{ "counts": { "adjacent": 15, "core": 2, "errors": 0, "negative": 67, "total": 84 }, "date": "2026-07-20", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-20T16:58:58Z", "items": [ { "age_days": 7, "arxiv_id": "2607.11258", "authors": [ "Burak S. Akbudak", "Zeynel A. Uluşan", "Can S. Erer", "Gözde Gül Şahin" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11258", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-13", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Tree search algorithms enable systematic exploration of the proof space in neural theorem proving. Existing LLM tree search libraries primarily target natural language reasoning and do not provide native integration with formal verifiers, while theorem proving systems often rely on task-specific search implementations. We introduce TreeThink, an open-source Python library for modular, fully asynchronous tree search in neural theorem proving. It integrates established tree search methods with vLLM-based inference pipelines and diverse node evaluation techniques, ranging from lightweight heuristics to neural evaluators. We support Lean~4, Rocq, and Isabelle/HOL alongside natural language. It connects directly to each language's Read-Eval-Print Loop (REPL) server for real-time verification and proof state extraction. We evaluate TreeThink on miniF2F and MATH500, demonstrating cross-language formal proof search, natural language reasoning support, and up to 6.3$\\times$ wall-clock speedup from asynchronous execution. Source code is released under the MIT license at https://github.com/GGLAB-KU/treethink , and the library is accessible as a downloadable package at https://pypi.org/project/treethink/ .", "title": "TreeThink: A Modular Tree Search Library for Mathematical Reasoning with LLMs", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11258" }, { "age_days": 7, "arxiv_id": "2607.11307", "authors": [ "Tian-Shuo Liu", "Shiyuan Zhang", "Zijie Geng", "Haoyu Liu", "Runjie Xu", "Pengyuan Wang", "Lei Yuan", "Yang Yu" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11307", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-07-13", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning. Unlike statement-level formalization, proof autoformalization is a long-horizon challenge requiring coordination of claims, contexts, and dependencies across many proof steps, yet has only recently come under focused study. Current approaches either rely on costly model training or apply excessive, unguided repair at inference time. To this end, we introduce ToMap, a multi-agent framework that structures proof autoformalization as a Decomposer-Formalizer-Prover pipeline with efficient test-time optimization guided by formal verification and semantic rubrics for proof quality. Rather than distributing test-time compute across all agents, we perform bottleneck analysis and identify the Decomposer as the critical bottleneck: the quality of its atomic, self-contained proof units directly determines whether downstream agents can successfully formalize and prove each step. ToMap therefore treats the Formalizer and Prover as downstream executors and efficiently focuses test-time compute on Decomposer refinement. This refinement follows a loop inspired by GEPA, evolving prompts over candidate decompositions and using formal verification progress together with semantic proof rubrics to define a Pareto frontier that guides the next decomposition update. Experiments on ProofFlowBench show that ToMap improves over the best previous method by 19.0% when evaluated by both syntactic correctness and semantic faithfulness, while requiring lower test-time cost. Scaling analysis shows that most gains emerge within a few iterations of decomposition evolution, guiding test-time budget selection.", "title": "Efficient Test-Time Optimization for Multi-Agent Proof Autoformalization", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11307" }, { "age_days": 3, "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": "2607.13225", "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": 8, "arxiv_id": "2607.10654", "authors": [ "Mahadee Al Mobin", "Md. Shariful Islam" ], "content_date": "2026-07-12", "freshness": "fresh", "id": "arxiv:2607.10654", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-12", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Let $S_n=\\{p\\in\\mathbb{P}:p<10^n\\}$, $N_n$ denote the total number of decimal digits occurring in the primes of $S_n$, $C_n(d)$ be the number of occurrences of a digit $d\\in\\{0,\\ldots,9\\}$ among those digits, and $P_n(d)$ be the probability of occurrence of a digit, $d$ among those digits. We prove that \\[ P_n(d)=\\frac{C_n(d)}{N_n} =\\frac{1}{10} +O\\!\\left(\\frac{\\log n}{n}\\right), \\qquad n\\to\\infty, \\] uniformly for every decimal digit $d$. The argument is entirely unconditional and combines the Prime Number Theorem, the Erdős--Turán discrepancy inequality, and classical Vaughan--Vinogradov estimates for exponential sums over primes. The principal step establishes quantitative equidistribution for interior digit positions, while the logarithmically many exceptional positions near the ends of the decimal expansion are shown to have asymptotically negligible influence after averaging over all digit positions and prime lengths. Consequently, the decimal digits occurring in primes, when pooled over all positions and all primes below $10^n$, become asymptotically equidistributed. We also clarify the precise scope of the theorem by distinguishing this averaged equidistribution result from the substantially stronger and presently unresolved questions concerning pointwise digit equidistribution, normality, and higher-order digit correlations in the sequence of prime numbers.", "title": "The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers", "updated": "2026-07-12", "url": "https://arxiv.org/abs/2607.10654" }, { "age_days": 3, "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": "2607.15174", "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": 4, "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": 4, "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": 5, "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": 5, "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": 5, "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", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "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": 6, "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" ], "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": 6, "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", "matched_signals": [ "lean_formal_proving_agents" ], "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": "2026-07-14", "url": "https://arxiv.org/abs/2607.13165" }, { "age_days": 6, "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": 6, "arxiv_id": "2607.12650", "authors": [ "Junyu Ren" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12650", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-14", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny. We present EG-VAR (Evidence-Grounded Verified Agentic Reasoning), a Lean 4-based tool-calling architecture in which the Lean kernel is the sole minter of Verified claims via tool-attestation axioms and declared source lifts. Every verified output structurally descends from an attested tool call (Thm. 3.1) and a kernel-checked chain of valid inference (Thm. 3.2); residual outputs are honest Abstain with a replayable audit trail. On a subcollection of TableBench numerical reasoning (n=120), EG-VAR attains 120/120 versus a 95% same-tool baseline; on counterfactual stress tests (5 domains x 2 models), EG-VAR stays 100% source-faithful while same-tool drops to 80-90% (no-tool 50-80%). With the LLM as deployment-time formalizer, residual semantic-formalization error is 3.3% on Sonnet and 1.7% on Opus. We position EG-VAR as a technical-governance interface for high-stakes empirical claims: a formal sidecar makes the target proposition, source scope, evidence boundary, proof obligation, and abstention condition auditable, eliminating unsupported Verified outputs today while turning formalization errors, lift and source-authority disputes, ambiguities, and abstentions into explicit audit targets. Over time, typed sidecars in datasets, APIs, public records, and AI-generated documents can amortize this formalization burden into reusable infrastructure.", "title": "Evidence-Grounded Verified Agentic Reasoning: A Path Toward Eliminating LLM Hallucination in Empirical Inference via Tool-Attested Kernel Proofs", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12650" }, { "age_days": 6, "arxiv_id": "2607.12981", "authors": [ "Mingrui Jing", "Lei Zhang", "Yusheng Zhao", "Hongshun Yao", "Xin Wang" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12981", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-14", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A central model in quantum machine learning is the quantum neural network (QNN), whose design requires balancing expressivity and trainability. Technically, expressivity is studied through circuit-function analysis, such as quantum signal processing, while trainability is analyzed using dynamical-Lie-algebra (DLA) methods. To support certified QNN design, we formalize these major components of QNN theory in a connected lean 4 development checked by a proof kernel, where every analytic input is either proved or exposed as a named hypothesis. On the expressivity side, we prove exact if-and-only-if characterizations of single-qubit QNNs, a resource-counted quantum phase processing theorem, and an overparameterization ceiling that bounds the quantum Fisher information rank by the DLA dimension. On the trainability side, we derive the direct-sum loss-variance law through a de-circularized second-moment interface. A parameterized Casimir-uniqueness engine discharges the required inputs for fully controllable, orthogonal, and matchgate circuit families, while single-qubit and product-Clifford ensembles close the two-design assumptions directly. A capstone theorem pairs the conditional variance law with exact loss reconstruction in DLA coordinates. The development record identifies eight corrections and clarifications that were not explicit in the informal arguments. We expect this work to provide a machine-checkable foundation for QNN theory and a step toward AI-assisted or automated design of quantum machine learning algorithms.", "title": "An Agentic Formalization for Certified Quantum Neural Network Design", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12981" }, { "age_days": 0, "authors": [ "Eric Wieser" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:33ae929879bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "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_decode_io_error` (#14423)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/33ae929879bfcec8c4bceadf3dbc91172b36365f" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:e1832d77d528", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `checkUnivs` takes other declarations and constructors into account (#14418)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/e1832d77d52843fb3e3470b6fe088c103a41c335" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:9a61e8345759", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: two-phase stateful linters (#14357)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/9a61e83457592524905308f1fb63b4a5ebdcebd1" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:29f574e27632", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: rename `[grind homo]` to `[grind hom]` (#14464)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/29f574e27632cb6df7a36c4d460e89fe0180a138" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:5ea1d325e15f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: record `[grind homo]` source types (#14457)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/5ea1d325e15ffa9fadba8308e1e560d4c9fec3be" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:1e207c48002b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lemmas about `Nat.nextPowerOfTwo` (#14458)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/1e207c48002b2c41a0deb304013532df64c99be7" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:323137b02236", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: drop internal-lemma references from `repeatM` docstrings (#14436)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/323137b022369d56a044ae5af01d1efd55872361" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:f3499e30634f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/f3499e30634f62806d97c51986f1a22418aae9da" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:e300ebc28765", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: revert \"fix: avoid the non-thread-safe `strerror` in `lean_deode_io_error` (#14423)\" (#14463)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/e300ebc2876521e1496db824fa4ad0cf9fc49be5" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover/lean4:19893d5cceb2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: avoid `grind` in core (#14455)", "updated": "2026-07-20", "url": "https://github.com/leanprover/lean4/commit/19893d5cceb2b7f974491e0d687c786fd68828fd" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4cb03f453732", "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: style: fix spacing around left arrows (#41937)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/4cb03f453732be00b43b623661457188c10c1149" }, { "age_days": 0, "authors": [ "David Kurniadi Angdinata" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:169c26b52a38", "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: refactor: rename restrict to domRestrict (#25980)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/169c26b52a38b704fad2c009372d76844a059bdf" }, { "age_days": 0, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:25b5fe90757b", "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: fix: add an adaptation note as a followup to the 4.33.0-rc1 bump (#41837)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/25b5fe90757b65d5d4e5edcd863a8293f34710ae" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:888e057fda8a", "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: feat: `Commute` and `IsCoprime` are `Std.Symm` (#41612)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/888e057fda8ac936fe2f6514937c5b78cb9c3d87" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4608056c77c5", "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: feat(NumberTheory/Height/NumberField): the absolute height of an algebraic number (#41605)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/4608056c77c52468b80773e8dcd585ef821c7c5e" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:970ca71b97ed", "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: feat(Combinatorics/SimpleGraph/Walk): relate `edges` and `darts` (#41720)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/970ca71b97ed15739cd2646bb2eb0f15724a8fc5" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b300f2cccef4", "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: feat(Combinatorics/SimpleGraph/Basic): `Disjoint` for graph sets (#41795)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/b300f2cccef44f3a31377e8dccfe366fa956902c" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fb6b1ce3f5e9", "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: feat(Combinatorics/SimpleGraph): basic `Adj.toWalk` API (#41797)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/fb6b1ce3f5e96319e0b29f9badf9b969fd8a3b9c" }, { "age_days": 0, "authors": [ "danderson70-UNL" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4b382654e5b6", "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: doc(RingTheory/MvPowerSeries/Evaluation): fix typo (#41836)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/4b382654e5b6ee85dd23c9ab6e8add18c241ab11" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-07-20", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c732b96d05ef", "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(Geometry/Euclidean/Sphere): drop unneeded distinctness hypothesis (#41582)", "updated": "2026-07-20", "url": "https://github.com/leanprover-community/mathlib4/commit/c732b96d05efdb1fb84511dfdc24a8f70005ae99" }, { "age_days": 0, "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": 1, "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": 1, "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": 1, "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": 1, "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": 1, "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": 1, "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": 1, "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, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-07-19", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cb31bafb0930", "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: chore(scripts): update nolints.json (#41908)", "updated": "2026-07-19", "url": "https://github.com/leanprover-community/mathlib4/commit/cb31bafb093067f5ec7df56724cf708940124295" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:bb32c6c88fde", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: for issues #14440 (#14445)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/bb32c6c88fdea2807b442275dbc3b8709fa245a3" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:5adc1e70895c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: restore ambient exporting scope in `mkAuxDefinition` (#14442)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/5adc1e70895ce44e2fa3f5141c06afd1f8276666" }, { "age_days": 2, "authors": [ "Aaron Liu" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:79d62bdacf81", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: pretty printing of `@[simp ←]` (#14367)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/79d62bdacf81ebe1ef583cd1be287a177bfd2cd2" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:49ff95727f98", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: don't resynthesize unwrapped nested proofs in the grind canonicalizer (#14439)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/49ff95727f98d43984726b26742d17a1ceea9dd5" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:ca190c9f5955", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: avoid expensive `isDefEqD` in `grind` (#14444)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/ca190c9f5955267ca3168454317fd3aeae8f7476" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover/lean4:5fe1ea9510d0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `[grind homo]` attribute (#14446)", "updated": "2026-07-18", "url": "https://github.com/leanprover/lean4/commit/5fe1ea9510d0a6a9a531920bfc044d80b3d67b8d" }, { "age_days": 2, "authors": [ "Thomas Browning" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:abb22825db7e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Localization/Integer): cardinality of `finsetIntegerMultiple` (#41688)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/abb22825db7e020c94f38a007ae3fffe6c3a7532" }, { "age_days": 2, "authors": [ "TJHeeringa" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9e039082d06a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed): add additional symm lemmas (#41149)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/9e039082d06a42911856d23d9adb22342796bd74" }, { "age_days": 2, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f10b8a1610b7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Convex/TotallyBounded): strengthen to an iff (#41226)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/f10b8a1610b7e4f55019a86bff5ca9d553b96b9b" }, { "age_days": 2, "authors": [ "Kim Morrison" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0ce75b01aba1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: fix typos in SimplicialSet docstrings (#41571)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/0ce75b01aba167cf198469d268db587948f44e5a" }, { "age_days": 2, "authors": [ "Attila Gáspár" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c81c5cbb1cbf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: fix the docstring of `IsTopologicalTorsor` (#41780)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/c81c5cbb1cbf71482901fd2f72ab66909ac54fe1" }, { "age_days": 2, "authors": [ "Kim Morrison" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:168b9f3a7b2a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: fix composition order in Presieve.pullback docstring (#41573)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/168b9f3a7b2a75315d46232ec28c97f66a467c61" }, { "age_days": 2, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f041774a2d62", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "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 2026-07-18 (#41901)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/f041774a2d6216174f56771a5e40e444b3a78f8a" }, { "age_days": 2, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1a9188a86477", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "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 2026-07-18 (#41894)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/1a9188a8647774da43efde12a5657f72b6f2ed67" }, { "age_days": 2, "authors": [ "Bhavik Mehta" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a68722614ca0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(SpecialFunctions/Log): fix naming typo (#41773)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/a68722614ca0ed25121e45d1295916a210f4b1b0" }, { "age_days": 2, "authors": [ "Snir Broshi" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ba2ac755bd0a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/Polynomial/Basic): golf `degreeLTEquiv` (#39514)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/ba2ac755bd0af40f773715e03e290d8ef9f73e72" }, { "age_days": 2, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:83a4552f285f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(MathlibTest): fix defLemma warnings (#40593)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/83a4552f285feb130cff762452c122a35c70e704" }, { "age_days": 2, "authors": [ "Bolton Bailey" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ecc9242d0502", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Vector): add `grind` to cons lemmas (#39098)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/ecc9242d05028b378accc9012574a95bb5aa5382" }, { "age_days": 2, "authors": [ "Artie Khovanov" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:be529d501846", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/SetLike/Basic): generalise instance (#40025)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/be529d50184614ea1391c2d5fcce169c89c59b7e" }, { "age_days": 2, "authors": [ "Kim Morrison" ], "content_date": "2026-07-18", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5f6fd26f8a2e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-18", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(AlgebraicTopology/Reedy): cosmetic cleanups (#41581)", "updated": "2026-07-18", "url": "https://github.com/leanprover-community/mathlib4/commit/5f6fd26f8a2e331274b6ce3103aaadca3cd2a33a" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "github:leanprover/lean4:5e4e690888b6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-17", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: drop the structural-combinator fast path in vcgen (#14433)", "updated": "2026-07-17", "url": "https://github.com/leanprover/lean4/commit/5e4e690888b6a1f3eb9c97b85753688c25d9ac31" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "github:leanprover/lean4:a8be62375b3b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-17", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: drive lattice saturation with Sym.simp rewriting (#14434)", "updated": "2026-07-17", "url": "https://github.com/leanprover/lean4/commit/a8be62375b3bef1a95967304b41933700b65647f" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "github:leanprover/lean4:42de3640be30", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-17", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: over-specialized backward rules in `vcgen`'s spec rule cache (#14431)", "updated": "2026-07-17", "url": "https://github.com/leanprover/lean4/commit/42de3640be30612edf12cb163c7fb6d3bae4fa20" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "github:leanprover/lean4:b9c91298fc96", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-17", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: don't expose inferInstanceAs wrapping aux defs for non-exposed types (#14437)", "updated": "2026-07-17", "url": "https://github.com/leanprover/lean4/commit/b9c91298fc961122eadfdf4ff2a3ee4ce6c2071b" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-17", "freshness": "fresh", "id": "github:leanprover/lean4:51b8e4a6e9d5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-17", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: apply specs with conjunctive preconditions without frame inference (#14383)", "updated": "2026-07-17", "url": "https://github.com/leanprover/lean4/commit/51b8e4a6e9d542e705c0e1d8e7a171603fc1b255" }, { "age_days": 4, "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": 5, "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": 5, "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": 5, "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": 5, "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": 5, "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": 6, "arxiv_id": "2607.12873", "authors": [ "Evan Chen", "Ken Ono", "Michal Mogielnicki" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12873", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-14", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Amdeberhan, Shareshian, and Stanley recently proved that a function $\\varphi$ arising in the theory of partition Eisenstein series counts the alternating permutations of $\\{1,\\dots,2n\\}$ with a given `record' partition, and they asked whether there is a similar theory for record compositions, suggesting a role for noncommutative symmetric functions. Here we solve their open problem by showing that the number of alternating permutations of $\\{1,\\dots,2n\\}$ with record composition $(α_1,\\dots,α_\\ell)$ is \\[ \\prod_{j=1}^{\\ell}\\binom{2s_j-1}{2α_j-1}E_{2α_j-1}, \\] where $s_j=α_1+\\dots+α_j$, $E_k$ is an Euler number, and the record composition of $w=a_1a_2\\dots a_{2n}$ (so $a_1>a_2\\dotsb$) lists the factor lengths obtained by cutting $a_1a_3\\dots a_{2n-1}$ before each left-to-right maximum other than the first. These numbers are the coefficients of a natural lift of the degree-$n$ sprout symmetric function with seed $\\sec(\\sqrt{t}\\,)$ to noncommutative symmetric functions, expanded in products of noncommutative power sums of the first kind. An analogous refinement holds for every sprout sequence whose seed is given by the exponential formula. AxiomProver autonomously produced and verified the results in this paper in Lean.", "title": "Record compositions of alternating permutations and noncommutative symmetric functions", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12873" }, { "age_days": 6, "arxiv_id": "2607.12226", "authors": [ "Jam Kabeer Ali Khan", "Petros Markopoulos", "Nico Lehmann", "Ranjit Jhala" ], "content_date": "2026-07-14", "freshness": "fresh", "id": "arxiv:2607.12226", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-14", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "SMT-based program verifiers are hamstrung by two problems: expressiveness, because predictable verification restricts to the boundaries of SMT decidability, and trust, because the solver is a large, unverified artifact whose soundness bugs may quietly compromise every tool built on it. We present FLEX, a foundational Constrained Horn Clause (CHC) solver implemented in LEAN, that reduces the trusted base to the kernel alone, and allows using LEAN's entire proof ecosystem to verify low-level systems code, via three contributions. First, FLEX encodes CHCs as plain LEAN propositions where the Horn variables are existentially bound predicates, and shows how to implement CHC solvers as tactics (meta-programs) that compute kernel checkable proofs of the CHC propositions. Second, we show how to implement two verified CHC generators in LEAN: a Floyd-Hoare style generator for an imperative language, and a refinement-type-based generator for a functional calculus, which can be composed with the solving tactics to yield the first end-to-end foundational CHC-based verifiers. Finally, we show how FLEX allows us to leapfrog the expressiveness limitations of SMT by unleashing LEAN's entire ecosystem of proof machinery to prove arbitrary functional correctness properties of various low-level Rust libraries using the FLUX refinement type checker, and demonstrate the viability of FLEX as a trustworthy CHC backend, by showing it automatically discharges 95.7% of the CHCs from FLUX's benchmark suite.", "title": "Foundational Constraint Solving for Expressive Refinement Typing", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.12226" }, { "age_days": 6, "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" }, { "age_days": 7, "arxiv_id": "2607.11648", "authors": [ "Ralf Stephan" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11648", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Write $(3/2)^n = m_n + \\eps_n$ with $m_n$ the nearest integer and $\\eps_n\\in[-\\tfrac12,\\tfrac12)$, and let $T=(t_n)$, $t_n=2m_{n+1}-3m_n$, be the resulting \\emph{steering word}: the step-by-step record of the map $x\\mapsto\\tfrac32 x$ on the orbit of $1$, coded by nearest-integer rounding. Using results by Corvaja--Zannier and Nair--Kumar--Rout we prove that the subword complexity $\\pT(k)$ of $T$ is superlinear, $\\pT(k)/k\\to\\infty$. The argument is completely formalized in Lean-4, depending only on the Subspace Theorem.", "title": "Superlinear complexity of the $(3/2)^n$ steering word", "updated": "2026-07-14", "url": "https://arxiv.org/abs/2607.11648" }, { "age_days": 7, "arxiv_id": "2607.12221", "authors": [ "Grace Barkhuff", "Ian Pruitt", "William Gregory Johnson", "Rodrigo Borela", "Ben Rydal Shapiro", "Anu G. Bourgeois" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.12221", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Industry is leaning into generative artificial intelligence (GenAI), and higher education is under pressure to prepare graduates for a GenAI-augmented workforce. Yet, there is still no clear structure for defining AI readiness across disciplines, programs, courses, and assignments. Current approaches often rely on broad institutional policies or individual course-level decisions, which can also create mixed messages for students, fragmented expectations across programs, and limited visibility for university leaders. In this paper, we argue that higher education needs a more coherent way to connect institutional priorities to curriculum-level action. We propose Program-Level AI Learning Outcomes (PLAI-LOs) as a framework for defining what students graduating from a program should know and be able to do with, without, and about GenAI in a given discipline. The PLAI-LOs framework complements existing program-level learning outcomes and supports alignment across institutional priorities, program-level AI learning outcomes, course-level learning outcomes, and assignment-level objectives. We illustrate the framework with examples from computing and music and show how PLAI-LOs can be implemented through artifact-level GenAI policies, helping programs decide where GenAI should be taught and used, and when students should be expected to work without GenAI. We offer PLAI-LOs as a concrete, measurable, and adaptable path for moving higher education from scattered GenAI rules toward a strategy with clear, learning-centered alignment.", "title": "From Chaos to Clarity: A Framework for Program-Level AI Learning Outcomes", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.12221" }, { "age_days": 7, "arxiv_id": "2607.11376", "authors": [ "Jeffrey Kuan" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11376", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The type D ASEP is an asymmetric two--species interacting particle system on $\\Z$, in which two separately conserved species hop, bind into a composite ``bound pair'', and split. The model, along with its reversible measures and orthogonal polynomial duality, was constructed using the representation theory of $U_q(\\so_{2n})$. The reversible measures and orthogonal polynomial duality are each a product of two copies of the single-species ASEP reversible measures and orthogonal polynomial duality. In this paper, we study the long-time asymptotics of the type D ASEP. In the fixed--$q$ regime, using an exact current--decoupling identity, we prove that the asymptotic hydrodynamic limit and Tracy--Widom fluctuations decouple, as predicted from the duality. In the weak--asymmetry (Edwards--Wilkinson) regime, when $q=1-c/N^2$, we prove that the two density fluctuation fields \\underline{decouple}: each converges to a linear stochastic heat equation, with no cross--coupling in either the drift or the noise, the limiting noises having vanishing cross--correlation. More surprisingly, we then prove that the two limiting normal random variables are \\underline{correlated} with a seemingly new correlation function. The correlation is exactly equal to $(1-e^{-4c})/(4c)$, with the positive parts of the normal random variables having correlations expressed by the Bessel--Struve function. This paper, with the exception of the abstract and introduction, was written entirely by Claude Opus 4.8 and Fable 5. The proofs were then formalized in Lean, using Aristotle by Harmonic AI. The human author of this paper verified the proofs manually.", "title": "Correlated and uncorrelated long--time asymptotics of type D ASEP", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11376" }, { "age_days": 7, "arxiv_id": "2607.11471", "authors": [ "Dmitry Nikolaev" ], "content_date": "2026-07-13", "freshness": "fresh", "id": "arxiv:2607.11471", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-13", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A lot of research attention has been devoted to checking whether large language models (LLMs) are politically biased. This work has largely focused on high-level ideological dimensions, such as left--right or progressive--conservative, and it has been shown that while LLMs are predominantly left and progressive leaning, largely mimicking the biases in the training data, they can be to some extent steered to change their preferences in post-training. In this short note, we check if LLMs have robust stances with regard to major substantive societal issues, on which members of the same ideological camp are often in disagreement, summarised in a novel dataset \\textsc{HardChoices}. We show that, faced with this line of questioning, LLMs, both large and small, surprisingly rarely declare neutrality, are often incoherent, and demonstrate a remarkable degree of agreement on issues where they do take stances.", "title": "Are LLMs ready for HardChoices?", "updated": "2026-07-13", "url": "https://arxiv.org/abs/2607.11471" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }