id": "2607.14087",
      "authors": [
        "Abhijeet Mulgund"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.14087",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-15",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "We prove a stochastic comparison for Gaussian maxima. Let $R$ be an $m\\times m$ correlation matrix satisfying $R-\\mathbf{1} \\mathbf{1}^{\\mathsf T}/m\\succeq0$, let $X\\sim\\mathcal{N}(0,R)$, and let $Z_1,\\ldots,Z_m$ be independent standard Gaussian random variables. Then $\\max_{1\\leq i\\leq m}X_i \\leq_{\\mathrm{st}} \\max_{1\\leq i\\leq m}Z_i$, or equivalently, $\\mathbb{P}\\{X_i\\leq c\\text{ for every }i\\}\\geqΦ(c)^m$ for every $c\\in\\mathbb{R}$. This comparison resolves the Weak Simplex Conjecture: among $d+1$ equiprobable equal-energy signals in $\\mathbb{R}^d$ transmitted over an additive white Gaussian noise channel, the regular simplex maximizes the probability of correct maximum-likelihood decoding at every signal-to-noise ratio. It also proves the inequality asserted by the Simplex Mean Width Conjecture and gives an exact formula for the largest number of equiprobable messages that can be sent at prescribed energy and error probability by a deterministic no-feedback AWGN code under a per-codeword energy constraint. The proof combines a Gaussian product inequality for log-concave functions with an adaptive tilting argument that makes the inequality applicable to the one-sided threshold events defining the maximum. A lean formalization of this argument is available at https://github.com/abhmul/weak-simplex-conjecture-lean.",
      "title": "Stochastic Domination of Gaussian Maxima: A Resolution of the Weak Simplex Conjecture",
      "updated": "2026-07-20",
      "url": "https://arxiv.org/abs/2607.14087"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.13225",
      "authors": [
        "Nikolay Ulyanov"
      ],
      "content_date": "2026-07-14",
      "freshness": "fresh",
      "id": "arxiv:2607.13225",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-14",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "We prove Sabidussi's compatibility conjecture. Let $G$ be a finite connected multigraph in which every vertex has even degree and the minimum degree is at least four, and let $T$ be a closed trail that traverses every edge exactly once. The edges of $G$ can be partitioned into circuits (connected 2-regular subgraphs) so that no circuit contains the two edges used consecutively anywhere in $T$. In fact, the edges can be four-coloured so that every such pair receives two different colours and the subgraph formed by the edges of each colour has even degree at every vertex. Formalization in Lean 4 is also available in the author's github.",
      "title": "Graph Puzzles III.1: A Proof of Sabidussi's Compatibility Conjecture",
      "updated": "2026-07-14",
      "url": "https://arxiv.org/abs/2607.13225"
    },
    {
      "age_days": 1,
      "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": 3,
      "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": 4,
      "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": 4,
      "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": 4,
      "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": 5,
      "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": 5,
      "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": 5,
      "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": 6,
      "arxiv_id": "2607.13531",
      "authors": [
        "Ho-Lin Chen",
        "Xiang Huang"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.13531",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-07-15",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present Ripple, an open, AI-formalized Lean 4 framework for the mathematics of computing real numbers with chemical reaction networks (CRNs). Ripple formalizes the full ladder of models -- the GPAC / CRN continuum and the CRN-computable reals, the large-population-protocol (LPP) compilation pipeline, and a continuous-time Markov chain (CTMC) layer bridged to the deterministic mean-field limit by three machine-checked versions of Kurtz's theorem, and two Turing-completeness results -- the Bournez-Graça-Pouly GPAC Turing-completeness construction and the Soloveichik-Cook-Winfree-Bruck stochastic-CRN universality theorem. The development is reliable (its core constructions are verified to depend on exactly the three Mathlib foundational axioms, with no sorry); it exposed genuine, fixable gaps in published proofs (the approximate-majority convergence argument and the LPP main theorem); and it proves new results -- a fully machine-checked construction of Apéry's constant ζ(3) as a CRN-computable number via its holonomic generating function, the same recipe turning the modular 1/π series of Ramanujan into a sharp open problem. The formalization was carried out predominantly by AI agents using only publicly available models, so the workflow is reproducible.",
      "title": "Ripple: An Open, AI-Formalized Lean 4 Framework for Computing with CRNs",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.13531"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.13921",
      "authors": [
        "Niels Mündler-Sasahara",
        "Hristo Venev",
        "Dawn Song",
        "Martin Vechev",
        "Jingxuan He"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.13921",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-07-15",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Languages with rich static semantics, such as Rust, provide stronger guarantees for AI-generated code, but their strictness makes generation more difficult. Off-the-shelf compilers can provide useful feedback post-generation, but does not guide intermediate generation steps, such as those during autoregressive LLM decoding. Constrained decoding intervenes earlier by rejecting invalid tokens during sampling, but requires white-box model access and costly reimplementation for semantic constraints. We introduce generative compilation, the first approach to obtaining compiler feedback on partial programs during generation. The core technical device is a sealor: a lightweight, mostly syntax-guided transformation that converts partial programs into complete ones that standard compilers can diagnose. It is designed such that possible-to-complete partial programs are never rejected, while preserving enough code context to catch genuine dead ends early. We construct such a sealor on a core Rust-like calculus and prove that it satisfies these properties, all mechanized in Lean. We extend it to the first partial-program checker for real Rust. We evaluate our method on challenging repository-level Rust coding tasks, across both frontier black-box and open-weight models. We show that generative compilation reduces non-compiling outputs and improves functional correctness, relative to standard post-generation feedback. It does so by detecting a broad range of errors close to their source and early during generation, thereby reducing errors cascades and enabling focused diagnostics. More broadly, generative compilation is a step toward making compilers a first-class citizen of AI-assisted programming active during generation, rather than a separate post-generation check.",
      "title": "Generative Compilation: On-the-Fly Compiler Feedback as AI Generates Code",
      "updated": "2026-07-16",
      "url": "https://arxiv.org/abs/2607.13921"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.14420",
      "authors": [
        "Thomas Lu",
        "Qiancheng Fu",
        "Kevin Batz",
        "Oliver Bøving",
        "Tiago Ferreira",
        "Mark Moeller",
        "Nate Foster",
        "Alexandra Silva"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.14420",
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      "published": "2026-07-15",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "When designing a network, engineers must navigate trade-offs (e.g., one topology offers more aggregate bandwidth, another lower latency or better resilience) that demand reasoning about quantitative properties. We present a fast analyzer for quantitative network properties based on weighted NetKAT (wNetKAT), a domain-specific language that provides a semantic foundation for quantitative reasoning by modeling network behavior using weights drawn from a semiring. At the core of our development is the design of a symbolic data structure -- weighted symbolic packet programs (wSPPs) -- that compactly represent the semantics of weighted policies, for which a direct implementation would be intractable. We show how to compute all policy constructs symbolically; unsurprisingly, the crux is Kleene star, for which we design a tailored algorithm. We further develop trace-carrying Pareto semirings, which compute multi-objective frontiers together with the network paths that realize them. We formalize the development in Lean and provide an optimized Rust implementation. Being parametric on a semiring, our implementation covers both classical and quantitative analyses: we show that it is competitive with KATch, a heavily optimized Boolean-reachability verifier, and orders of magnitude faster than McNetKAT and Storm on probabilistic analyses. A case study comparing Fat-tree and Jellyfish data-center topologies shows the framework supports multi-objective design-time analysis.",
      "title": "A Fast Quantitative Analyzer for NetKAT",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.14420"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.13292",
      "authors": [
        "Marcus J. Min",
        "Mike He",
        "Zhaoyu Li",
        "Zixuan Yi",
        "Sharad Malik",
        "Aarti Gupta",
        "Xujie Si",
        "Osbert Bastani"
      ],
      "content_date": "2026-07-14",
      "freshness": "fresh",
      "id": "arxiv:2607.13292",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
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      "published": "2026-07-14",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Autoformalization translates informal natural language into formal, machine-verifiable languages. While most work focuses on individual statements, real formalization efforts are inherently theory-level: they require an entire web of axioms, definitions, and lemmas before target theorems can even be stated. In this position paper, we argue for theory-level autoformalization: formalizing complete theories, including all their inter-dependencies, as structured libraries. We examine the significance of this shift, address alternative views, identify open challenges, and propose three promising paths forward. Our survey of autoformalization is available at https://github.com/marcusm117/Awesome-Autoformalization.",
      "title": "Theory-Level Autoformalization: From Isolated Statements to Unified Formal Knowledge Bases",
      "updated": "2026-07-14",
      "url": "https://arxiv.org/abs/2607.13292"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.13165",
      "authors": [
        "Jeffrey S. Baggett",
        "Huiya Yan"
      ],
      "content_date": "2026-07-14",
      "freshness": "fresh",
      "id": "arxiv:2607.13165",
      "kind": "paper",
      "label": "adjacent",
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        "lean_formal_proving_agents"
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      "published": "2026-07-14",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "For integer vectors R,S let A(R,S) denote the class of (0,1)-matrices with row sum vector R and column sum vector S. Its interchange graph G(R,S) has A(R,S) as its vertex set, two matrices being adjacent when they differ by a single 2 x 2 interchange. Brualdi conjectured that G(R,S) is Hamiltonian for every R,S. We prove the stronger statement that G(R,S) is maximally Hamiltonian: Hamilton-laceable when bipartite, and Hamilton-connected when not. The proof is a structural induction on the number of matrices in the class, organized by the structure theory of interchange graphs. Deleting inactive lines and splitting invariant positions expresses any class as a Cartesian product, reducing the argument to the prime factors. The bipartite classes are products of complete transposition graphs; we settle them together, without induction, by proving they are paired 2-disjoint-path-coverable and hence Hamilton-laceable, using a recent theorem of Coleman, Fischberg, Gong, Harrington and Wong on paired disjoint path covers. The non-bipartite classes divide into three cases: products assembled from smaller factors, a base of Johnson graphs and small classes, and the large prime classes, treated by a pivot-and-fiber construction whose line quotients are matroid base-exchange graphs. The complete argument has been machine-checked in the Lean 4 proof assistant from first principles together with seven cited results of the literature; the disjoint-path-cover results it imports are themselves proved within the formalization.",
      "title": "Interchange graphs of (0,1)-matrices are maximally Hamiltonian",
      "updated": "2026-07-17",
      "url": "https://arxiv.org/abs/2607.13165"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.13303",
      "authors": [
        "Hongyi Liu",
        "Madhusudan Parthasarathy",
        "Adithya Murali"
      ],
      "content_date": "2026-07-14",
      "freshness": "fresh",
      "id": "arxiv:2607.13303",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
      ],
      "published": "2026-07-14",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Formal contracts are essential for software testing and verification, yet writing them remains labor-intensive and error-prone. LLMs offer a promising path toward autoformalization: synthesizing executable assertions from natural-language specifications and thereby bridging the gap between informal developer intent and formal executable specifications. We present Monty: an autoformalization framework for assertions that tackles the challenges of expectations of validity of assertions and ambiguity in natural-language. Our techniques are based on filtering formalizations using a novel conformance score metric and validity scores obtained from testing the code against formalized assertions. We evaluate our approach on 541 assertion-generation tasks derived from 22 collection-like Java classes, and show that our technique produces the ground truth more reliably (improving upto 20 points in precision on average) than when using LLMs naively to translate assertions.",
      "title": "Faithful Autoformalization of Natural Language Assertions",
      "updated": "2026-07-16",
      "url": "https://arxiv.org/abs/2607.13303"
    },
    {
      "age_days": 0,
      "authors": [
        "Thomas Zhu"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:ac2a7e7d041f",
      "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: fix: make `replay` output a kernel environment (#14391)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/ac2a7e7d041f38ab8831287e83bc4bdd277a96f3"
    },
    {
      "age_days": 0,
      "authors": [
        "Eric Wieser"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:49ac957e1c1c",
      "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: fix: do not pass an unitialized variable in `run_init` (#14471)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/49ac957e1c1c3bd461e30466093445023469f4a1"
    },
    {
      "age_days": 0,
      "authors": [
        "Joachim Breitner"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:be66a4456e3d",
      "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: fix: `fun_induction` rejecting names for all hypotheses with `let` and `generalizing` (#14475)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/be66a4456e3d03d1d6cf1a479c37e4c20906b8ec"
    },
    {
      "age_days": 0,
      "authors": [
        "Robin Arnez"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:87843ad848e4",
      "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: improvements to the floating-point API (#14481)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/87843ad848e45a904e662755ac37cf18b381b63c"
    },
    {
      "age_days": 0,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:aacd6121be3b",
      "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: forbid non-reserved identifiers via `withForbidden` (#14432)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/aacd6121be3b52724ac1cd63ea5eca9f4b1c3c09"
    },
    {
      "age_days": 0,
      "authors": [
        "Julien Cretin"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:3cdf38cc88c8",
      "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: doc: add blank line after list in omega docstring (#14381)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/3cdf38cc88c854dafc4c87372b5c24b9f487f915"
    },
    {
      "age_days": 0,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:e695749528f4",
      "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: rename `Nat.div_eq` to `Nat.div_eq_ite` (#14462)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/e695749528f42a8bce47c40c253f5ab460a6349a"
    },
    {
      "age_days": 0,
      "authors": [
        "Eric Wieser"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0e8a9ebad99e",
      "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: improve diagnostics when thread creation fails (#14082)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover/lean4/commit/0e8a9ebad99e0a41dbd7655f5a4e9993d4dc07f1"
    },
    {
      "age_days": 0,
      "authors": [
        "Pepa Montero Jimena"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:db19808db24f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: scalar multiplication by a group element is a diffeomorphism (#41832)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/db19808db24fab3f99fc1309a0fe84190ea8f88f"
    },
    {
      "age_days": 0,
      "authors": [
        "Yaël Dillies"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3ad2bbaa4afb",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: correspondence between affine group schemes and Hopf algebras (#40500)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3ad2bbaa4afbcac3bf0f30c13ec558ecc9217eac"
    },
    {
      "age_days": 0,
      "authors": [
        "ayhon"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:f02ed5416051",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: binder plicity code action (#40641)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/f02ed541605188aecbda9c6cca3eedd237bd3260"
    },
    {
      "age_days": 0,
      "authors": [
        "Kamille Bidan"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:a6b233c22a6c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Topology/CantorBendixson): add iterated derived sets and perfect kernel (#37376)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/a6b233c22a6c17c412ebd5c31dd4235927368d3c"
    },
    {
      "age_days": 0,
      "authors": [
        "Bingyu Xia"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:530c505eca7d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(RingTheory/MvPowerSeries): multivariable power series ring is a noetherian ring when the index is finite (#40205)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/530c505eca7d1431ff06275e3bd377cf940e5c52"
    },
    {
      "age_days": 0,
      "authors": [
        "David Loeffler"
      ],
      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:55b7917b4724",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(NumberTheory/LSeries): Define the L-series of a modular form (#31187)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/55b7917b472489c7c56a0fa6393af05cfd536599"
    },
    {
      "age_days": 0,
      "authors": [
        "Nicola Falciola"
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      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:f2d15f30b3be",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Algebra/FreeAbelianGroup/Finsupp): rw a as sum over the elements in its support (#40288)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/f2d15f30b3beb63a70672caee898437e0a61e2e9"
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    {
      "age_days": 0,
      "authors": [
        "Yongle Hu"
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      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:3dfea7c0c262",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: doc(RingTheory/Ideal/IsPrincipal): fix a typo in the module docstring (#41970)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/3dfea7c0c262200402250f503f76826c50e08fcd"
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      "age_days": 0,
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        "mathlib-update-dependencies[bot]"
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      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1e3b447b6258",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-07-21 (#41977)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/1e3b447b6258c052c9a666c9d392bd6ba5c9433b"
    },
    {
      "age_days": 0,
      "authors": [
        "Oliver Nash"
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      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:6e593caa39bb",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: make Cartan subalgebra a parameter of `LieAlgebra.Basis` rather than field (#41972)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/6e593caa39bbd85e5b437ad7e69eb2e5beb1e0fa"
    },
    {
      "age_days": 0,
      "authors": [
        "Thomas Browning"
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      "content_date": "2026-07-21",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:bc63109edf78",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-21",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(RingTheory/Localization/Integer): fix typo in theorem name (#41897)",
      "updated": "2026-07-21",
      "url": "https://github.com/leanprover-community/mathlib4/commit/bc63109edf7834d3037842895ad82b7602b1c1f6"
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    {
      "age_days": 0,
      "authors": [
        "Nailin Guan"
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Geometry/Euclidean/Sphere): drop unneeded distinctness hypothesis (#41582)",
      "updated": "2026-07-20",
      "url": "https://github.com/leanprover-community/mathlib4/commit/c732b96d05efdb1fb84511dfdc24a8f70005ae99"
    },
    {
      "age_days": 1,
      "authors": [
        "Snir Broshi"
      ],
      "content_date": "2026-07-20",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:b9a117e2e3e3",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-20",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Combinatorics/SimpleGraph/Finite): fix `Fintype` instances in `edgeFinset_inf` (#41789)",
      "updated": "2026-07-20",
      "url": "https://github.com/leanprover-community/mathlib4/commit/b9a117e2e3e3a0443ee381bd514bcbff36b51950"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:263276d3777f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: validate `[grind homo]` theorems (#14452)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover/lean4/commit/263276d3777fbdc560181903085d25e94cda14c5"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2cf39b81995e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `[grind homo_pred]` attribute (#14451)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover/lean4/commit/2cf39b81995e4c97c08bb5d54adae45bb8bb0f62"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:5772089c4134",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add `[grind homo]` and `[grind homo_pred]` (#14454)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover/lean4/commit/5772089c41349fc2e3e40b1d885bd90ca31db99f"
    },
    {
      "age_days": 2,
      "authors": [
        "Michael Rothgang"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:d0f60b500739",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: sections of a fiber bundle with `Subsingleton` fiber are smooth and differentiable (#41027)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/d0f60b50073983b3f2ab5b5ba68632cb7e9c0a54"
    },
    {
      "age_days": 2,
      "authors": [
        "Paul Cadman"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:c2ea7ca1e55e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: add theorem that Bird's determinant algorithm computes Matrix.det (#41160)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/c2ea7ca1e55ede82135eb79555926975d87bd264"
    },
    {
      "age_days": 2,
      "authors": [
        "rshlyakh"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:8c79cb4f540e",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal): add Algebra.HasGoingUp (#40911)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/8c79cb4f540eeb519b1a2187009a1916521fd168"
    },
    {
      "age_days": 2,
      "authors": [
        "Bhavik Mehta"
      ],
      "content_date": "2026-07-19",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:d0060d7bbba5",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-19",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(Data/Finset/Card): iterating a function's image on a finite set stabilises (#38488)",
      "updated": "2026-07-19",
      "url": "https://github.com/leanprover-community/mathlib4/commit/d0060d7bbba57d53450b2ebe84d015f5e926793a"
    },
    {
      "age_days": 1,
      "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": 1,
      "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": "2607.16997",
      "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": 4,
      "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": 5,
      "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"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.13612",
      "authors": [
        "Fabio Arnez",
        "Alexandra Gomez-Villa"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.13612",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [
        "lean_formal_proving_agents",
        "negative:vision_world_models"
      ],
      "published": "2026-07-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle. We show that the choice of anti-collapse regulariser determines whether a JEPA's training objective, a prediction loss plus a weighted embedding regulariser, is a valid Active Inference (AIF) variational free energy. We organise four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, and show that the gap's sign, whether the estimator bounds the latent entropy from above or below, decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist a safe lower bound, and SIGReg eliminates the gap. We then prove a correspondence theorem: under the standard constant-noise encoder model and successful SIGReg enforcement (isotropic-Gaussian embeddings), the gap vanishes, the objective becomes an exact information bottleneck, the surprise bound is preserved, and the latent goal cost becomes an exact proxy for AIF pragmatic value, whereas VICReg leaves an irreducible second-order anisotropy term. We extend the correspondence to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime, and we identify the one AIF term no current JEPA world model computes: the state-epistemic value, a future-state coverage signal. The predictions differ in kind, not degree, and are stated here as theoretical consequences left for empirical test in separate work; full proofs are in Appendix A, and the algebraic core of every result is machine-verified in Lean 4 (Appendix D).",
      "title": "The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.13612"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.14015",
      "authors": [
        "Harrison J. Piehowski"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.14015",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Inspired by the notion of tricolorability of knots, we introduce the concept of lean coloring for hypergraphs and the associated lean number of a hypergraph. Lean coloring often involves very few colors, yet still requires the methods of usual graph coloring, forcing the overall complexity to be NP-Hard. We provide two alternative formulations of the lean coloring problem that involve a type of coloring on abstract simplicial complexes and a partial coloring on bipartite graphs. We then provide bounds for the lean numbers of hypergraphs that are $k$-uniform, $k$-partite, wide-path connected, or $r$-complete. Python-like script is included to allow the implementation and study of a lean coloring algorithm. We conclude with some directions for future work and present the lean numbers of $130$ knots and links.",
      "title": "The Lean Number of a Hypergraph",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.14015"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.13662",
      "authors": [
        "Mario Carneiro",
        "Thierry Coquand",
        "Adrien Frabetti Mathieu",
        "Meven Lennon-Bertrand",
        "Paul-André Melliès",
        "Stephanie Weirich"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.13662",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We contribute a new proof technique, based on domain theory, to prove key meta-theoretic properties of dependent type systems: definitional inversion properties, i.e. injectivity and no-confusion of type constructors. This proof technique is independent of normalisation, and indeed applies even for the \"type-in-type\" rule of Martin-Löf's original type theory. Our proof is the first to establish injectivity of type constructors for such a system in the presence of $η$ laws. More generally, the technique is motivated by, and intended for, the metatheory of systems such as Idris, Lean, or dependent Haskell, whose underlying type theory is known to be non-normalising, as well as projects such as MetaRocq or Lean4Lean, where Gödel's second incompleteness theorem means we cannot show normalisation of the object logic in itself. We showcase the method on a small type theory, then explain how it extends to more ambitious extensions.",
      "title": "Definitional Inversion, Without Normalisation",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.13662"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.13896",
      "authors": [
        "Angelo F. Andreoli",
        "Gabriela B. Ribeiro",
        "Guilherme C. Stumpf",
        "Maria F. L. Valverde",
        "Gustavo Bertoli",
        "Vinícius P. Bacurau",
        "David D. S. Silva",
        "Pedro H. F. Oliveira",
        "Eric M. Mazzer",
        "Mamta Silwal",
        "Garritt J. Tucker",
        "Rodrigo Freitas",
        "Martin Sahlberg",
        "Daniel Miracle",
        "Francisco G. Coury"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.13896",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Chemical short-range order (CSRO) is an intrinsic feature of complex concentrated alloys (CCAs), yet its influence on deformation mechanisms is controversial because of the inconclusive state of concurrent CSRO quantification during deformation. Here, we provide experimental evidence that CSRO acts as an intrinsic thermodynamic state variable governing stacking-fault energetics and deformation pathways in a Co30Cr40Ni30 alloy. By comparing quenched (CSRO-lean) and aged (CSRO-enriched) conditions with equivalent grain structure and phase constitution, we isolate the influence of atomic-scale chemical ordering on mechanical behavior. Calorimetry confirms reversible CSRO formation, while synchrotron X-ray diffraction and electron microscopy reveal that CSRO suppresses deformation-induced fcc-hcp martensitic transformation at both room and cryogenic temperatures. Despite differences in transformation dynamics, the macroscopic tensile response is still broadly similar. Atomistic simulations show that CSRO increases both stable and unstable stacking-fault energies, raising the energetic barrier for partial-dislocation activity and stabilizing the fcc lattice against transformation. Together, the experimental and computational results establish CSRO as an added degree of freedom for tuning stacking-fault energetics and controlling deformation pathways in complex concentrated alloys.",
      "title": "Chemical short-range order controls deformation pathways in a complex concentrated alloy",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.13896"
    },
    {
      "age_days": 6,
      "arxiv_id": "2607.14082",
      "authors": [
        "Lei Zhang",
        "Yusheng Zhao",
        "Hongshun Yao",
        "Xin Wang"
      ],
      "content_date": "2026-07-15",
      "freshness": "fresh",
      "id": "arxiv:2607.14082",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-15",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Large language models are increasingly assisting with demanding formal theorem-proving tasks, particularly when grounded in machine-checked libraries such as Lean. Agentic systems further amplify this process by searching, reusing, and extending existing formal developments to uncover new discoveries. In quantum computing, Shor's algorithm and its variants present such a demanding case for Lean formalization. In this work, we formalize this algorithm family in Lean through agentic formalization: software agents analyze sources, write Lean code and repair proofs, with human review of the scientific claims and machine checking of the resulting formal proofs. Our formalization develops the mathematical foundations for analyzing quantum attacks in two cryptographic settings: a 2048-bit modulus in the RSA-2048 and the standardized elliptic curve over a 256-bit prime field (P-256). To support these analyses, the formalization ranges from quantum algorithms for order finding to reversible quantum circuits for modular and elliptic-curve arithmetic. Based on [Quantum 5, 433] and [ASIACRYPT 2017, 241--270], we formalize the logical resource estimates for RSA-2048 and P-256, respectively, and provide additional estimates of classical operations. We expect the results pave the way for broader machine-checked quantum cryptanalysis and represent a step toward AI-assisted design and verification of quantum algorithms.",
      "title": "Building Shor's Algorithm in Lean: An Agentic Formalization of Quantum Attacks on RSA-2048 and P-256",
      "updated": "2026-07-15",
      "url": "https://arxiv.org/abs/2607.14082"
    },
    {
      "age_days": 7,
      "arxiv_id": "2607.13159",
      "authors": [
        "Claudia Alfes",
        "Ken Ono",
        "Ashvin Swaminathan"
      ],
      "content_date": "2026-07-14",
      "freshness": "fresh",
      "id": "arxiv:2607.13159",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-07-14",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "When $m = 1$, the Dyson rank generating function is a classical bridge between partition theory, Ramanujan's mock theta functions, and the theory of harmonic Maass forms and nonholomorphic Jacobi forms. The rank is a statistic on partitions, and the higher Dyson systems, for $m \\geq 2$, are a natural multivariable refinement of it, combining $m$ graded rank contributions. Unlike the classical case, these higher systems are not expected to fit the mock-modular framework, which raises the question of what analytic structure governs them. We show that their root-of-unity specializations carry a hidden elliptic structure. A finite $q$-difference recurrence produces an explicit polynomial obstruction to the expected index $m$ elliptic transformation law, and because the obstruction is finite, its partial fractions canonically determine finitely many Appell--Lerch correction terms that remove it. The corrected functions satisfy a twisted index $m$ elliptic law; a natural translation removes the twist, and their holomorphic finite parts admit finite theta decompositions. Thus, the natural analogue of Dyson's mock-modular phenomenon at higher $m$ is not mock modularity but a finite theta decomposition governed by an index $m$ elliptic transformation law. These results grew out of a human--AI collaboration, and the key new formulas were formalized and machine-verified in Lean/Mathlib by AxiomProver.",
      "title": "Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks",
      "updated": "2026-07-14",
      "url": "https://arxiv.org/abs/2607.13159"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}