{ "counts": { "adjacent": 14, "core": 2, "errors": 0, "negative": 73, "total": 89 }, "date": "2026-08-10", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-10T16:24:32Z", "items": [ { "age_days": 3, "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": 3, "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": 4, "arxiv_id": "2608.06440", "authors": [ "Abhishek Saigal", "Akaash R. Parthasarathy" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06440", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-06", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "For every odd integer $t\\ge17$, we prove that an explicit circulant graph on $5t-10$ vertices is doubly saturated $R(3,t)$-good. The graph is triangle-free and has independence number $t-1$. Adding any nonedge creates a triangle, whereas deleting any edge creates an independent set of order $t$. This settles Conjecture 2 of Przybocki, Mackey, Heule, and Subercaseaux. A cyclic sumset identity and explicit witnesses prove the local saturation properties. Writing $t=2m+1$, a five-layer reduction proves the independence bound via a uniform affine certificate for $m\\ge30$ and an exhaustive checker for $8\\le m\\le29$. The checker soundness and the complete argument are formalized in Lean 4.32.2. Consequently, $2t-1\\le \\operatorname{DS}(3,t)\\le 5t-10$ for odd $t\\ge17$.", "title": "An infinite family of doubly saturated $R(3,t)$-good graphs", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06440" }, { "age_days": 3, "arxiv_id": "2608.06682", "authors": [ "Mayank Pandey" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "arxiv:2608.06682", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We make explicit and formalize a result of the author on squarefree numbers in short intervals, showing that for $0 < \\varepsilon\\le 1/90935 $, $X\\ge \\exp(10^{27}/\\varepsilon^2)$, $H = X^{1/5 - 2/90935 + \\varepsilon}$, we have that \\[ \\biggl|\\sum_{X\\le n\\le X + H } μ(n)^2 - \\frac{6}{π^2}H\\biggr| \\le \\frac{10^{450}}{\\varepsilon} H X^{-\\varepsilon/10^{25}}. \\] This article gives an account of what went into making the exponent explicit. The Github repository linked contains the formalization in Lean 4 as well as an account of what went into the largely automated formalization.", "title": "Squarefree numbers in short intervals: explicit and formalized", "updated": "2026-08-07", "url": "https://arxiv.org/abs/2608.06682" }, { "age_days": 3, "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": 3, "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": 4, "arxiv_id": "2608.06261", "authors": [ "Stefan Dziembowski", "Grzegorz Fabiański", "Daniele Micciancio", "Rafał Stefański" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06261", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We present HOPSCOTCH, a Lean 4 framework for mechanizing computationally sound, game-based cryptographic proofs. Security definitions are expressed as indistinguishability between stateful probabilistic oracles, and proofs follow the standard game-hopping paradigm. HOPSCOTCH uses a shallow embedding: oracles and reductions are ordinary Lean definitions, enabling direct integration with the full Lean ecosystem, including general mathematical theories from Mathlib, such as finite-group theory. A game-hopping proof in HOPSCOTCH is represented as an explicit formal object whose constructors correspond to the standard steps of a game-hopping argument, making proofs easier to construct, automate, and inspect. We prove a general computational soundness theorem that interprets these proof objects by constructing reductions against the assumptions they use and deriving a concrete bound on the advantage of any distinguisher. Observational equivalence between oracles is established using a state-abstraction methodology: a simple yet powerful approach that supports transformations such as adding or forgetting state and replacing eager sampling with lazy sampling. We illustrate the framework with formalized proofs of the IND-CCA security of encrypt-then-MAC, the security of ElGamal encryption from DDH, the implication from one-time secrecy to public-key IND-CPA security, and the GGM pseudorandom-function construction. To the best of our knowledge, the last is the first mechanized proof of GGM for non-constant depth.", "title": "Game Hopping in Lean", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06261" }, { "age_days": 4, "arxiv_id": "2608.06531", "authors": [ "Milos Tatarevic" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06531", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove the inequality $R(k+1,s+1) \\ge R(k,s) + 2k + 2s$ for classical Ramsey numbers, valid for all $5 \\le k \\le s$, and formalize the proof in Lean 4. As a consequence, we obtain the new lower bound $R(12,12) \\ge 1641$.", "title": "A constructive two-parameter Ramsey increment", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06531" }, { "age_days": 4, "arxiv_id": "2608.06315", "authors": [ "Kevin Morio", "Yavor Ivanov", "Robert Künnemann" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06315", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-08-06", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Tamarin and ProVerif are two prominent tools for the formal verification of security protocols. They share the same high-level goal but differ significantly in their underlying formalisms and verification techniques, making a systematic comparison challenging: Tamarin uses multiset rewrite rules with sound and complete verification, whereas ProVerif employs an extension of the applied-pi calculus that provides fast but potentially incomplete results. We present a sound translation from Tamarin to ProVerif that enables a rigorous comparison of the two tools. It introduces novel techniques for formula rewriting, encoding multiset rewrite semantics, and handling simultaneous events, supporting an extensive subset of Tamarin's features, including multiset rewrite rules, lemmas, and restrictions, while precisely characterizing the cases where faithful translation is not possible. We provide formal proofs: within the faithful fragment, soundness ensures that any property verified in ProVerif also holds in the original Tamarin model, and completeness ensures that exists-trace properties not involving attacker knowledge are preserved. Best-effort encodings, in particular XOR, are reported separately and are outside these guarantees. Finally, we evaluate our translation on 121 Tamarin models. The translation covers 562 of 566 lemma tasks. Among non-XOR tasks with definitive results from both tools, 246 of 247 agree, with the remaining verdict explicitly flagged as using an incomplete model. Among the 362 tasks for which Tamarin returns a Boolean result and ProVerif completes with a logical result, ProVerif is faster in 334 cases (92.3%), with median per-task runtime and peak-memory ratios of 6.74x and 6.24x, respectively.", "title": "A Sound Translation from Tamarin to ProVerif: Enabling Comparative Analysis", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06315" }, { "age_days": 5, "arxiv_id": "2608.04645", "authors": [ "Bruno Rucy Carneiro Alves de Lima", "Victor Henrique Cabral Pinheiro", "Evgenii Dolzhkov", "Joseph Haske" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04645", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Quantum annealers solve problems by finding the lowest-energy (ground) state of a programmable physical system, a 2-local Ising model, whose energy function is the Hamiltonian. We compile recursive Datalog programs into such models so that the ground state projects onto the program's minimal Herbrand model. The compiler has four stages: binarization, grounding, reduction to a Min-Ones SAT formula, and Ising encoding. Each rule becomes an energy penalty on the one assignment that violates it, and a small uniform cost on every true atom selects the minimal model. We contribute both in theory and in practice with per-stage correctness lemmas and a correspondence theorem, verified in Lean 4, establishing that the ground state of the compiled model projects onto the program's minimal Herbrand model. We map the compiled models onto the topologies of commercial annealers and characterize, under classical and simulated-quantum annealing, whether and when that certified ground state is attained.", "title": "Towards Datalog on Quantum Annealers: Compiling Recursive Logic Programs with Bottom-up Semantics to 2-local Ising Models", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04645" }, { "age_days": 5, "arxiv_id": "2608.04992", "authors": [ "Jaume de Dios Pont", "Karlheinz Gröchenig", "Lukas Liehr", "Irina Shafkulovska", "Mitchell A. Taylor" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04992", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the set of time-frequency shifts $\\{e^{2πi βl t} g(t-αk) : k,l \\in \\mathbb{Z}\\}$ with a continuous, integrable totally positive function $g$ and lattice parameters $α,β>0$ generates a frame for $L^2(\\mathbb{R})$ if and only if $αβ<1$. This fully settles the so-called frame set problem for the class of totally positive functions. As a closely related result we prove a sharp Kadets-type theorem for every shift-invariant space generated by a continuous totally positive function. The proofs are based on Fredholm theory and limit-operator theory. A formalization of our main result in Lean 4 is also provided.", "title": "Gabor Frames of Totally Positive Functions: A Complete Characterization", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04992" }, { "age_days": 5, "arxiv_id": "2608.04457", "authors": [ "Hans-Martin Will", "Allen L. Brown", "Matthew Fuchs" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04457", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "As \"AI Scientists\" emerge to drive research via the Model Context Protocol (MCP), systems relying on ephemeral scripts will fail. The sheer scale of stateful, interconnected evidence requires a machine-walkable warranty grounded in a purpose-built database architecture. Eigenius is an open-source, typed knowledge-graph DBMS built on a single premise: answering the audit question (\"what do you know, and what is your warranty?\") requires a unified kernel. By tightly coupling the type system, storage engine, and integration protocol, Eigenius turns data provenance into a structural invariant rather than a property reconstructed across subsystem boundaries. The kernel rests on three pillars: a dependent type theory woven through the core, institutions acting as strongly typed integration boundaries, and a content-addressed immutable storage layer. On this foundation, epistemic status (declared/observed/derived/verified) is enforced as a strict commit-time invariant. Cross-system translations (comorphisms) are checked at commit and materialized directly into the graph as durable, first-class resources. To eliminate O(N^2) polystore bottlenecks, shared on-chain intermediate representations (IRs) collapse multi-system translations to identity. Crucially, this architecture unifies both domains of scientific epistemology: it relies on justification logic for empirical science, while embedding a fast, in-process term checker to safely evaluate formal mathematical proofs (via Lean 4) without IPC overhead. In an end-to-end recomputation of a published Nature study from fragile scripts to a materialized evidence graph, all 52 derived conclusions hold from pinned data, surfacing four machine-checked discrepancies in the original study.", "title": "Eigenius: A Typed Knowledge-Graph DBMS with Epistemic Stratification and Institution-Mediated Reasoning", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04457" }, { "age_days": 5, "arxiv_id": "2608.05420", "authors": [ "Ahmed Ryan", "Md Erfan", "Akond Ashfaque Ur Rahman", "Md Rayhanur Rahman" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05420", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-05", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness. A formal proof checker verifies whether each proof step follows established logical rules. Coq bases its rules on the Calculus of Inductive Constructions, a logical framework that defines which proof steps the system may accept. This pilot study evaluated six open-weight LLMs on the same 100 theorems from CoqStoq, a benchmark derived from real Coq projects. Each LLM received one attempt per theorem with the temperature set to 0, and Coq checked every proposed proof in the theorem's original project environment. We counted a proof as successful only if the Coq kernel accepted it. Gemma 4 verified 12 of 100 theorems, Llama 3.3 verified 8, and DeepSeek Coder V2 Lite verified 1. Qwen 3.5, Mistral Small 3.1, and GPT-OSS verified none. The 21 successful model-theorem results covered 15 distinct theorems, 11 of which were not solved by a baseline of standard Coq tactics. All verified theorems had short or medium human-written reference proofs; no model verified a theorem with a long reference proof. Because the proof-length analysis was exploratory, this pattern does not establish that proof length caused the difference. For the three models with at least one success, the total generation cost per verified proof ranged from 741 to 36,193 output tokens, 14.9 to 178.0 seconds, and 0.0167 to 0.2000 aggregate GPU hours. We could not calculate these ratios for models with no verified proofs. Across 600 attempts, the models produced 21 kernel-verified proofs, giving an overall success rate of 3.5%. The study reports descriptive differences among the models but does not statistically test whether one model outperforms another. Therefore, the results do not establish a universal ranking of the six models.", "title": "Can Open-Weight LLMs Produce Kernel-Verified Coq Proofs? A Pilot Study", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05420" }, { "age_days": 6, "arxiv_id": "2608.04228", "authors": [ "Arthur Freitas Ramos", "Ruy J. G. B. de Queiroz", "Anjolina Grisi de Oliveira", "Tiago M. L. de Veras" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.04228", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-04", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Computational paths record equality as explicit finite traces of primitive steps. We give a topological semantics for a scoped rewrite presentation whose steps have continuous geometric realizations and whose named rewrites carry endpoint-fixed homotopies. For every presentation we construct a quotient arrow space with a canonical final-domain groupoid structure: multiplication is continuous on the quotient of explicitly composable representatives. We prove an exact four-way criterion for this final composable topology to agree with the ordinary pullback topology, together with a compact-Hausdorff sufficient condition. Thus the unconditional construction exposes, rather than hides, the product-quotient issue in ordinary topological groupoids. The realization map to geometric homotopy classes is a continuous groupoid morphism and is faithful exactly under a separate geometric-completeness condition. In the universal presentation, a continuous section identifies the coherent-path quotient homeomorphically with the usual quotient-topologized fundamental groupoid. We then give finite-generator circle and genuine torus examples, with winding-based normal forms and classifications by Z and Z^2. A Lean 4.24.0 development checks the theorem package; the mathematical presentation is independent of the implementation.", "title": "Topological Semantics for Scoped Computational Paths", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.04228" }, { "age_days": 6, "arxiv_id": "2608.03327", "authors": [ "Siqi Fan", "Minghao Li", "Xiaoqian Ma", "Wenhui Tan", "Xiusheng Huang", "Juntong Wu", "Liujie Zhang", "Shuo Shang", "Weihang Chen" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.03327", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation", "tool_use_agents" ], "published": "2026-08-04", "score": 3.3, "source": "arxiv-ai4math-core", "summary": "Hybrid computer-use agents can act through screenshots or call text tools. We find that having a tool available does not settle which way the effect goes. Under one identical GUI-MCP harness on the OSWorld-MCP benchmark (309 tasks), the same MCP tools improve a reasoning model by +4.0pp and degrade a non-reasoning model by -5.9pp (5 runs each, both beyond 2 SE). What separates the two is tool-decision behavior. The non-reasoning policy ignores, misnames, or falsely terminates around tools. The reasoning model avoids these failures, yet still calls a tool on only 55/309 tasks, 23.9% of the tool-reachable ones. We call this shortfall the adoption gap. Both levels of the problem share one cause: the model already has a cheaper route and is never trained to take it. Multi-turn RL probes that cause. At the action level, a dense tool bonus raises spreadsheet adoption 0.03 -> 0.33 and carries into greedy decoding, but held-out accuracy does not follow. Behavior is steerable; competence is not. The bottleneck lies in tool-call semantics. At the context level, a successful tool call often makes the next screenshot redundant. Dropping it and halving image history cuts input tokens by about a third, at a small accuracy cost. Retraining under the same observation rule removes that cost. The compressed agent then reaches 37.8% against 33.0% for the uncompressed operating point, at 53% of the input cost, and closes the rich-lean gap on a pre-registered degraded subset to zero. Tools help when the model chooses and integrates them, and current hybrid agents leave many such choices unused. Code and checkpoints: https://github.com/redai-infra/hybrid-routing-agent", "title": "Screenshots or Tools? Eliciting Tool Use and Managing Multimodal Context in Hybrid GUI-MCP Computer-Use Agents", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.03327" }, { "age_days": 4, "arxiv_id": "2608.05480", "authors": [ "Kenny Lau", "Ken Ono" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.05480", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-06", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "For coprime $1`/`≥` (#41503)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/64f19e7068d432daae06604b912b2c6278595dbb" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6cf26736859c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FieldTheory): typeclass for field extension with finite transcendence degree (#42152)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/6cf26736859c0f0a57cc556c9872cdecdceb76ce" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b0f879696f35", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/ENNReal): add `sum_div` (#40855)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/b0f879696f350a2db0660e13525306be48fbd322" }, { "age_days": 0, "authors": [ "Weiyi Wang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:06b00bfa6f4a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Affine): mapping dist with homothety (#41910)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/06b00bfa6f4aefe4a569810f5485671b56ef9295" }, { "age_days": 0, "authors": [ "Weiyi Wang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cfcc13573e63", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc: add theorem 8 (straightedge-and-compass construction) to 100.yaml (#41757)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/cfcc13573e637ca0cab6f40fd0076c11c19278e5" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6bb0d815ead7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci: retire legacy zulip emoji workflows, enable emojis on mathlib4-nightly-testing (#41965)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/6bb0d815ead7cf9e231062bf5b359989bd62ed08" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5e5cca6719ae", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-08-10 (#42609)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/5e5cca6719ae2f225b1c323009b1a994ea5d824c" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4171fb412ebc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: tweak API for modelWithCornersEuclideanHalfSpace (#42281)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/4171fb412ebc3792af3f7fbb86c3c91f69fbaa42" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5d2a6a322723", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove `IsDedekindDomainDvr` (#42367)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/5d2a6a322723360b7094f2ed1b9774e0fc7da21d" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:db584cd6d46c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: bump toolchain to v4.33.0 (#42604)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/db584cd6d46c92f209a44c0f1c829460d327499d" }, { "age_days": 0, "authors": [ "dependabot[bot]" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5b210d51481c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(deps): bump the actions-version-updates group across 1 directory with 11 updates (#42329)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/5b210d51481ca525052f7baec785ec4f86dbf11f" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3ef2c2e23a8b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(WhatsNew): rename `whatsnew` to `#whats_new` (#42537)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/3ef2c2e23a8b5a46554fa771969b89287972b616" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b8d43c430c6b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/CompleteBooleanAlgebra): use `to_dual` (#41792)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/b8d43c430c6bd3c785f434ec8720b49904fd3f86" }, { "age_days": 0, "authors": [ "Attila Vajda" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3cf9c0a79c84", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(GroupTheory/Complement): deduplicate IsComplement.card_mul (#42493)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/3cf9c0a79c84574b37b77b7031cd56e9d0760fea" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f51789c952c8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Geometry/Manifold/Notation): avoid more superfluous work in cus… (#42491)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/f51789c952c8445ca120c8107aee04b3956058e9" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e662f417a91c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Geometry/Manifold): avoid some underscore soup (#42205)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/e662f417a91ca629ad934cca6536e621b499d67c" }, { "age_days": 0, "authors": [ "Francesco Chotuck" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3f69b1bad169", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Finset/Prod): state `singleton_product`/`product_singleton` via `sectR`/`sectL` (#42418)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/3f69b1bad1693a2905ff8e9254744fa21ef5f57f" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f7699dd3e2e2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory): composition implicit reducible in `Type` (#42529)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/f7699dd3e2e2f90ab1a45531bbd84b2bcbc8f76d" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1c6e94193fdd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory): `implicit_reducible` for compositions of natural transformations (#42528)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/1c6e94193fdde9efb39255989a4214ea8da576a2" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f46a87e8e1b7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Order): bound on `|n / m|ₘ` and `|n - m|` (#37232)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/f46a87e8e1b7fd68c94b6e16cad91d47bcc0cc93" }, { "age_days": 0, "authors": [ "Fanping Jiang" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bcbf492c34a0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Group/WithOne): remove stale TODO (#40904)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/bcbf492c34a082ce5a96588cd7a70ea4ebc992f9" }, { "age_days": 0, "authors": [ "Attila Vajda" ], "content_date": "2026-08-10", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4a3cbc9c7606", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-10", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/BigOperators): generate sum_Ico_reflect/sum_range_reflect with to_additive (#42592)", "updated": "2026-08-10", "url": "https://github.com/leanprover-community/mathlib4/commit/4a3cbc9c7606e4706507e1c2e3af21c148b72d63" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-08-09", "freshness": "fresh", "id": "github:leanprover/lean4:b1cd183c9978", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: demote cache failures to `trace` (#14720)", "updated": "2026-08-09", "url": "https://github.com/leanprover/lean4/commit/b1cd183c9978c3bedddc33baf7c9599baaeca046" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-08-09", "freshness": "fresh", "id": "github:leanprover/lean4:7c90644a5f2a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-09", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: `leanExit` test flakiness (#14721)", "updated": "2026-08-09", "url": "https://github.com/leanprover/lean4/commit/7c90644a5f2a8a62e0cfc1dcf7a19c0d6c70c6ce" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-08", "freshness": "fresh", "id": "github:leanprover/lean4:f29e9e488ea8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-08", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support well-founded and state-dependent termination measures in Spec.repeatM (#14507)", "updated": "2026-08-08", "url": "https://github.com/leanprover/lean4/commit/f29e9e488ea8242c875806e4b0564820c2d553b2" }, { "age_days": 3, "authors": [ "Mac Malone" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover/lean4:bd97ed8e3563", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: lake: mock remote cache artifact transfers (#14700)", "updated": "2026-08-07", "url": "https://github.com/leanprover/lean4/commit/bd97ed8e35639e17a11d1490cbc46d994e7b4513" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover/lean4:10d40baf2b2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: apply beta when canonicalizing types in `grind` (#14709)", "updated": "2026-08-07", "url": "https://github.com/leanprover/lean4/commit/10d40baf2b2bb80fde528102d0d0eb55b52f526c" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover/lean4:87e7204456bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: bv_decide grind integration (#14713)", "updated": "2026-08-07", "url": "https://github.com/leanprover/lean4/commit/87e7204456bfca901bdc724c996030e13c2f80c6" }, { "age_days": 3, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-07", "freshness": "fresh", "id": "github:leanprover/lean4:0dfa5c0f9bc5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `cbv` annotations to `HashMap`/`HashSet` operations (#14707)", "updated": "2026-08-07", "url": "https://github.com/leanprover/lean4/commit/0dfa5c0f9bc53364943dd4b98defcfa809957481" }, { "age_days": 4, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover/lean4:4a37393b74d1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: add code quality mode to `lake lint` (#14622)", "updated": "2026-08-06", "url": "https://github.com/leanprover/lean4/commit/4a37393b74d177d5e32f06cfd097ff6eb9f507b8" }, { "age_days": 4, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "github:leanprover/lean4:ddc2f3345704", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-06", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: accept match alternatives in an `ensures` clause (#14701)", "updated": "2026-08-06", "url": "https://github.com/leanprover/lean4/commit/ddc2f33457048b96700ac50ac4badf818fc50763" }, { "age_days": 5, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:e5a38df11cfe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: stack with an allocator in the vcgen separation logic demo (#14685)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/e5a38df11cfe1e806b9f57b65b338117c33ed33e" }, { "age_days": 5, "authors": [ "Henrik Böving" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:4c29de6f2cb9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use after free in String.extract for gigantic slices (#14687)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/4c29de6f2cb93ffdabd2838c1eed6f55061bb605" }, { "age_days": 5, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:c4e6b62c3d95", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: support for assigned mvars at `SymM` discr trees (#14694)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/c4e6b62c3d955ef20da94310797072f7c4c5fa2b" }, { "age_days": 5, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:16fafca7fe94", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: support for `Expr.mdata` at `SymM` matcher (#14691)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/16fafca7fe94ea23edc0ddab9bb2f98f603df7d5" }, { "age_days": 5, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "github:leanprover/lean4:6c50efd414df", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep type ascriptions on contract clause binders (#14686)", "updated": "2026-08-05", "url": "https://github.com/leanprover/lean4/commit/6c50efd414dff04789a802cefc395fadbc549ac8" }, { "age_days": 3, "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": 3, "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": 3, "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": 3, "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": 4, "arxiv_id": "2608.05863", "authors": [ "Fanzhe Wei", "Li Liu", "Ziyang Wang", "Chenyu Wang" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.05863", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Modern models no longer keep a plain KV cache: latent caches, learned sparse selectors and recurrent states each carry the model's memory in a different form, and each fails differently under compression. We give a runtime observability contract that covers all four memory classes with three operators, instantiate it on six model configurations across five architecture families, and compose the per-stage bounds into an executable request-level risk ledger. Contracts carry their error metric as a type -- composition is only defined when metrics match, and this check rejected our own first composed chain; the repaired chain crosses metrics through two proved bridges, and whatever no formal system can certify is measured instead, dropping the composed tier to empirical automatically: every claim is certified, partially certified, or empirical, composition inherits the weakest tier, and the tier is decided by the machine. Replayed over $12.4$M entry reads and run under eight-way concurrency with per-request budgets and fail-closed identity attribution, the ledger quantifies the honest trade-off on today's witness and holds its risk budget with zero violations. A fused always-on probe observes a declared one-layer subset under CUDA graphs inside the serving noise floor. Applied to a served DeepSeek-V4 stack with a packed compressed-KV prototype, the same machinery localizes a silent corruption to a precise structural boundary -- exact in the eviction-free, identity-isolated regime, with every observed failure in an eviction or slot-reuse regime -- through a machine-adjudicated discrimination campaign whose calculus rejected two of our own confounded inferences along the way. All artifacts, guards, and the Lean development are released at https://github.com/metask-ai/witprobe-attention-memory; every number in this paper regenerates from the shipped artifacts by one command.", "title": "Runtime Observability for Heterogeneous Attention Memory", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.05863" }, { "age_days": 4, "arxiv_id": "2608.06235", "authors": [ "Zhi Li", "Xiaofei Shi" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06235", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "To probe a bipartite quantum system, one may use arbitrary global operators or restrict to product operators acting separately on the two subsystems. We determine the sharp universal comparison between the resulting norms. For every $z\\in M_n\\otimes M_m$, we prove $\\|z\\|_1\\leq\\sqrt{2}\\min\\{n,m\\}\\|z\\|_\\varepsilon$, where $\\|\\cdot\\|_1$ is the trace norm and $\\|\\cdot\\|_\\varepsilon$ is the injective tensor norm associated with the trace norms on $M_n$ and $M_m$. To prove the upper bound, we establish an $L_1$ noncommutative Khintchine inequality whose random coefficients are the entries of a Haar unitary. We also show that the coefficient $\\sqrt{2}$ is sharp. As applications, we show that the same sharp constant governs the gap between bipartite correlation measured in trace norm and that measured by a correlation function, and obtain an improved universal upper bound for quantum data hiding. The upper bound has also been formalized and machine-checked in Lean.", "title": "Global vs. Product Observables in Bipartite Quantum Systems: The Sharp Bound", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06235" }, { "age_days": 4, "arxiv_id": "2608.06652", "authors": [ "Alexandria Leto", "Rohan Das", "Juan Vásquez", "Abram Handler", "Maria Leonor Pacheco" ], "content_date": "2026-08-06", "freshness": "fresh", "id": "arxiv:2608.06652", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-06", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Conceptual metaphors guide our thinking and actions by allowing us to reason about more abstract experiences (e.g., paying taxes) in terms of more concrete or embodied experiences (e.g., carrying a physical load) (Lakoff and Johnson, 2011). It follows that different conceptual metaphors can result in different reasoning: framing paying taxes as an investment in a community rather than a physical load leads to a very different outlook on taxation. Identifying the conceptual metaphors guiding a speaker or writer thus helps to reveal their framing of events. Though these metaphors can't be observed directly, groups of linguistic metaphors, metaphorical expressions as they appear in language, serve as evidence for them. Motivated by this, we present an unsupervised method that extracts linguistic metaphors from a corpus and uses a structured clustering approach to form groups corresponding to conceptual metaphors. Using this method, we point to key topical and framing differences in left- vs. right-leaning podcasts. For example, left-leaning podcasts tend to conceptualize media stories as a weapon, while right-leaning sources commonly discuss the economy as a system subject to vertical changes.", "title": "Discovering Conceptual Metaphors Across Topics and Media Types", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.06652" }, { "age_days": 5, "arxiv_id": "2608.05451", "authors": [ "Zhengyao Lin", "Yi Cai", "Milijana Surbatovich" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05451", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Dataflow architectures have gained renewed interest due to their balance between power efficiency and performance. In (spatial) dataflow architectures, a program is represented as a set of entirely distributed and dynamically scheduled dataflow operators that communicate through asynchronous channels, which greatly improves data locality and parallelism. However, compiling to dataflow architectures remains an error-prone process, in order to maintain determinacy while enabling pipelining. Determinacy means that the result of a dataflow program is deterministic and independent of the schedule of operator execution, and pipelining is an important optimization in spatial dataflow that enables parallelism across loop iterations. In this work, we present Wavelet, the first effort to formally verify a compiler for asynchronous dataflow. We use a mix of techniques to achieve this goal. Our frontend uses a novel capability type system with fences to synchronize conflicting memory accesses and enable pipelining. We then verify a Lean formalization of two core passes of our compiler that translates elaborated programs from the type checker to dataflow graphs, proving important properties of forward simulation and determinacy. Notably, our formalization semantically propagates the soundness guarantees of the frontend type system, ensuring modularity between simulation and determinacy proofs. In evaluation, we show that dataflow graphs compiled by Wavelet have comparable sizes to those produced by an unverified optimizing compiler for the RipTide spatial dataflow architecture.", "title": "Let it Flow: A Formally Verified Compilation Framework for Asynchronous Dataflow", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05451" }, { "age_days": 5, "arxiv_id": "2608.05075", "authors": [ "Peer Saleth", "Segun T. Aroyehun", "Fabio Carrella", "Christoph M. Abels", "Stephan Lewandowsky", "David Garcia" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05075", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The spread of misinformation is widely perceived as a threat to democratic deliberation, yet how political elites' rhetorical commitments to truth shift alongside the rise of populist actors remains poorly understood. Analysing 4.5 million tweets and 59,170 parliamentary speeches by German political elites between 2015 and 2025, we measure evidence-based and intuition-based rhetoric using a validated distributed dictionary representation. Across both arenas, intuition-based language has become more prominent, and right-leaning actors consistently exhibit the lowest Evidence Minus Intuition (EMI) scores. The parliamentary entry of the extreme-right Alternative for Germany (AfD) in 2017 coincides with sharp downward shifts in EMI across the broader chamber, while a more gradual decline is observed on Twitter. These findings document an association between far-right visibility and a changing approach to truth in elite discourse in a multiparty European democracy.", "title": "German parties shifted towards intuition-based rhetoric after the far right's parliamentary breakthrough", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05075" }, { "age_days": 5, "arxiv_id": "2608.04516", "authors": [ "David Victor Feldman" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.04516", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Given finitely many compact convex bodies in $\\R^n$, one seeks translates maximizing the volume of their common intersection. A lazy solver merely translates each body so as to place its centroid at the origin. We prove that the lazy strategy always captures strictly more than $\\left(\\tfrac{2}{n+1}\\right)^n$ of the optimal volume, and that this constant is sharp: families of cones over tangent disks, indexed by finite nets on the sphere, approach it. The infimum is not attained. For two convex bodies in the plane the resulting sharp constant $4/9$ closes a gap open since 1996, when de Berg, Cheong, Devillers, van Kreveld and Teillaud proved that centroid alignment of two convex polygons captures at least $9/25$ of the maximum overlap and exhibited examples capturing only $4/9$. The proof rests on the following identity: for a convex body $K$ with centroid at the origin, the intersection of all centroid-recentered compact convex supersets of $K$ equals $\\tfrac{1}{n+1}(K-K)$. We close with a promise-problem variant in which the lazy strategy captures at least $\\left(\\tfrac{n}{n+1}\\right)^n > \\tfrac1e$ of the optimum, uniformly in the dimension. All results below have been checked in Lean~4; the one classical input quoted rather than proved is the equality case of the Brunn--Minkowski inequality, which enters only for $n\\ge2$.", "title": "Arranging convex bodies for maximum intersection volume: the sharp efficiency of centroid alignment", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.04516" }, { "age_days": 5, "arxiv_id": "2608.05142", "authors": [ "Michal Mogielnicki", "Ken Ono", "Niels Voss", "Jujian Zhang" ], "content_date": "2026-08-05", "freshness": "fresh", "id": "arxiv:2608.05142", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-05", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In 2016, Berkovich and Uncu proved that, for all nonnegative integers $i$, $j$, and $n$, the number of strict partitions of $n$ with $i$ odd-indexed odd parts and $j$ even-indexed odd parts equals the number of strict partitions of $n$ with $i$ parts congruent to $1$ modulo $4$ and $j$ parts congruent to $3$ modulo $4$. Their proof used generating functions, and they asked for a combinatorial proof. We answer their question with an explicit bijection, assembled from three classical ingredients: $2$-modular diagrams, an insertion algorithm of Chen, Gao, Ji, and Li, and Glaisher's bijection. AxiomProver autonomously formalized and verified the proof of the main theorem in Lean.", "title": "A bijective proof of a partition theorem of Berkovich and Uncu", "updated": "2026-08-05", "url": "https://arxiv.org/abs/2608.05142" }, { "age_days": 6, "arxiv_id": "2608.03803", "authors": [ "Tomáš Burkert", "Angelika Peljak-Łapińska", "David Zelený" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.03803", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Multilingual language models are deployed across a hundred or more languages, yet most benchmarks test whether a model can perform a task _in_ a language rather than whether it commands the language itself, conflating fluency with proficiency. We introduce M-GATE (Multilingual Grammar, Accuracy in Translation, and Efficiency), a benchmark of linguistic proficiency spanning 30 typologically diverse languages from high- to low-resource. M-GATE comprises three tasks: grammatical error detection on linguist-crafted, adversarially selected sentences that turn on hard, language-specific phenomena; round-trip translation of shared English sources across 29 target languages, scored by a three-provider LLM judge panel validated against professional annotators; and a supplementary tokenizer-efficiency measure. We evaluate over 50 models in more than 80 configurations. Fluency and proficiency come apart sharply: models that translate competently sit near chance on the adversarial grammar items, the best reaching a Matthews correlation coefficient (MCC) of only 0.36, and their errors lean systematically toward under-flagging, accepting ungrammatical text rather than raising false alarms. Translation quality closely tracks a language's share of pretraining data (r = 0.86 against log Common Crawl share), producing a steep low-resource penalty that is nonetheless narrowing with successive model releases. Enabling reasoning reliably improves translation, while its effect on error detection is smaller and for some models negative, so the best configuration is task-dependent. To resist contamination, test items are kept private behind a continuously updated public leaderboard, with illustrative examples released (https://m-gate.ai).", "title": "M-GATE: Multilingual Grammar, Accuracy in Translation, and Efficiency Benchmark for Large Language Models", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.03803" }, { "age_days": 6, "arxiv_id": "2608.02970", "authors": [ "Richie Sater" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.02970", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove that every finite group that is the product of every pair of its non-conjugate maximal subgroups is soluble, answering Problem 10.34 of the Kourovka Notebook (V. S. Monakhov, 1986) in the negative. Tikhonenko and Tyutyanov settled the almost simple case in 2010. What remains is the possibility of a minimal counterexample whose unique minimal normal subgroup is S^k, with S non-abelian simple and k >= 2. Because k is unbounded, no bound depending on a fixed ratio of subgroup orders can handle all such groups. We rule out this possibility with a divisibility criterion: a single pair of automorphism-stable conjugacy classes of subgroups of S, satisfying a valuation inequality, excludes the configuration for every k >= 2 and every admissible embedding. Such pairs are constructed uniformly for every infinite family of finite simple groups, with Zsigmondy primes as the arithmetic obstruction. The sporadic groups and the finitely many exceptional cases are handled by independently checkable GAP certificates.", "title": "Finite groups that are the product of every pair of non-conjugate maximal subgroups are soluble", "updated": "2026-08-06", "url": "https://arxiv.org/abs/2608.02970" }, { "age_days": 6, "arxiv_id": "2608.04061", "authors": [ "Carl Dickinson", "Gaetano Di Caterina" ], "content_date": "2026-08-04", "freshness": "fresh", "id": "arxiv:2608.04061", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Utility poles are an essential part of the infrastructure used to support power distribution systems and other critical public services. Their regular inspection is crucial to ensure the stability and safety of the electrical grid. A deep learning framework is presented for the automated detection, segmentation and lean angle estimation of wooden utility poles, and classification of attached electrical warning signs, using ground-level imagery. The system is trained on a custom dataset of 4,570 annotated images extracted from Google Street View, featuring challenging real-world scenes with visually ambiguous wooden poles lacking distinctive features. The proposed model is based on the Detection Transformer (DETR), suitably modified and trained on the custom dataset. The model outperforms standard object detectors (RetinaNet, Faster R-CNN, YOLOv3-Tiny), achieving a mean average precision of 90.43% for pole detection and 88.26% for sign detection. Extending this model with a segmentation head enables per-instance mask generation, which is then used to estimate pole lean angle. The model accurately estimates lean for 1,367 out of 1,433 test-set poles, with a mean absolute error of 1.01 degrees. Moreover, the custom dataset created in this work is also made publicly available to be used as a benchmark.", "title": "Advancing Utility Pole and Sign Detection Through Deep Learning", "updated": "2026-08-04", "url": "https://arxiv.org/abs/2608.04061" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }