{ "counts": { "adjacent": 14, "core": 3, "errors": 0, "negative": 73, "total": 90 }, "date": "2026-08-13", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-13T16:27:03Z", "items": [ { "age_days": 6, "arxiv_id": "2608.07388", "authors": [ "David Muñoz-Lahoz" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07388", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "lean_formal_proving_agents", "mathlib_retrieval" ], "published": "2026-08-07", "score": 9.5, "source": "arxiv-ai4math-core", "summary": "We present a Lean 4 library for the theory of Banach lattices. Its purpose is to support the systematic formalization of contemporary research in Banach lattices and related areas. As evidence of this, we describe three research-level formalizations built using the library. Writing the library at scale was made possible by the use of LLMs with careful human supervision and planning. Unlike autoformalization, this approach allows for an actual understanding of the code. This, in turn, led to new mathematical insights that are also discussed. Judging by the interest expressed by other researchers, we expect the library to become a communal effort in the near future. For this reason, we also describe several parts of the theory that could be added next.", "title": "The Banach lattice Lean library", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07388" }, { "age_days": 2, "arxiv_id": "2608.11394", "authors": [ "Yueke Zhang", "Zihan Fang", "Kevin Leach", "Yu Huang" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.11394", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-11", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Code large language models (LLMs) can generate syntactically plausible programs that nevertheless violate hidden semantic constraints. Existing execution-feedback training methods identify whether a completed program fails, but provide limited supervision about how a correct solution should be organized. We introduce GraphAlignCoder, a training framework that transfers explicit correctness structure into code generation. GraphAlignCoder constructs an implementation graph that captures control and dependence among program regions. In parallel, a constrained Lean pipeline produces proof traces, from which we extract a formal proof-flow graph. The model first learns executable code together with graph-derived descriptions of why individual program regions are correct, and then consolidates this knowledge into code generation. GraphAlignCoder consistently outperforms the base model, code-only SFT, and CodeRL across all benchmarks. Compared with CodeRL, it increases the solved count from 38 to 50 on LiveCodeBench v6 and from 16 to 23 on BigCodeBench Hard, corresponding to relative gains of 31.6% and 43.8%, while also improving BigCodeBench Full from 359 to 363 tasks. The ablation study further shows that verification-graph injection produces the initial reasoning gain, while verification to code consolidation is essential for robust cross-benchmark transfer.", "title": "GraphAlignCoder: Aligning Program and Proof Graphs for Code Generation", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.11394" }, { "age_days": 6, "arxiv_id": "2608.07407", "authors": [ "Heechang Kim", "Ernest K. Ryu", "Shuvomoy Das Gupta" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07407", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-07", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We present AutoOPT, a domain-specific harness for end-to-end automation of optimization research. AutoOPT organizes the discovery of optimal first-order methods into four stages: numerical design through the BnB-PEP methodology; symbolic discovery of the analytic description and a convergence proof through frontier large language models (LLMs); formal verification in the Lean 4 proof assistant; and human interpretation and write-up. We demonstrate the framework on two case studies, each of independent interest. The first, lemniscate acceleration, is a new accelerated gradient method for minimizing the gradient norm of a smooth convex function: after $N$ gradient steps it reduces the squared gradient norm at the optimal $O(1/N^{4})$ rate, with a constant governed by the lemniscate constant $\\varpi$, a classical elliptic-integral constant. The second is the analytic description of ITEM-f, a method previously known only numerically: for $L$-smooth, $μ$-strongly convex minimization it contracts the function-value gap at an accelerated linear rate with a per-step factor $(1-\\sqrt{μ/L})^{2}$. The convergence theorems of both case studies are formalized and machine-checked in Lean 4.", "title": "A Domain-Specific Harness for End-to-End Automation of Optimization Research", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07407" }, { "age_days": 2, "arxiv_id": "2608.11023", "authors": [ "Tomoki Uda" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.11023", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-11", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "For a discrete topological space $D$, let $\\mathrm{Met}(D)$ denote the set of metrics on $D$ that are compatible with the discrete topology, equipped with the topology induced by the supremum distance. Ishiki's Conjecture 5.1 asserts that $\\mathrm{Met}(D)$ is not completely metrizable when $\\lvert D\\rvert = \\aleph_1$. We prove this in ZFC by constructing a set $A \\subseteq [0,1]$ of cardinality $\\aleph_1$ that is not $F_σ$ and embedding its complement as a closed subspace of $\\mathrm{Met}(D)$. The proof has also been formalised in Lean 4.", "title": "On Ishiki's Conjecture: $\\mathrm{Met}(D)$ Is Not Completely Metrizable for $\\lvert D\\rvert=\\aleph_1$", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.11023" }, { "age_days": 2, "arxiv_id": "2608.10894", "authors": [ "Tianjiao Nie", "Ao Zhang", "Yusen Tang", "Damiano Testa", "Shing-Tung Yau", "Peng Li", "Yuan Zhou" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.10894", "kind": "paper", "label": "adjacent", "matched_signals": [ "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-08-11", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Large-scale formalization of advanced mathematics requires more than translating individual statements: it must reconstruct a coherent theory distributed across heterogeneous sources. This process raises four challenges: discovering implicit dependencies, correcting source defects, preserving semantic fidelity, and reconciling cross-source misalignments. We present FormaTheoria, an end-to-end, AI-assisted workflow that coordinates source acquisition, formalization, proof construction, recursive dependency discovery, independent review, and reconciliation, while preserving provenance and protecting approved declarations. A shared agent framework supports long-horizon execution through tool use, context compaction, review-gated termination, section-level source context, and dependency-aware batch parallelization. Applying FormaTheoria to major components of the Classification of Finite Simple Groups (CFSG), we construct a machine-checked Lean development extending through the Bender--Suzuki theorem and encompassing the Feit--Thompson Odd Order Theorem, Glauberman's $Z^*$ theorem, and the Brauer--Suzuki theorem. This development verifies an extensive body of deeply interdependent finite-group theory while providing a foundation for continuing the CFSG formalization. An empirical analysis of the code and recorded construction process supports the practical relevance of the identified challenges and illustrates the roles of the corresponding workflow components. Together, these results demonstrate how AI-assisted workflows can reconstruct mathematically significant formal theories from distributed literature by combining language-model agents with formal verification, structured review, and explicit dependency management.", "title": "FormaTheoria: Constructing Large-Scale Lean Theories from Mathematical Literature $-$ Toward the Formalization of the Classification of Finite Simple Groups", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.10894" }, { "age_days": 3, "arxiv_id": "2608.10288", "authors": [ "Burc Gokden" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "arxiv:2608.10288", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-10", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "The Large Language Model from Power Law Decoder Representations (PLDR-LLM) and its attention, Power Law Graph Attention (PLGA), replace the fixed bilinear form of scaled dot-product attention (SDPA) with a learned, input-generated bilinear operator $G_{LM}$, built from a positive tensor $A_{LM}$ by elementwise power laws. The architecture is fully specified, verified against pinned reference releases; claims are labeled theorem, conditional theorem, measurement, or conjecture. Unconditionally: PLGA contains SDPA exactly at $G_{LM}=I$; $A_{LM}$ and $A_P$ are strictly entrywise positive, with Perron-Frobenius structure on $A_{LM}$; the DAG regularizer has the NOTEARS walk-counting form and positivity obstructs exact acyclicity; and, under nonresonance (satisfied by standard rotary frequencies), a commutant criterion identifies which operators preserve relative-position dependence. An inference-collapse theorem: exact input invariance of deductive outputs collapses inference to generalized SDPA with a constant operator. Measured invariance: relative fluctuations of $10^{-6}$ and below; perturbation bounds quantify but do not certify cached inference; the assembled proxy misses the decoding margin. A conditional three-stage mechanism (rotary twirl, concentration, row-map contraction) is measured on a released checkpoint. Blockwise training and scoring under the global Gram are stated with explicit target exposure; on tested samples, block and sequential scoring select identical answers and agree on the published TruthfulQA probability-mass metric within $5\\times 10^{-5}$ per item. Self-organized criticality enters as a phenomenological framework with an intrinsic order parameter; open claims become falsifiable conjectures. Selected proof cores are machine-checked in Lean 4.", "title": "Power law graph attention: exact generalization of scaled dot-product attention, empirical collapse at inference", "updated": "2026-08-10", "url": "https://arxiv.org/abs/2608.10288" }, { "age_days": 4, "arxiv_id": "2608.08643", "authors": [ "A. Mayeux" ], "content_date": "2026-08-09", "freshness": "fresh", "id": "arxiv:2608.08643", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "verifier_guided_reasoning" ], "published": "2026-08-09", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "The paper \\emph{Conjecture: the set of prime numbers is supernatural} conjectures that no non-constant function built from the identity and constants by finitely many pointwise additions, multiplications, and exponentiations maps every positive integer to a prime. We give a complete Lean~4 formalization of that paper over Mathlib: every definition, example, remark, numbered result, and experimental table row has a machine-checked counterpart, with no \\lcode{sorry}. The conjecture and similar generalizations are stated exactly, as named open problems. So stated, the conjecture becomes a precise target: an automated reasoning system can now attempt a kernel-checked proof.", "title": "The set of primes is supernatural: a Lean formalization of the statement of the conjecture", "updated": "2026-08-09", "url": "https://arxiv.org/abs/2608.08643" }, { "age_days": 1, "arxiv_id": "2608.12242", "authors": [ "Hongru Zhao" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.12242", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-12", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Let $\\widehat R$ be the Pearson sample correlation matrix formed from $n$ independent Gaussian observations in $p$ dimensions, and write $m=n-1\\ge p$. Under the null correlation $R=I_p$, the classical independent beta product, exact cumulants, and full Fourier inversion yield, along every sequence $p\\to\\infty$ with $m\\ge p$, a uniform first Edgeworth expansion for $\\log\\det\\widehat R$, centered by its exact mean and scaled by its exact standard deviation. The expansion identifies the exact finite dimensional skewness correction and gives the sharp Kolmogorov equivalent $A_{m,p}/\\{6\\sqrt{2π}V_{m,p}^{3/2}\\}$, where $V_{m,p}$ is the exact variance and $A_{m,p}$ is the absolute third cumulant. This equivalent unifies the square, fixed gap, growing gap, proportional, and dilute regimes; in the square regime the error has order $(\\log p)^{-3/2}$ with an exact constant. For every positive definite population correlation matrix $R$, we prove a uniform finite sample Berry-Esseen bound that explicitly tracks population dependence. All theoretical results have exact or proved equivalent Lean 4 formulations whose declarations and dependencies are kernel checked.", "title": "Sharp Berry-Esseen Bounds for the Log Determinant of a Gaussian Sample Correlation Matrix", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.12242" }, { "age_days": 1, "arxiv_id": "2608.12280", "authors": [ "Lukas Liehr", "Mitchell A. Taylor", "Peiyang Yu" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.12280", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-12", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We establish a sharp version of Grothendieck's theorem for Bessel sequences. Precisely, given a Bessel sequence $\\{ x_j \\}_{j\\in\\mathbb{N}}$ with Bessel bound $1$ in a Hilbert space, we show that there exists functions $\\{ f_j \\}_{j\\in\\mathbb{N}}$ belonging to the unit ball of $L^\\infty([0,1])$ such that for all $j,k \\in \\mathbb{N}$ one has $$ \\langle x_j,x_k\\rangle = \\int_0^1 f_j(x)\\overline{f_k(x)}\\,dx.$$ As an application, we give an affirmative answer to an extension problem of Olevskii: if $E \\subset [0,1]$ is a Lebesgue measurable set such that $[0,1]\\setminus E$ has positive measure, then every Bessel sequence in $L^2(E)$ with Bessel bound $1$ extends to an orthonormal system in $L^2([0,1])$ that is bounded by the (optimal) constant $λ([0,1]\\setminus E)^{-1/2}$ on $[0,1]\\setminus E$. A formalization of our main result in Lean 4 accompanies the paper.", "title": "Grothendieck's theorem for Bessel sequences", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.12280" }, { "age_days": 2, "arxiv_id": "2608.10572", "authors": [ "Zehan Lin", "Shengxin Liu", "Biaoshuai Tao", "Shengwei Zhou" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.10572", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-11", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We study the existence of envy-free up to any item (EFX) allocations of indivisible chores when agents have monotone cost functions with binary marginals. For indivisible goods, the corresponding existence question is known to have an affirmative answer for general monotone functions with binary marginals. For chores, however, the existence of EFX allocation was previously known only for more restricted classes, while the general binary-marginal case remained unresolved. In this paper, we provide two counterexamples based on the same 18-agent, 53-chore word gadget, with one cost profile for binary XOS costs and another for binary supermodular costs. In both cases, a complete EFX allocation need not exist. Finally, we formalize and verify our main results in Lean 4.", "title": "Non-Existence of EFX Chore Allocations for Monotone Cost Functions with Binary Marginals", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.10572" }, { "age_days": 2, "arxiv_id": "2608.11173", "authors": [ "Eric A. F. Reinhardt", "Adam J. Hauser" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.11173", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-11", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.", "title": "A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.11173" }, { "age_days": 3, "arxiv_id": "2608.09858", "authors": [ "Ioseph L. Buchbinder", "Petr M. Lavrov", "Thomas M. Sangy", "Ilya L. Shapiro" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "arxiv:2608.09858", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "One-loop divergences in classically conformal theory in curved spacetime is a nontrivial issue if the theory under consideration possesses gauge invariance. In this case, quantization involves introducing the gauge-fixing term and the action of ghosts, both of which are not conformal. The formal proof of the conformal invariant renormalizability in this situation, including interacting theories, has been given in the paper from 1984 by one of the present authors. Owing to BRST symmetry, the contributions of the gauge-fixing and ghost sectors to the conformal variation of the effective action cancel each other. This cancellation does not hold in the finite part of the one-loop and higher-loops effective action, that results in the anomaly. In this paper, we extend the early results on conformal matter fields in external gravitational field and apply them to conformal quantum gravity, including the case of conformal gravity coupled to other conformal matter fields. The gauge-fixing in the Weyl-squared gravity is more complicated, nevertheless, the proof of the one-loop conformal invariant renormalization using BRST symmetry is possible. As a preliminary to conformal quantum gravity, we also present a detailed general proof of conformal invariant one-loop divergences in the corresponding semiclassical theory.", "title": "On the Renormalization in Conformal Quantum Gravity", "updated": "2026-08-10", "url": "https://arxiv.org/abs/2608.09858" }, { "age_days": 4, "arxiv_id": "2608.08421", "authors": [ "Bernardo Subercaseaux", "Benjamin Przybocki" ], "content_date": "2026-08-09", "freshness": "fresh", "id": "arxiv:2608.08421", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-08-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Tarski's high school algebra problem asks whether every true identity concerning addition, multiplication, and exponentiation of positive integers follows from a list of 11 elementary identities. Surprisingly, Wilkie showed that the following identity is valid over the positive integers and yet does not follow from Tarski's axioms: \\begin{align*} &\\left((1+x)^y + (1+x+x^2)^y\\right)^x \\cdot \\left((1+x^3)^x + (1+x^2+x^4)^x\\right)^y = \\\\ &\\left((1+x)^x + (1+x+x^2)^x\\right)^y \\cdot \\left((1+x^3)^y + (1+x^2+x^4)^y\\right)^x. \\end{align*} Gurevič gave an algebra on 59 elements that satisfies Tarski's axioms but not Wilkie's identity, and over the years several authors whittled down the size of such a countermodel, culminating in a countermodel of size 12 due to Burris and Yeats. On the other hand, Zhang proved that there is no countermodel with fewer than 11 elements. Using SAT, we prove that the smallest countermodels are of size 12, as conjectured by Burris and Yeats. Moreover, we show that there are exactly 8,957,952 countermodels on 12 elements up to isomorphism and provide a simple classification of them. Our SAT approach outperforms dedicated tools for finding countermodels in equational theories, namely Mace4 and SEM. Furthermore, using autoformalization, we prove the correctness of our main result in Lean.", "title": "A SAT Attack on Tarski's High School Algebra Problem", "updated": "2026-08-09", "url": "https://arxiv.org/abs/2608.08421" }, { "age_days": 6, "arxiv_id": "2608.07366", "authors": [ "Daniel Goldberg", "Antoine Vinciguerra" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07366", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We formalize the Dirichlet integral and several of its classical applications in the Lean~4 proof assistant. Since the sinc function is not Lebesgue integrable on the positive half-line, the Dirichlet integral must be represented as the limit of integrals over bounded intervals. To avoid the difficulty of removing an exponential factor from a conditionally convergent integral, we instead pass through the absolutely integrable function \\(\\operatorname{sinc}^2\\). We evaluate its integral by differentiation under the integral sign and dominated convergence, and then recover the Dirichlet integral from an identity between truncated integrals. Using these results, we formalize the convergence of the Dirichlet cutoff to the Heaviside function and derive several quadratic and bilinear trigonometric integral identities. Finally, we formalize Lobachevsky's integral formula for continuous periodic functions satisfying a reflection symmetry, using the density of cosine polynomials obtained from Mathlib's Fourier analysis on the additive circle.", "title": "From the Dirichlet Integral to Lobachevsky's Formula: A Formalization in Lean 4", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07366" }, { "age_days": 6, "arxiv_id": "2608.07384", "authors": [ "Daniel Goldberg", "Antoine Vinciguerra" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07384", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We present a Lean 4 formalization of the Laplace transform for complex-valued functions, its fundamental operational rules, and a Bromwich-type inversion theorem proved through real-variable integration and the Dirichlet integral. As an application, we formalize the Laplace-domain solution of the harmonic oscillator and identify its transform with that of $\\sin(ωt)$. We also discuss the principal analytic and formalization challenges encountered in the development.", "title": "A Formalization of the Laplace Transform and Its Inversion in Lean 4", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07384" }, { "age_days": 3, "arxiv_id": "2608.09277", "authors": [ "Zenan Li", "Ziran Yang", "Peiyang Song", "Zhaoyu Li", "Kaiyu Yang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "arxiv:2608.09277", "kind": "paper", "label": "adjacent", "matched_signals": [ "seed_author:Kaiyu Yang", "seed_author:Ziran Yang" ], "published": "2026-08-10", "score": 2.9, "source": "arxiv-ai4math-core", "summary": "Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction. The de facto workflow decouples the two halves of the problem: first synthesize a program, then attempt to prove it correct. We observe that this sequential pipeline can be both ineffective and inefficient in practice. A program generated without anticipating its proof can be subtly incorrect or structurally difficult to verify, forcing the LLM into brittle repair loops that alternate between patching the code and patching the proof. Inspired by Dijkstra's view that a program and its correctness argument should be developed hand in hand, we propose $P^3$, an LLM-based agentic workflow that first derives a unified program-and-proof plan from the specification, then elaborates the implementation and proof scaffold under this shared plan. To evaluate verified code generation in realistic settings, we further introduce Lean4Commit0, a repository-derived, library-level benchmark built by extracting core APIs from real-world software repositories and translating their requirements, including relational specifications across APIs, into Lean tasks. Using four frontier LLM backends, we evaluate $P^3$ on Verina, AlgoVeri, and our Lean4Commit0 benchmark, where it achieves the highest solve rate in every benchmark--model setting. Compared with the stronger baseline, it improves solve rates by 4.6--11.2 percentage points and reduces per-task API cost by up to roughly 40\\% and wall-clock time by up to roughly 37\\% on the difficult subset of each benchmark. A targeted ablation further shows gains of 3.3--8.3 points over implementation-only planning, isolating the benefit of planning the program and proof jointly.", "title": "P$^{3}$: Joint Program-and-Proof Planning for Verified Code Generation", "updated": "2026-08-10", "url": "https://arxiv.org/abs/2608.09277" }, { "age_days": 2, "arxiv_id": "2608.10916", "authors": [ "Rob Cornish", "Iacopo Ghinassi", "Po-Hung Yeh", "Shuqi Liu", "Qiyuan Xu", "Haoxuan Yin", "Dominik Wagner", "Wenda Li", "Yee Whye Teh", "Luke Ong" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.10916", "kind": "paper", "label": "adjacent", "matched_signals": [ "seed_author:Wenda Li" ], "published": "2026-08-11", "score": 1.7, "source": "arxiv-ai4math-core", "summary": "Autoformalisation (AF) systems map natural language reasoning steps into formal statements in a proof assistant such as Lean. We consider how to assess the faithfulness of these systems. Existing approaches require expensive human-annotated ground truth, or rely on LLM judges or embedding models, which come with limited guarantees of accuracy. In addition, these methods typically only consider inputs that are known to be correct, and therefore do not assess whether the AF translates incorrect inputs faithfully. To address these limitations, we propose a new benchmark for AF faithfulness that is cheap to apply, sound under weak assumptions, and assesses both positive and negative examples. Our method is based on automatically generating perturbed reasoning steps that are designed to be invalid, and then measuring validity preservation on unperturbed steps and invalidity preservation on perturbed steps. We apply our method to eight AF systems across four mathematical datasets, and observe pervasive sycophancy: many AFs \"silently correct\" invalid inputs into provable statements. The most validity-preserving fine-tuned AFs are also the most sycophantic, suggesting a tension between validity and invalidity preservation in current AF systems.", "title": "FaithformBench: Benchmarking Faithfulness of Mathematical Chain-of-Thought Autoformalisation", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.10916" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:ff241b91982f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: convert the VERINA benchmark to intrinsic verification (#14759)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/ff241b91982f64295d4495387bc4c864b7cd15bd" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:ae17c03b0bf6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: state the frame closure over `PredTrans` and move both to the order library (#14774)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/ae17c03b0bf6ed8af6a1a06ee8b39e3d6ceb6da2" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:537e47ab40ae", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: split `Std.Internal.Do.Order` by subject (#14764)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/537e47ab40ae11dd67a4024d2b5aad3bdbfd6e7a" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:0bfd59222048", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: separate the generic and the monadic weakest-precondition modules (#14778)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/0bfd592220485d30e1d7e2d8ca2ee7cf5d471f0f" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:bc59d63228f0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: move the `vcgen` tactic to `Lean.Elab.Tactic.VCGen` (#14777)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/bc59d63228f0a0fa569480b161e304ff54d4ec84" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:cdfe9b3a66f5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: drop borrow annotations from scalar IR parameters (#14773)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/cdfe9b3a66f52e984d367066d3263e9e4b11f480" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:0f051d91d36a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: leak when the IR interpreter passes a borrowed scalar argument (#14749)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/0f051d91d36accf02d502235ebf12edfe702f728" }, { "age_days": 0, "authors": [ "Paul Reichert" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover/lean4:5847d9b42750", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: defer stuck exceptions from `isDefEqApp`'s `isDefEqOnFailure` fallback (#14583)", "updated": "2026-08-13", "url": "https://github.com/leanprover/lean4/commit/5847d9b42750a5a1552088d483fd05b97743cb13" }, { "age_days": 0, "authors": [ "Jireh Loreaux" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3fd5f0b49909", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: generalize type class assumptions for `PositiveLinearMap.preGNS` and prove the Cauchy-Schwarz lemma (#42415)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/3fd5f0b49909e7e6b44b014a6c41e19dfb3b3493" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ae26804842dd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add `contDiffWithinAt_clm_apply` (#42497)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/ae26804842dd341fb1c52e81d71f1a105ef4ca34" }, { "age_days": 0, "authors": [ "Alex Korbonits" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:652d7e3b3f24", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Connected): transport path-connectedness along homeomorphisms (#41665)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/652d7e3b3f242c04dbb0e23c55fdf37ffe2bdc84" }, { "age_days": 0, "authors": [ "Xavier Roblot" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:130d6f7afed9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Localization/FractionRing): add IsFractionRing.fixingSubgroup_range_algebraMap (#40864)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/130d6f7afed95e0e88cefbb18986af4a9d376379" }, { "age_days": 0, "authors": [ "Moritz Firsching" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:debf93c6ee84", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/LaurentSeries): `derivative_map` and friends (#42469)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/debf93c6ee848af194e8d8250f1ffef6aa1e72b0" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4bd9cb09931c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/AdjoinRoot): `AdjoinRoot` over a field is a field iff polynomial is irreducible (#42333)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/4bd9cb09931c1c36d71420b69e50bfa88f3d2568" }, { "age_days": 0, "authors": [ "Eureka Zheng" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6fe686bdbdb0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Matrix): add the generalized E-type Cartan matrix family (#42157)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/6fe686bdbdb05f0a118f9ffb0e6d990bffdc0f2c" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:654601e0aa5f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): pure morphisms (#41200)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/654601e0aa5f2f95145e3da308285cd2e5536dce" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9c493c0e616a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): functors which preserve κ-presentable objects (#41190)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/9c493c0e616a91a8c9d825d91851b942d62e9bd6" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:60e232025644", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): equivalence between the various definitions of sharply smaller regular cardinals (#41232)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/60e2320256446029d87234045060e36fb3fbd99b" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cea6c18db8df", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): constructor for `IsCardinalPresentable` (#41187)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/cea6c18db8dfa8adf0045a53b7fc684677907e2b" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e3f7d8d44d12", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Presentable): `PUnit` is locally presentable (#41240)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/e3f7d8d44d1268b1960042ad9648b598f1353a84" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0a3be1339403", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory): the right derived functor commutes with the shift (#39117)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/0a3be13394036755359bc0bfdaeaecd0b44dd18b" }, { "age_days": 0, "authors": [ "teorth" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3cdc35c530a0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Archive/RiemannStieltjes): archived version of the Riemann-Stieltjes and Riemann integrals (#41596)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/3cdc35c530a0db6e3463dad8b1bbc16a7d822beb" }, { "age_days": 0, "authors": [ "Pepa Montero Jimena" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d16a3fccfa0e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/SpecificLimits/Normed): the sum ∑' n, n ^ k * r ^ n via Stirling numbers (#41498)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/d16a3fccfa0e7ba10b678da6ae01e6e306a6619a" }, { "age_days": 0, "authors": [ "Evgenia Karunus" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ac8f622cc262", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/SpecialFunctions/ImproperIntegrals): add not_integrableOn_Ioi_rpow_of_neg_one_le (#42254)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/ac8f622cc262c0a0eb60ef0acc0b4d2f717ce59a" }, { "age_days": 0, "authors": [ "TJHeeringa" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:29946e911fb2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "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 `LinearMap.extendOfIsometry` (#42375)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/29946e911fb2fc5a6563cd680901fb6b7dc0bd71" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c9526e38603f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AlgebraicTopology/SimplicialSet/KanComplex): MulStruct.assoc (#38216)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/c9526e38603f2cbbbf7791e39aea23155f7be474" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f385f9fd18ab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AlgebraicTopology): the truncated quasicategory induced by a quasicategory (#42473)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/f385f9fd18abed332ebcd3df239cb357e264aceb" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:32aa3e890c95", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AlgebraicTopology): non-degenerate simplices in `Δ[p] ⊗ Δ[q]` (#41624)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/32aa3e890c95390c12fc06719177e2f341c57f75" }, { "age_days": 0, "authors": [ "Xavier Roblot" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5f9b8f6063f1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/QuadraticAlgebra): discriminant and field criterion (#42206)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/5f9b8f6063f1c0597de9aafae94abee04c71600a" }, { "age_days": 0, "authors": [ "Monica Omar" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3d9e8eefcf2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra): `IsUnital` and `IsNotUnital` classes (#41923)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/3d9e8eefcf2bd41f3ce5932cd079edfec0d84bad" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fbb6fa0e3054", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `Set.exists_mem_of_nonempty` (#42546)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/fbb6fa0e30546451b7708f7765c800971b17d5d4" }, { "age_days": 0, "authors": [ "Nathanael Thompson" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:026dd116f139", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename MvPolynomial.monomial_mul to monomial_mul_monomial (#42586)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/026dd116f139bc35a036e7e3d29ba2db3a3f00ce" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:51c80a99cdb5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove AI tools from Authors lines (#42727)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/51c80a99cdb5e352e0871dae67039335d16e49c6" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6da1b08df6f1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: mark `Monotone.functor` as `implicit_reducible` (#42726)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/6da1b08df6f1ea976cff62775881612e0a036d70" }, { "age_days": 0, "authors": [ "Artie Khovanov" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:72f9c607bb3a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/Ideal/Maximal): simplify proof (#42618)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/72f9c607bb3a3e3a9fbe2a0513c7c79f998b9944" }, { "age_days": 0, "authors": [ "Francesco Chotuck" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:38d7e035092b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Logic): remove all `backward.isDefEq.respectTransparency` and `backward.defeqAttrib` options (#42179)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/38d7e035092bc92de3e8ff9ccb4a1e31ac90bc05" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4fae4090fac7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Nat/GCD/Basic): automated extraction from #40597 (#42712)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/4fae4090fac768a5f28c40290d3b3b80a1365c1a" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6ee17e62cf98", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Functor/Category): don't expose `NatTrans.hcomp` (#40925)", "updated": "2026-08-13", "url": "https://github.com/leanprover-community/mathlib4/commit/6ee17e62cf985bc299a232c2d27995678b99980c" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:929ad9473c99", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: contracts on a `while` loop and on nested loops (#14758)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/929ad9473c9926588a664c97741d4035259e8836" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:d53748c39df1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: bv_decide's collection of facts in grind mode (#14757)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/d53748c39df143bc55a140cb0ee0c5127fc40e3f" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:b73bcf5ac408", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: make `@[spec]` annotations non-blocking on the proof (#14765)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/b73bcf5ac408d274130e5fdf0850e275f7b41151" }, { "age_days": 1, "authors": [ "maxc-osec" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:8f0ceabca35e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use CAS when swapping reference values (#14585)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/8f0ceabca35e829d3be972645b6b29d4ddfb4ee8" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:e27622c69c50", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: mark `Grind.nestedDecidable` as an abbreviation (#14770)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/e27622c69c5014b09cf14cb8f6a343b5c66985c9" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:67b968efe621", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep a schematic exception postcondition when applying a spec (#14766)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/67b968efe621aa15586e8d688055af4fb31550f7" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:70119c2657a9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: ignore heterogeneous equalities in `grind hom` solver hooks (#14769)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/70119c2657a9748337e175e53d1ae480dbed0475" }, { "age_days": 1, "authors": [ "Joachim Breitner" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:6eb06a5ed101", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: check uniformity of occurrences of the datatypes being declared (#14582)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/6eb06a5ed101549d51de5ed2f81bb0454d9e6779" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:4678eb199469", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: introduce `bv_decide_push` for incremental `bv_decide` pre-processing (#14763)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/4678eb199469493f92e376d45afb4c43ed1d6e46" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:2906af0d8ddd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: homomorphisms for `grind` (#14727)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/2906af0d8dddb71e584f53ba1e6e70d91b805677" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:6e48bb21718c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `lift_lets` tactic for `sym =>` mode (#14768)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/6e48bb21718c8f7d792df392fe21bbbb491bd8b3" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "github:leanprover/lean4:a3fbf67ce3bc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: dynamically link test binaries (#14760)", "updated": "2026-08-12", "url": "https://github.com/leanprover/lean4/commit/a3fbf67ce3bc4eb2e4214506767659a0008a316d" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:d440736fc52e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: a loop over an iterator states its invariant (#14752)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/d440736fc52eed6157663de824b8c97a9a6ceedc" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:5fa9c43648da", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: one loop gadget per set of annotations a loop states (#14751)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/5fa9c43648da5097d347c25d0af63cd99bc5270d" }, { "age_days": 2, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:e98a70f4a7fc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: typos in diagnostics (#14743)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/e98a70f4a7fcce0d76f3ef032aef59534fa78431" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:cb5bb5f19c70", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: step vcgen through specs whose program applies a continuation variable (#14747)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/cb5bb5f19c70334ff803cf1f21eb4bfafb017bda" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:9a36a53c968b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: fold vcgen's symbolic state as it is produced (#14745)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/9a36a53c968b04dbd4a67b5f29c897317d60c4b8" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:797673556afd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `invariant` and `decreasing` clauses on `repeat` and `while` loops (#14703)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/797673556afd616765d5b0a7692f4872039452f7" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:8e0b5589d6ad", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `grind` reads a loop's measure through the states of the assertions (#14744)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/8e0b5589d6ad6e4181bc4a98b7dfb17c6c305ba2" }, { "age_days": 2, "authors": [ "Garmelon" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "github:leanprover/lean4:42a250c81d82", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update release scripts (#14736)", "updated": "2026-08-11", "url": "https://github.com/leanprover/lean4/commit/42a250c81d82d0fc39015b71319e4af7f2b91b5d" }, { "age_days": 3, "authors": [ "Garmelon" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover/lean4:6aec22b9d2b2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: prepare development cycle for v4.35.0 (#14735)", "updated": "2026-08-10", "url": "https://github.com/leanprover/lean4/commit/6aec22b9d2b2ac082c480b5890a0cb87cdd2b81c" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover/lean4:1d2dde6d64cb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: do not attempt to upload missing cache during release build (#14738)", "updated": "2026-08-10", "url": "https://github.com/leanprover/lean4/commit/1d2dde6d64cb3da989bab118f4d386eb55237fe5" }, { "age_days": 1, "arxiv_id": "2608.11941", "authors": [ "Tom Adamczewski" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.11941", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-12", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al. Whereas these conjectures had previously been attempted only with a bespoke agent, our open-source evaluation code runs any generic language model (LM) against them, and is secure against LM cheating attempts. We find that LMs equipped with a minimal set of tools resolve 147 of these conjectures with a budget of \\$50 per attempt, scoring 30% on OEIS Open. OEIS Open Lite is a random subset of 100 conjectures for cheaper evaluation. When evaluated with a budget of \\$200 per attempt, the best current LM scores 44% on OEIS Open Lite. Giving LMs access to the mathematics literature via 476,000 papers from arXiv did not increase performance on OEIS Open Lite, and nor did using more sophisticated agent loops. The conjectures covered in this work are of uncertain mathematical significance, and most have likely received little previous attention. Nevertheless, our results show that LMs can resolve open research conjectures autonomously and at modest cost.", "title": "OEIS Open: How many conjectures can language models turn into theorems?", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.11941" }, { "age_days": 1, "arxiv_id": "2608.12223", "authors": [ "Ivan S. Yakovenko", "Alexey D. Kiverin" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.12223", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-12", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Ultra-lean hydrogen flames under terrestrial gravity are governed by a coupled interaction among preferential diffusion, thermal diffusion, heat loss, and self-induced convection. This study numerically examines combustion in a quiescent 6~vol.\\% H$_2$--air mixture using detailed chemistry and a low-Mach-number formulation. A complete calculations set was considered, with Soret diffusion and optically thin radiative heat loss independently enabled and disabled. One-dimensional spherical calculations were used to isolate the initial post-ignition flame kernel growth, while two-dimensional planar and axisymmetric simulations described its subsequent buoyant rise, deformation, and breakup. Over the analyzed interval, the spherical flame-front radius followed $R_f^2\\approx Kt$ rather than constant-speed expansion. Soret diffusion increased the effective growth coefficient $K$, whereas radiation reduced it. The axisymmetric calculations reproduced the experimentally measured leading-point trajectory substantially better than the planar formulation. Soret diffusion produced larger, faster-rising kernels and maintained a more nearly circular upper cap, whereas radiation had a weaker effect on trajectory but increased relative lateral flattening. In all cases, a toroidal vortex stretched the flame segment and caused local extinction and fragmentation. Soret diffusion delayed breakup, while radiation advanced it; their combined effect on breakup time was nearly compensating. The results show that Soret transport and radiation primarily alter kernel growth and resistance to vortex-induced extinction, while the qualitative breakup pathway remains hydrodynamically controlled.", "title": "Effects of Soret Diffusion and Radiative Heat Loss on the Evolution of Buoyant Flame Kernels in Ultra-Lean Hydrogen-Air Mixture", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.12223" }, { "age_days": 1, "arxiv_id": "2608.11792", "authors": [ "Lin Mai", "Yaobo Zhang" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.11792", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-12", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We study whether a tree-level MHV gravity numerator is determined by its degree and by vanishing on $\\langle ij\\rangle=[ij]=0$ for every pair. A flag-variety standard-monomial basis and an $S_n$-resolved restriction map reduce the problem to exact finite-dimensional calculations. At seven points we find $W_{7,\\mathbb{Q}}\\simeq S^{(2,1^5)}\\oplus S^{(1^7)}$. The Hodges numerator spans the sign summand, while the six-dimensional hook gives additional algebraic solutions. The pair-ideal conditions therefore do not determine a unique algebraic solution, but Bose symmetry selects the Hodges line. At eight points, pair-ideal conditions and Bose symmetry leave a two-dimensional alternating space. Same-helicity BCFW scaling, normalized collinear factorization, and the leading soft coefficient impose the same linear condition and select the Hodges line. We also prove that, at arbitrary multiplicity, an alternating fixed-degree numerator is determined by its full value on one collinear boundary with the marked legs and their spinor ratio fixed. Together with standard factorization, this determines the numerator up to normalization within the fixed-common-denominator ansatz. All rank and ideal-membership calculations use exact integer or rational arithmetic, and their finite-dimensional consequences are checked separately in Lean.", "title": "Algebraic versus physical uniqueness of MHV gravity numerators", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.11792" }, { "age_days": 2, "arxiv_id": "2608.11008", "authors": [ "Ilias Chalkidis" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.11008", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Political stance detection in LLMs has long been dominated by closed-ended, multiple-choice political survey questions---originally designed for humans, and thus lacks the realism and nuance of human-AI interactions in the wild, while also being susceptible to sandbagging. The recent IssueBench framework substantially mitigates these limitations with templated prompts anchored in real-world chat logs. Given the rise in non-work-related use of GenAI assistants, we extend IssueBench beyond writing assistance to include two additional tasks, information seeking and opinion sharing. We argue that templated prompts still lack the nuance of real ones, especially for open-ended tasks, and remain recognisable as evaluation artefacts. We propose the use of fully synthetic (LLM-generated) prompts, produced under detailed instructions with real prompts as seeds. We assess the ecological validity of real, templated, and LLM-generated prompts in a small-scale study covering 3 highly contested policy issues and 3 recent geopolitical conflicts. Human and LLM annotators rank LLM-generated prompts as no less realistic than real ones and clearly more realistic than templated ones, and find that they carry their intended intent and stance more clearly; the LLMs separate templated prompts from the other two far more sharply than the humans do. In a case study, templated and LLM-generated prompts yield systematically different stance estimates for the same model, most visibly under neutral framings, where templated prompts overstate the model's leaning in the direction encoded by the topic-and-stance text (filler) slotted into their templates.", "title": "Templated or fully synthetic? Prompt construction as a confound in measuring LLM political stance beyond writing assistance", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.11008" }, { "age_days": 2, "arxiv_id": "2608.10869", "authors": [ "Xiaoyu Li", "Andi Han", "Jiaojiao Jiang", "Junbin Gao" ], "content_date": "2026-08-11", "freshness": "fresh", "id": "arxiv:2608.10869", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-11", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself. For a class of Natarajan dimension $d_N$ and Daniely-Shalev-Shwartz dimension $d_{DS}$, the optimal excess risk is known at the two endpoints ($d_{DS}/n$ realizable, $\\sqrt{d_N/n}+d_{DS}/n$ agnostic [HMZ24, CEH+26, Pab26]) and open in between. We close the gap: at every fixed oracle risk $L^\\star$, the optimal excess risk is $\\widetildeΘ(\\sqrt{L^\\star d_N/n}+d_{DS}/n)$, uniformly in the alphabet size, attained by a learner that knows neither $L^\\star$ nor the confidence level. The upper bound composes the cover-menu-compression architecture of [CEH+26], at the realizable rate of [Pab26], with a new comparator-facing relative compression theorem: a size-$k$ compression rule that empirically dominates a comparator $h$ has population risk at most $L(h)+O(\\sqrt{L(h)Γ}+Γ)$ with $Γ=(k\\log n+\\log(1/δ))/n$, without stability; this transfers the comparison principle of the sharp binary theory [MQZ26] while discarding its Boolean-cube geometry, which does not lift to multiclass labels. The lower bound forces both terms using one class and one distribution at every fixed $L^\\star$, by a pair-Assouad scheme calibrated to $L^\\star$ and a fiber argument on the pseudo-cubes underlying the Natarajan-versus-DS separation of [BCD+22]. Both theorems extend to list learning: against the best $r$-tuple of hypotheses, the same architecture and the same two engines yield an optimistic rate and a lower bound of the same shape, forcing the fluctuation term that [Pab26] expected to be necessary against list comparators, and removing the factor $r$ from the known realizable list lower bound.", "title": "Optimistic Rates for Multiclass PAC Learning", "updated": "2026-08-11", "url": "https://arxiv.org/abs/2608.10869" }, { "age_days": 3, "arxiv_id": "2608.09305", "authors": [ "Arnaud Mayeux" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "arxiv:2608.09305", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Given a category $\\calC$ and a center, that is a collection of pairs $(d_i, N_i)$ consisting of a morphism $d_i$ and a sieve $N_i$ over its codomain, the dilatation of $\\calC$ is a new category $\\calC'$ in which every $n \\in N_i$ factors, uniquely and functorially, through $d_i$. This paper presents the theory of dilatations of categories through a full formalization of the construction and its main theorems in the Lean~4 proof assistant, on top of the Mathlib library. An appendix collects a systematic dictionary between the mathematical statements and the Lean declarations that formalize them.", "title": "Dilatations of categories, via their lean formalization", "updated": "2026-08-10", "url": "https://arxiv.org/abs/2608.09305" }, { "age_days": 4, "arxiv_id": "2608.08897", "authors": [ "Wesley H. Holliday" ], "content_date": "2026-08-09", "freshness": "fresh", "id": "arxiv:2608.08897", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A common problem in social choice is to determine whether there is a social choice procedure, such as a voting method, satisfying some desired criteria. Computer-aided methods such as SAT solving can sometimes answer these questions. However, under typical encodings, a SAT solver may only synthesize a voting method on a finite domain, while we may want one on an infinite domain, such as the domain of all preference profiles for a fixed number of candidates but any finite number of voters. In this paper, we use an approach based on reasoning with constrained Horn clauses and computation with polyhedra to synthesize a voting method on an infinite domain. We then use SMT and Lean to verify its properties. Our main result is a possibility theorem about four well-known criteria from voting theory: the Condorcet winner and loser criteria, positive involvement, and resolvability. Previous work has shown that for five or more candidates, there is no voting method satisfying these axioms, and that for four candidates, there is no method satisfying these core axioms plus one more invariance axiom. Here we show that for four candidates, there does exist a method satisfying the core axioms and more.", "title": "Voting Method Synthesis on an Infinite Domain: A Possibility Theorem for Positive Involvement", "updated": "2026-08-09", "url": "https://arxiv.org/abs/2608.08897" }, { "age_days": 5, "arxiv_id": "2608.07979", "authors": [ "William J. Dwyer" ], "content_date": "2026-08-08", "freshness": "fresh", "id": "arxiv:2608.07979", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Testing independence in an R by C table is usually posed as one omnibus statistic against a dense alternative. When the departure is sparse, concentrated in a few cells, the sharp object is instead a detection boundary: the weakest signal any test can find. This paper treats independence through that lens, in three parts. Part I specializes sparse-signal detection theory (Ingster 1997; Donoho and Jin 2004; Chhor, Mukherjee and Sen 2024) to the table: it is a heteroscedastic Gaussian sequence whose variance profile is the expected-count table, fixed by the two margins through the product-CV identity CVe^2 = (1 + CVr^2)(1 + CVc^2) - 1, so marginal heterogeneity is exactly the heteroscedasticity profile; a variance-stabilizing root transform gives the exact standardized amplitude 2 sqrt(m)(sqrt(1 + a) - 1) and a closed-form separation radius, valid under a growing-count condition and provably failing at fixed small counts. Part II casts independence as goodness of fit of the log-linear no-interaction model and shows that higher criticism, with its closed-form Jaeschke-Eicker null, attains that boundary adaptively over the unknown sparsity, while being candid that in the very sparse strong regime the maximum-cell rule dominates and exact-conditional optimality is conjectural. Part III measures the small-count calibration failure (size 0.3 to 0.6, even under uniform margins, so the driver is the per-cell tail, not heterogeneity), removes it with the exact margin-conditional reference laws, and shows conditioning on both margins is the complete treatment for a test (no oracle; size 0.003 to 0.009); a routing rule keyed to the margin profile sends large-count tables to the asymptotic gate and small-count tables to the exact anchor. Two-thirds of a 5,543-table public corpus route to the exact anchor. Every claim is confirmed numerically from openly deposited, deterministically seeded code.", "title": "Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor", "updated": "2026-08-08", "url": "https://arxiv.org/abs/2608.07979" }, { "age_days": 6, "arxiv_id": "2608.07360", "authors": [ "Zeru Zhu", "Jinzheng Li", "Yuanjie Ren", "Ji Liu" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07360", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Kolokolnikov conjectured that, among finite simple graphs on $n$ vertices with exactly $2(n-2)$ edges, the complete bipartite graph $K_{2,n-2}$ maximizes algebraic connectivity. We prove the conjectured statement for every $n\\ge123$: every such graph has algebraic connectivity at most $2$, while $K_{2,n-2}$ attains $2$. The proof begins with explicit Rayleigh-quotient certificates that exclude several local configurations from a hypothetical counterexample. A global degree count then controls the number and total excess of vertices of degree at least $5$ and bounds the edge excess of the subgraph induced by vertices of degree at most $4$. A Moore-type breadth-first-search criterion uses this excess to guarantee a short cycle, while a spectral criterion excludes cycles in the same length range. An explicit arithmetic estimate shows that the two criteria apply simultaneously once $n\\ge123$. A Lean formalization covering every $n\\ge4$, including the complementary range $4\\le n\\le122$, has been produced with MerLean and checked by the Lean kernel; the present paper gives a self-contained mathematical account of the large-order component.", "title": "Maximizing Algebraic Connectivity with $2(n-2)$ Edges: The Large Vertex Number Case", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07360" }, { "age_days": 6, "arxiv_id": "2608.07396", "authors": [ "Jaume de Dios Pont", "Lukas Liehr", "David Muñoz-Lahoz", "Mitchell A. Taylor", "Pedro Tradacete" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.07396", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The ability of large language models to assist professional mathematicians has been progressing rapidly. Earlier this year, a group of researchers in Banach lattice theory and phase retrieval began incorporating this technology into their research workflows. Facing challenges about the reliability of these models, they also decided to couple the discovery process with Lean verification. Here, we present a case study of how this has led to a more united community and a deeper understanding of our field.", "title": "Banach lattices and phase retrieval: A case study for the use of AI in mathematics", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.07396" }, { "age_days": 6, "arxiv_id": "2608.06996", "authors": [ "Eunkyu Choi", "Joonho Seo", "Seungmin Lee", "Seokhwan Jeong" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.06996", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "This paper presents a sensor-minimal automated assembly system for bidirectional single-row flat ribbon cable harnesses (FRCHs). Unlike conventional peg-in-hole or single-terminal insertion tasks, FRCH assembly involves mechanically coupled multi-terminal insertion under flexible and dense geometric constraints. To address this problem, the proposed system performs the assembly through a purely mechanical sequence consisting of Cable Alignment, Lean & Slide, Weaving, and Clamping, without relying on active sensing or vision. Each mechanism is designed to progressively reduce correlated terminal misalignment, insertion interference, and instability before final locking. Experiments on bidirectional single-row FRCHs achieved an 83.75% end-to-end process success rate over 80 trials, with success rates of 85.0% and 82.5% in the first and second halves, respectively. The cycle time was 33 s under half-speed operation. To the best of our knowledge, this work presents the first automated prototype for FRCH terminal-to-housing assembly for multi-pin housings.", "title": "Automated Terminal-to-Housing Assembly System for Flat Ribbon Cable Harness", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.06996" }, { "age_days": 6, "arxiv_id": "2608.06728", "authors": [ "Jiao-Long Cao", "Ye Yuan" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.06728", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-07", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "For an odd prime $p$, let $m(p)$ be the minimum cardinality of a set $A\\subseteq \\mathbb Z/p\\mathbb Z$, with $|A|\\geq2$, such that no sum in $A+A$ has a unique representation as an unordered pair from $A$, with repetition allowed. Bedert proved \\[ m(p)\\gg \\log p\\, \\frac{\\sqrt{\\log^{(3)}p}}{\\log^{(4)}p}. \\] We prove the stronger lower bound \\[ m(p)\\gg \\log p\\,\\log\\log p. \\] More generally, if $G$ is a finite Abelian group and $q(G)$ is the least prime divisor of $|G|$, then the same explicit estimate holds whenever $q(G)>2$, and in particular every subset $A\\subseteq G$ with $|A|\\geq2$ and no unique sum has cardinality $\\gg \\log q(G)\\,\\log\\log q(G)$ as $q(G)\\to\\infty$. The proof has two structural inputs. First, a maximum subset of $A$ whose distinct-element subset sums of size at most four are all different has cardinality $\\gg\\log p$. This follows from a short-coordinate lemma and a collision-lattice determinant argument. Second, we refine Bedert's density increment. Alternative representations are oriented toward an uncovered endpoint, coalesced by their translation, and separated into wide, exposed, and recurrent batches. A load-sensitive entropy lemma codes the recurrent translations using their actual final fibre multiplicities. The resulting global shift-set complexity is $\\exp(O(K))$, where $K$ is the ratio of $|A|$ to the level-four additive dimension. This forces $K\\gg\\log\\log p$, and the theorem follows. All headline statements and the structural implications used to derive them have also been checked in Lean~4 with explicit integer constants. As a secondary and logically independent result, we construct weakly ternary-balanced sets and obtain \\[ m(p)\\leq \\frac{(\\log p)^2}{2(\\log 3)^2} +\\left(\\frac{2}{\\log 3}+o(1)\\right) \\frac{(\\log p)^2}{\\log\\log p}. \\]", "title": "A Second-Logarithm Lower Bound for Sets with No Unique Sums", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.06728" }, { "age_days": 1, "arxiv_id": "2608.12179", "authors": [ "Yung-Hsu Yang", "Luigi Piccinelli", "Samuel Rota Bulò", "Sunghwan Hong", "Denis Rozumny", "Johannes Schönberger", "Zuria Bauer", "Hermann Blum", "Peter Kontschieder", "Marc Pollefeys" ], "content_date": "2026-08-12", "freshness": "fresh", "id": "arxiv:2608.12179", "kind": "paper", "label": "negative", "matched_signals": [ "negative:vision_world_models" ], "published": "2026-08-12", "score": -2.5, "source": "arxiv-ai4math-core", "summary": "Metric 3D object detection is a core capability for embodied agents, yet most reliable systems lean on depth sensors, trading away cost, power, and integration simplicity. This motivates monocular 3D detection, which avoids additional constraints, yet it faces a major obstacle: from a single image, depth, and especially absolute scale, are underconstrained. As a result, the prevailing pattern of detecting in 2D and then predicting 3D attributes is often brittle, since modest range errors can dominate 3D localization, and the learned scale prior can fail when cameras, motion, or environments undergo domain shifts. To address this, we propose Map-Det3D, an online multi-view 3D object detection model that brings detection directly into a 3D space reconstructed from RGB. We map a short temporal window into multiple views and repurpose a feed-forward metric 3D reconstruction model as our geometric backbone while tuning its object-aware capabilities. Building on this representation, Map-Det3D directly predicts boxes in metric 3D space, without the widely used 2D-to-3D lifting. Experiments across different benchmarks show that this design supports strong online performance and robust transfer without adaptation, suggesting that training reconstruction priors for detection is a practical route to stable metric 3D detection from monocular video. Code and models are available at https://royyang0714.github.io/Map-Det3D.", "title": "Map-Det3D: Metric Feed-Forward 3D Reconstruction Prior for Multi-view 3D Object Detection from Streaming Inputs", "updated": "2026-08-12", "url": "https://arxiv.org/abs/2608.12179" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }