{ "counts": { "adjacent": 13, "core": 5, "errors": 0, "negative": 71, "total": 89 }, "date": "2026-08-27", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-28T00:33:03Z", "items": [ { "age_days": 1, "arxiv_id": "2608.25449", "authors": [ "Jiaxin Yuan", "Connor Martinez Lockhart", "Xiaoyu Liu", "Jiaqi Wang", "Chenghao Deng", "Xiayimei Han", "Vlasios Mastrantonis", "Dmitrii Gudin", "Shaopeng Zhu", "Abdirisak Abdullahi Mohamed", "Bilal Hamdi Aytekin", "Jiewen Lang", "Zezheng Song", "Furong Huang" ], "content_date": "2026-08-26", "freshness": "fresh", "id": "arxiv:2608.25449", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-26", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Formal theorem proving enables machine-verifiable evaluation of mathematical reasoning, yet existing benchmarks often emphasize aggregate proof accuracy, concentrate on a narrow range of mathematics, and provide limited evidence of robustness to equivalent reformulations. We introduce MathAdv, a diagnostic benchmark spanning 13 domains across undergraduate- and graduate-level mathematics. Alongside Lean 4 theorem proving, MathAdv provides up to three auxiliary tasks: multiple-choice questions that probe mathematical knowledge, fill-in-the-blank problems that isolate informal reasoning, and expert-crafted transformations that test robustness to problem presentation. Our evaluation of contemporary theorem provers yields four findings: formalization remains a major bottleneck; performance varies substantially across mathematical domains; natural-language guidance helps general-purpose LLMs but can hinder proof-specialized models; and mathematically equivalent reformulations expose substantial robustness limitations. Together, these results show how component-wise evaluation can reveal model capabilities and failure modes that aggregate theorem-proving accuracy obscures. The dataset and evaluation scripts are available at https://github.com/margotyjx/MathAdv.git.", "title": "MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize", "updated": "2026-08-26", "url": "https://arxiv.org/abs/2608.25449" }, { "age_days": 2, "arxiv_id": "2608.25117", "authors": [ "Hwei-Shin Harriman", "Wode Ni", "Yuchen Jin", "Dominik Moritz", "Joshua Sunshine" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.25117", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-25", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Geometric proof is a foundational yet challenging topic in mathematics, requiring students to integrate visual, logical, and notational skills. While technology has enhanced learning in other mathematical domains, its impact on geometric proof remains limited. To investigate this gap, we interviewed 18 geometry teachers to establish the technical requirements of educational proof tools. These requirements inform our review of 33 commercial and research tools. Our findings reveal a critical mismatch: while teachers value certain digital tools for initial planning and exploration activities, they revert to pen-and-paper for formal proof because it supports diagram annotation and provides space for multiple approaches to proof-solving. Annotating the diagram is a key component of the proof-solving workflow that existing tools do not support. We propose four technical and human-centered design guidelines for educational proof tools to meet teacher needs at scale: integrating diagram and proof, generating problems and feedback automatically, supporting multiple proof formats, and reducing accidental complexity in the user experience.", "title": "Teaching Geometric Proof with Tech: Pitfalls and Possibilities", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.25117" }, { "age_days": 3, "arxiv_id": "2608.23281", "authors": [ "Ludovic Tagnon" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23281", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-24", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Hermite asked in 1848 for a representation of real numbers whose eventual periodicity characterizes cubic irrationals. The totally real case was solved by Karpenkov's $\\sin^2$-algorithm; the complex case, signature (1,1), is his Problem 4. We study a deterministic algorithm implementing his suggested analytic extension: the score expression is strictly negative on (1,1) data (closed form proved), the most negative score is selected, and exact score ties are resolved by a declared ordering. On a sample of 205 complex cubic polynomials, every run closes projectively with an exact unit certificate, each transition certified by exact comparisons in $\\mathbb{Q}(α)$. An exhaustive campaign over the full box $[-3,3]^3$ closes 194/194. Across 457 deformed bases, the terminal cycle is an invariant of the marked lattice. Certified finite transition graphs are computed for four fields; the plastic case is machine-checked in Lean 4, kernel-only. All data ship in a public archive with a portable verifier.", "title": "A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23281" }, { "age_days": 6, "arxiv_id": "2608.20793", "authors": [ "Sihai Jin" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "arxiv:2608.20793", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-21", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We report a Lean 4 formal verification accompanying the paper \"Subregular Affine Cells and the Level -1 Vertex Algebra of Type D\" (arXiv:2608.11997). The formalization kernel-checks substantial internal parts of the proof architecture, including the Section 4 membership/descent chain, the type-D norm-gap argument, zero-orbit energy and signed-permutation rigidity, node-weight and numerical rigidity calculations, the exhaustion logic, the passage to the candidate quotient classification, the simple-object count, the final additive Grothendieck-group comparison, and the coefficient-substitution layer of the uniform character formula. Higher representation-theoretic results whose foundational infrastructure is not presently constructed in the file are isolated as explicit semantic interfaces rather than introduced as Lean axioms. Thus the precise claim is a kernel-checked internal deduction from explicit representation-theoretic boundary inputs, not a from-scratch formalization of vertex algebras, BRST reduction, finite W-algebras, or affine Hecke theory inside Mathlib.", "title": "A Lean 4 Verification Report for Subregular Affine Cells and the Level $-1$ Vertex Algebra of Type $D$", "updated": "2026-08-21", "url": "https://arxiv.org/abs/2608.20793" }, { "age_days": 7, "arxiv_id": "2608.20432", "authors": [ "Shane Caldwell" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.20432", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-20", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Formal proofs in Lean 4 that pass the kernel's type checker can nonetheless vary widely in quality. We introduce ProofJudge, an agentic LLM-as-judge system that scores formal proof quality along five dimensions beyond correctness: library leverage, automation fit, structural clarity, statement quality, and Mathlib conventions. We evaluate ProofJudge on a novel dataset of 218 declarations drawn from distinct Mathlib PRs. The judge agent is grounded by tool access to the commit the PR is applied to, enabling it to query the library state when scoring. A judge is considered aligned with human preferences when it rates the version of the PR Mathlib accepted above the initial version that was sent back for revision. All six judge models evaluated recover the reviewers' preference well above chance, from 80.8% to 63.5%, and two open-weight judges reach roughly 70% at a tenth of the best judge's cost. We release the judge harness, evaluation dataset, and evaluation traces as open-source artifacts to support further research.", "title": "ProofJudge: Tool-Grounded LLM Evaluation of Formal Proof Quality in Mathlib", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.20432" }, { "age_days": 8, "arxiv_id": "2608.19093", "authors": [ "Mengwei Su", "Kaiwen Yang", "Hao Xu", "Chih-Lin I" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.19093", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-19", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Among $n+1$ equiprobable equal-energy signals in $\\R^n$ under additive white Gaussian noise with maximum-likelihood decoding, which arrangement maximizes the probability of correct decoding? The question is Shannon's, recorded by Rice in 1950. Mulgund proved in 2026 that the regular-simplex value bounds the correct-decoding probability of every signal set at every signal-to-noise ratio, leaving open whether the simplex is the only maximizer. This paper determines the equality cases in a form stronger than uniqueness. A signal set other than a regular simplex falls strictly below the bound at every positive signal-to-noise ratio. Hence a code meeting the bound at one positive operating point is already a regular simplex, up to vertex relabeling and an orthogonal map. In probabilistic form, among the correlation matrices that signal sets induce, any matrix other than the identity gives a lower-orthant probability strictly above its independent counterpart at every finite threshold, leaving no room for a nontrivial equality. No code of ambient dimension below $n$ attains the bound. Under an energy budget $E$ with unrestricted blocklength the optimal codebook is uniquely the regular simplex of circumradius $\\sqrt{E}$. Every optimal codeword therefore exhausts its allowance. Equality in the Simplex Mean Width Conjecture likewise occurs only at the regular simplex. The proof strengthens the first self-convolution step of Mulgund's argument with Royen's correlation theorem. The single-parameter rigidity is machine-checked in Lean 4.", "title": "The Equality Cases of the Weak Simplex Conjecture", "updated": "2026-08-19", "url": "https://arxiv.org/abs/2608.19093" }, { "age_days": 2, "arxiv_id": "2608.25057", "authors": [ "Dakota Charles Baker" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.25057", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A point lies in the kernel of a polygon if it can see the entire polygon. Thus the kernel measures how much of the polygon is available to a single guard, while the convex hull measures how far the polygon is from being convex. We prove that these two losses are linked by a sharp factor of two: the area lost between a polygon and its kernel dominates twice the kernel-weighted area missing from the polygon's convex hull. In terms of Sibley's guard-point ratio $G$ and exterior ratio $E$, which we denote by $A$, the result is $G \\leq A/(2-A)$, which improves Nakano's inequality $G \\leq A$ whenever $A < 1$. The proof passes through a convex-body cap union. From a compact convex body $K$ and finitely many points whose convex hull contains it, we join every point to $K$ and take the union $U$ of the resulting caps. Cyclically sorting the directed boundary edges of a polygonal $U$ produces a convex companion $H$. A boundary-reversal argument gives $|H| + |U| \\geq 2|\\mathrm{conv}\\, U|$, while a support-function identity and Minkowski's mixed-area inequality give $|U|^2 \\geq |K||H|$. Inner polygonal approximation handles every positive-area compact convex $K$, while a separate null-area branch covers points, segments, and all other lower-dimensional cases. Both main theorems have machine-checked Lean 4 proofs whose final statements were audited against the informal statements after kernel checking.", "title": "The Kernel Deficit Dominates Twice the Hull Deficit: A Sharp Strengthening of Nakano's Inequality", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.25057" }, { "age_days": 2, "arxiv_id": "2608.25194", "authors": [ "Ashutosh S. Jogalekar" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.25194", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "RNA inverse folding asks for an RNA sequence whose prescribed secondary structure is the unique maximum-base-pair compatible fold. In the four-letter Watson-Crick model (A-U and C-G pairs only, no pseudoknots, and zero minimum base-pair span), Hales et al. introduced a separated-coloring certificate and an even-odd device, while Boury et al. generalized this to modulo-$m$ separability, gave an $O(n 2^m)$ decision algorithm, and guaranteed designability when every helix has length at least 3. We prove that the guarantee still holds when a motif-free target has at most two maximal helices of length 2, no maximal helix of length 1, and all remaining helices of length at least 3. The proof builds on Boury et al.'s local helix-coloring transfers and adds a global counting argument showing that the demands created by at most two short helices can always be coordinated. This is a structural success guarantee for the existing modulo-2 algorithm, not a new general decision capability. The resulting coloring yields an explicit sequence whose every distinct compatible noncrossing fold has fewer pairs. No claim is made for nearest-neighbor thermodynamic energy models. The theorem and supporting lemmas are formalized in Lean 4 against pinned Mathlib and reproduced from a frozen public artifact; the kernel-reported axiom set is $\\{\\mathrm{propext},\\mathrm{Classical.choice},\\mathrm{Quot.sound}\\}$. The work was developed with foundational generative-AI assistance under the author's direction and has not yet received independent human expert review.", "title": "Designability of RNA Targets with Up to Two Length-2 Helices", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.25194" }, { "age_days": 2, "arxiv_id": "2608.24750", "authors": [ "Ludovic Tagnon" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.24750", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We develop the structure theory of the deterministic $\\sin^2$-type algorithm for complex cubic fields introduced in the companion paper, addressing the complex-signature case of Karpenkov's Problem 4. The selection rule is shown to be, exactly, the minimization of a conformal module: the hyperbolic cosine of the distance between the transverse complex structure of the state and the round point. All governing quantities are exact elements of the real embedding of the field and satisfy closed dual-type identities; in particular no isotropic candidate ever arises, and the transverse deviation lattice has exactly pinned covolume. We prove an unconditional soft-rebound lemma (the module can grow by at most the factor $\\varphi^2 = 2.618\\ldots$ in one step), a finiteness theorem for states of bounded module and height at fixed coordinate discriminant, with explicit static constants, and a per-field periodicity theorem under two named hypotheses: $(C_κ)$, contraction of the module in the high phase, partially reduced here to a fixed finite minimax over a five-parameter compact with rational objective; and (B), recurrence of bounded height, which we then prove under $(C_κ)$ alone: a height-descent theorem shows the height can never exceed $\\max(H(s_0), C_H)$ with an explicit constant. The remaining program for per-field periodicity is reduced to (R) on the compact and to the proved stretched subcases. All proved statements and certificates are finite and exact. A machine-checked core of the paper is sealed in Lean 4, kernel-only, under the standard axioms: the analytic core of the height-descent theorem, the finiteness pigeonhole, the dual and conformal identity layer, and an abstract assembly theorem composing them through named interface hypotheses.", "title": "A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.24750" }, { "age_days": 3, "arxiv_id": "2608.23659", "authors": [ "Cătălin I. Cârstea" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23659", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-08-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "This reports on an experiment in autoformalization of arxiv:2606.15977, an inverse problems result for piecewise polynomial anisotropic conductivities, using Isabelle/HOL. The proof of the result is relative to a number of external results which were deemed to be well known and generally accepted to be true. The formalization files are made available at a GitHub repository. Translation issues are discussed.", "title": "Relative formalization in Isabelle/HOL of a result in inverse problems", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23659" }, { "age_days": 3, "arxiv_id": "2608.23247", "authors": [ "Ryuta Arisaka", "Hirotaka Ono" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23247", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We introduce multi-winner voting with argumentative ballots (MVArg) and investigate theoretical properties. As our conceptual contribution, we generalise approval ballots to argumentative ballots, thereby allowing voters to express defeasible preferences over candidates. We accordingly generalise voter cohesion and justified representation axioms JR, PJR and EJR. As our theoretical contribution, we establish several key results. First, MVArg is strictly more expressive than multi-winner voting with approval ballots (MV). Second, our notions of cohesion and justified representation are conservative generalisations of their counterparts in MV. Third, the MVArg counterpart of JR can always be satisfied, whereas the counterparts of PJR and EJR cannot always be. Fourth, although verifying whether a winner set satisfies the MVArg counterpart of JR is already coNP-hard, such a winner set can be constructed in polynomial time. All definitions, propositions, auxiliary lemmas and theorems have been formalised and mechanically checked in Lean 4.", "title": "Multi-Winner Voting with Argumentative Ballots", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23247" }, { "age_days": 3, "arxiv_id": "2608.23652", "authors": [ "Glauco Rampone" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23652", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For integers $k,g \\ge 3$ let $n_g(k)$ denote the minimum order of a graph with chromatic number $k$ and girth at least $g$. Exoo and Goedgebeur (DMTCS 2019) proved $26 \\le n_6(4) \\le 66$; their 66-vertex witness has remained the smallest known 4-chromatic graph of girth 6. We improve both bounds to $29 \\le n_6(4) \\le 64$. The upper bound is witnessed by an explicit 4-chromatic graph of girth 6 on 64 vertices with 152 edges; it is vertex- and edge-critical, and its automorphism group is cyclic of order 8 and acts semiregularly. The lower bound is an exhaustive isomorph-free computation in the SAT modulo symmetries framework with co-certificate learning, driven by the Liu-Postle edge-density bound for 4-critical graphs of girth five; it re-derives $n_6(4) \\ge 26$ by a disjoint method and is validated on the known values $n_4(4)=11$ and $n_5(4)=21$. We complement the bounds with structural obstructions: no smaller witness arises from either known witness by local modifications; no 4-chromatic Cayley graph of girth 6 exists on 54-63 vertices (for orders 59 and 61 no vertex-transitive witness exists at all); and no witness on at most 63 vertices admits a semiregular automorphism group with two or three vertex orbits, for any finite group. Since every known witness of an $n_g(4)$ record with $g \\ge 6$ is a lift of a small base graph along a semiregular action, these results close the most symmetric part of that regime below 64 vertices. All properties of the new graph are verified by independent programs and formally certified in the Lean 4 proof assistant: the non-3-colourability is established inside Lean by a formally verified checker that re-validates a 219,532-node refutation certificate, with a machine-checked soundness theorem.", "title": "Improved bounds for the smallest 4-chromatic graph of girth six", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23652" }, { "age_days": 5, "arxiv_id": "2608.21712", "authors": [ "Deyi Li", "Qi Xu", "Lingyao Li", "Tiansheng Wang", "Muxuan Liang", "Mei Liu" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "arxiv:2608.21712", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-08-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Transformer-based models are widely used for clinical prediction from electronic health records (EHRs), yet their architectures require manual tuning, and the optimal configuration may vary across tasks and hospitals. Neural architecture search (NAS) automates architecture design, but conventional methods are computationally costly for Transformer-based EHR models. Recent large language model (LLM)-guided NAS methods reduce manual search design but conduct each search independently, without reusing architecture knowledge across hospitals. In this study, we propose ATHENA (Agentic Transfer across Hospitals for EHR Neural Architecture Search), a knowledge-guided agentic NAS framework for Transformer-based EHR modeling. ATHENA uses a weight-sharing supernet that is pretrained once per hospital, allowing candidate architectures to be instantiated as inherited subnetworks and evaluated through fine-tuning rather than independent pretraining. It incorporates a two-layer cross-hospital architecture prior. The first layer retrieves high-performing architecture examples from source sites based on task descriptors, while the second estimates the effects of architectural components using SHapley Additive exPlanations (SHAP)-based meta-regression. These priors guide a multi-agent LLM search using validation feedback from the target hospital. Across six clinical prediction tasks evaluated at one held-out OneFlorida+ site and one external MIMIC-IV site, ATHENA significantly outperforms all four baselines in 9 of 12 site-task evaluations under a strict equal-compute comparison. Using a common pretrained AutoFormer supernet for candidate evaluation, ATHENA ranks first in 9 of 12 evaluations at a search budget of 30. It also shows more consistent architecture selection across repeated searches. ATHENA provides a practical approach for reducing manual architecture tuning in Transformer-based EHR modeling.", "title": "ATHENA: Knowledge-guided agentic neural architecture search for AutoFormer-based electronic health record modeling", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.21712" }, { "age_days": 6, "arxiv_id": "2608.21356", "authors": [ "Jason Hickey" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "arxiv:2608.21356", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-21", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI inverts this relationship: at AI speed, machine verification is not only economical but essential to productivity --- it is the incorruptible referee that lets one person safely direct autonomous machine work at scale. In five weeks, one researcher on consumer AI subscriptions directed a small fleet of AI agents from application code, through a verified compiler and executive, to a RISC-V processor taped out on a community silicon shuttle; no proof passed through human review, and no RTL was written by a human. The working discipline --- the Salt method --- rests on a proof kernel no hallucinated proof can pass: mathematical claims travel between agents as kernel-checked artifacts, and human attention is reserved for statements, designs, and rulings. Verification is stated link by link, from the Lean 4 kernel to SAT-checked equivalence at the silicon boundary. We publish the complete accounting: theorem provenance, a pre-registered token meter, floor-bounded human time, and an error ledger whose catch numbering runs to #256 --- a monotone counter over the mathematics campaign's append-only flags ledger, maintained 2026-07-07 to 2026-07-20 (one number, #79, was never assigned; later catches are recorded un-numbered) --- against zero incorrect proofs reaching the record.", "title": "AI with Authority, from Application to Silicon", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.21356" }, { "age_days": 7, "arxiv_id": "2608.20153", "authors": [ "Dingzirui Wang", "Xuanliang Zhang", "Keyan Xu", "Qingfu Zhu", "Wanxiang Che" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.20153", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-08-20", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) have shown growing potential for automated theoretical computer science (TCS) research, yet existing benchmarks remain far from realistic research settings. We introduce \\ourbenchmark, an expert-validated benchmark for evaluating LLMs on frontier, end-to-end TCS research. \\ourbenchmark contains $175$ instances drawn from papers accepted to STOC, FOCS, SODA, and COLT in 2025-2026, preserving paper-specific definitions, assumptions, and proof dependencies, with expert-verified Lean formalizations and proofs. Evaluations of leading LLMs reveal that current models remain far from reliably completing the full research pipeline. In particular, autoformalization is the sharpest bottleneck: the best model achieves only $11.5$ on translating natural-language claims into formal theorem statements, compared with $28.6$ Pass@8 when proving human-provided formal statements. Building on \\ourbenchmark, we further develop an automated TCS research framework that generates, formalizes, filters, and proves new claims. Of $64$ generated claims, only $6$ ultimately pass expert evaluation and proof verification, indicating that beyond formalization, limited research taste remains another major barrier to autonomous TCS research.", "title": "FormalTCS: Benchmarking End-to-End Frontier Formal Theoretical Computer Science Research of Large Language Models", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.20153" }, { "age_days": 7, "arxiv_id": "2608.19847", "authors": [ "Benqi Liu", "Kangkang Deng", "Zichen Wang", "Zaiwen Wen" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.19847", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-20", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Augmented Lagrangian methods are effective for nonlinear equality-constrained optimization, but solving their nonlinear primal subproblems can be expensive. For smooth nonconvex problems with deterministic or stochastic objectives, we propose a nonlinear-residual linearized augmented Lagrangian method (NR-LALM) that replaces this subproblem by a regularized Gauss-Newton-type step while retaining the classical multiplier update based on the nonlinear constraint residual. The resulting step is computed from one symmetric positive-definite linear system, but the mismatch between the linearized primal model and the nonlinear-residual update produces a quadratic constraint-linearization error in the multiplier identity. We show that this error can be controlled under local regularity; multiplier boundedness and trajectory localization are derived rather than assumed. With fixed, accuracy-independent parameters, deterministic NR-LALM finds an $\\varepsilon$-approximate Karush-Kuhn-Tucker (KKT) pair in $O(\\varepsilon^{-2})$ iterations and first-order oracle evaluations. For stochastic objectives, a projected stochastic path-integrated differential estimator with safeguarded restarts requires, in expectation, $O(\\varepsilon^{-3})$ stochastic-gradient evaluations and $O(\\varepsilon^{-2})$ constraint and Jacobian evaluations. Compactness and a Kurdyka-Lojasiewicz condition further yield finite-length convergence of the deterministic primal-dual sequence. An optional minimum-norm second-order correction reduces the constraint-linearization error from second to fourth order without changing the complexity orders. All theoretical results are formalized in Lean 4. Numerical experiments confirm the predicted error orders and show favorable performance on high-dimensional deterministic and stochastic problems.", "title": "A Fixed-Penalty Linearized Augmented Lagrangian Method with Classical Multiplier Updates", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.19847" }, { "age_days": 8, "arxiv_id": "2608.19058", "authors": [ "Mahadee Al Mobin", "Md. Shariful Islam" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.19058", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-19", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We state and prove the Theorem: for primes $p < 10^n$ with base-$10$ expansion $p = \\sum_{k=0}^{n(p)-1} d_k(p) 10^k$, the positional digit probabilities $P_n(d \\mid k)$ satisfy \\[ \\lim_{n \\to \\infty} P_n(d \\mid k) = \\begin{cases} 1/10, & k \\ge 1,\\ d \\in \\{0,\\dots,9\\}, \\\\[4pt] 1/9, & k = \\mathrm{lead},\\ d \\in \\{1,\\dots,9\\}. \\end{cases} \\] The limiting behavior splits cleanly into two distinct mechanisms: an arithmetic regime for interior digits and an Archimedean regime for the leading digit. For fixed interior positions ($k \\ge 1$), digit extraction modulo $10^{k+1}$ reduces the problem to prime counts in reduced residue classes, where uniform distribution follows from Siegel--Walfisz (with Bombieri--Vinogradov allowing $k$ to grow with $n$). For the leading digit, the $1/9$ limit is not a Benford-type scale invariance, but arises from the local near-constancy of the prime density $1/\\log t$ within single decades combined with a Toeplitz-type error averaging. Explicit classical and conditional error bounds are recorded for both regimes.", "title": "The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers", "updated": "2026-08-19", "url": "https://arxiv.org/abs/2608.19058" }, { "age_days": 5, "arxiv_id": "2608.21749", "authors": [ "Siwei Zeng" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "arxiv:2608.21749", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-22", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "The general subgroup permanental-dominance conjecture was previously known only through matrix order three. This paper proves its complete order-four case: for every subgroup $H\\leq S_4$, every irreducible complex character $χ$ of $H$, and every $4\\times 4$ Hermitian positive-semidefinite matrix $A$, it establishes $d_χ^H(A)/χ(1)\\leq \\operatorname{per} A$. Unlike the usual immanant specialization, the result covers all thirty-seven irreducible-character cases arising from the eleven conjugacy classes of subgroups of $S_4$. Thirty-five cases follow from general principal-minor, moment, and block-contraction inequalities. The two non-real $A_4$ characters are reduced to polynomial nonnegativity on the cone of $3\\times 3$ positive-semidefinite Gram matrices and are resolved by a rank-one sum-of-squares identity, an exact positive-definite interior certificate, rational Gram certificates, and closure of the Gram cone.", "title": "The General Subgroup Permanental-Dominance Conjecture in Order Four", "updated": "2026-08-22", "url": "https://arxiv.org/abs/2608.21749" }, { "age_days": -1, "authors": [ "Marcelo Lynch" ], "content_date": "2026-08-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5ba951246811", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(cache): retry transport errors, improve transfer robustness (#43145)", "updated": "2026-08-28", "url": "https://github.com/leanprover-community/mathlib4/commit/5ba95124681110751345e9bd360994de8541027c" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:f3c6b8462d6c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: new LRAT checker (#14842)", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/f3c6b8462d6cbfcd2fb09599bf5820c59ca6773c" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:e991a05e359a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: initialize only the core modules `leanchecker-paranoid` needs (#14936)", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/e991a05e359a25988f49bff3ab8af986e959b866" }, { "age_days": 0, "authors": [ "Salkutsan Aleksey" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:459d43013417", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: avoid exposing Fin.foldl implementation (#14554)", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/459d4301341708de7c16350aeea647b112c62321" }, { "age_days": 0, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:b66d310c2420", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: sane `rwa` (#14937)", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/b66d310c242069d99fccc0d5dd30ef72aec090c7" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:61bb5655d092", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: read persisted code quality entries in `lake lint --code-quality` (#14933)", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/61bb5655d092c910d5f1b9f671ceeab87db6a964" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover/lean4:342db4dbdb3a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-08-27", "url": "https://github.com/leanprover/lean4/commit/342db4dbdb3aab611e0b92ddba0c134c9b28b2f9" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e7b8da838099", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor: definition and notation for `EventuallyEq` on `Set` (#41533)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/e7b8da838099d0bfea089b70a448e3c9b6cdbffd" }, { "age_days": 0, "authors": [ "Anatole Dedecker" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6adc76237854", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: the set of Fredholm operators between two Banach spaces is open (#42742)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/6adc762378546d91bfc6c56d3f0baa805ffe00a9" }, { "age_days": 0, "authors": [ "Anatole Dedecker" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a835c1cf4553", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: the index of Fredholm operators is locally constant (#43085)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/a835c1cf45531b86d17b382318fd1cb2cfb22eb0" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cd5cc699bb5d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: expand API around LinearMap.index (#43146)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/cd5cc699bb5d2f3c75b14d50f03d054cb58150a2" }, { "age_days": 0, "authors": [ "Riccardo Brasca" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:33bca90bdcde", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add ModularForm.qExpansionAlgHom (#42331)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/33bca90bdcde97c36db11e9a8fd0eec79bc71d73" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b42d4552187a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/MetricSpace): variant of the Lebesgue number lemmas (#43171)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/b42d4552187a13b5d9dfc793a6d2cb53ced8e88b" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1b878ee44e04", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Covering): introduce Deck transformation group (#40135)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/1b878ee44e04e5971ec37a53edc9be687080d545" }, { "age_days": 0, "authors": [ "Lexa" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:287cf38f7f33", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/Wilson): explicit square root of -1 modulo a prime (#42326)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/287cf38f7f3366ab5954f0d91c915f26a9adfcb4" }, { "age_days": 0, "authors": [ "David Loeffler" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:900e11b053a9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/Padics): the Amice transform (#42832)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/900e11b053a9fddbec281694eadb75a6331e4573" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:39c86ed8eb69", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/NumberField/AdeleRing): define the idele class group (#40735)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/39c86ed8eb69c9ef854f1f2de1b7b7bd171fef15" }, { "age_days": 0, "authors": [ "Seewoo Lee" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:89fb8862028f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/ModularForms): `E₂` is 1-periodic (#42210)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/89fb8862028fb67d078d483330cbaa7f72c8929e" }, { "age_days": 0, "authors": [ "Seewoo Lee" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e2147bb9454f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(ModularForms): Ramanujan formula for derivatives (#42211)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/e2147bb9454ffd030794d5545c2f9cd225e5ac49" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:aa28759c5b07", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(GroupTheory/Perm): another decomposition of permutations of `Fin (n + 2)` (#43168)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/aa28759c5b076f5def19d019f7f501215264603b" }, { "age_days": 0, "authors": [ "Thomas Krishna Waring" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9b198489cafe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(GroupTheory/Nilpotent): elements with coprime orders commute (#43071)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/9b198489cafef0ae46ce9557b9730f5c231e2582" }, { "age_days": 0, "authors": [ "Joseph Myers" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9791f8f704c1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Euclidean/Sphere/PolePolar): poles and polars (#31892)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/9791f8f704c10ddd96219f87083f1cf87677ab0a" }, { "age_days": 0, "authors": [ "Wenrong Zou" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:415467484431", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FieldTheory/Finite): add variant theorems for `expand_card` (#39219)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/41546748443172d634b273da9da143d3d2f22bb2" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:589208471b29", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/Trails): the support of an Eulerian trail equals the support of the graph (#41632)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/589208471b29b1f0220edd901c62ad81d0b12333" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:baa74fbf3951", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/LapMatrix): 0 is always an eigenvalue (#39627)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/baa74fbf3951dc5007d840c201f6f3911a9dbfd5" }, { "age_days": 0, "authors": [ "Dhruv Gupta" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b9d865b99bfd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SetFamily): Assouad's dual VC bound (#38319)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/b9d865b99bfd8ca8b6624dd13056fccdc61a531a" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d9a2cf3a0edf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Preadditive): existence of a zero object from coproducts (#43173)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/d9a2cf3a0edf529bcfd6f2f684ca6cbaab5ecdff" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cc2a4a8ff4c7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Ring/WithAbs): add `AbsoluteValue.under` (#42566)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/cc2a4a8ff4c7143b6bdf4faaa418f97721a3efb5" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1f495c611d05", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Field/WithAbs): algebra structure on `AbsoluteValue.Completion` (#42542)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/1f495c611d05d2215058cd77c7897d625bc3b445" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:008a61c197c3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(Algebra): fix typo (#43151)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/008a61c197c3e2f4bdcc0243eb1821da18f6cfef" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d9fa3cd07a7d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: variations of `ContinuousLinearEquiv.isOpen` (#43147)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/d9fa3cd07a7d01f2c23ded95b5e1cbf2a873d933" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c8de5d090adc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "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 2026-08-27 (#43164)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/c8de5d090adcfc9b5a17fa4610cc8ff9874e83a6" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b5b6c07984d2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Util): tidy markdown headers (#43126)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/b5b6c07984d223ce4413bb764051ce3552b18ce9" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b40b7830487a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Fin/Basic): avoid importing lattices (#43156)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/b40b7830487aa1477ecf73a9437c45e613292bae" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f988eda5de1a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Combinatorics/SimpleGraph/CycleGraph): golf `cycleGraph_isContained_iff` (#42964)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/f988eda5de1aff03157c116b01178564a2ad1c01" }, { "age_days": 0, "authors": [ "Moritz Doll" ], "content_date": "2026-08-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a09ee8556b32", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Analysis/LocallyConvex): add missing lemmas (#42848)", "updated": "2026-08-27", "url": "https://github.com/leanprover-community/mathlib4/commit/a09ee8556b328b3976c273a283e6979a1c1f8ae6" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-26", "freshness": "fresh", "id": "github:leanprover/lean4:31aea96d017b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: persist code quality entries in an environment extension (#14914)", "updated": "2026-08-26", "url": "https://github.com/leanprover/lean4/commit/31aea96d017b53c6acf56577b20e4ef48421af9e" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-08-26", "freshness": "fresh", "id": "github:leanprover/lean4:940c33d992b8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support some symbolic `Nat` operations in `bv_decide` (#14928)", "updated": "2026-08-26", "url": "https://github.com/leanprover/lean4/commit/940c33d992b87d120c1b28e2732bad5ec3790186" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-26", "freshness": "fresh", "id": "github:leanprover/lean4:ec5816f82fab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add a `leanchecker-paranoid` binary with mimalloc mitigations (#14884)", "updated": "2026-08-26", "url": "https://github.com/leanprover/lean4/commit/ec5816f82fabf7d0982f388a19694a926c9ec5ac" }, { "age_days": 2, "authors": [ "Henrik Böving" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:4620e4d94695", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: make `UIntX.ofNatClamped` use `BitVec.ofNatClamped` (#14917)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/4620e4d946957ae7c582764c79eb93cc779f77e2" }, { "age_days": 2, "authors": [ "Joachim Breitner" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:0dc10a41e6be", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: skip data-valued constructions for small-eliminating inductives (#14909)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/0dc10a41e6be57ef72d7f103c98c263620076b6c" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:761d5b7c2cfc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: enforce set notation per-element indentation (#14350)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/761d5b7c2cfc38528e6c1b31cbc393c0d26038a8" }, { "age_days": 2, "authors": [ "Joachim Breitner" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:60bc92ddcc5b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: do not register the well-founded recursion simprocs globally (#14922)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/60bc92ddcc5bb9db94f5835a55771f110dcb55df" }, { "age_days": 2, "authors": [ "Joachim Breitner" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:111a89710343", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: do not apply simproc candidates selected for a rewritten expression (#14921)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/111a89710343cd087b6a2c93e1e9b3a845245eee" }, { "age_days": 2, "authors": [ "Fawad Haider" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:8af42c4eb193", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: correct lean_kernel_diag_is_enabled declaration to match generated C (#14886)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/8af42c4eb193246a86bf97c72f58dc03b29a4216" }, { "age_days": 2, "authors": [ "Joe Hendrix" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:6f48b8aa6a15", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: correct LEAN_EXPORT attribute order in ffi.cpp (#14888)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/6f48b8aa6a15ca7cce1fa5d79265185d2ea7bffd" }, { "age_days": 2, "authors": [ "Joachim Breitner" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:30ad6f54fd4a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: build `casesOn` for propositions from projections (#14925)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/30ad6f54fd4a9e3193156fbb25c7f0e76a50d927" }, { "age_days": 2, "authors": [ "Robert J. Simmons" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:b9c9eb9a3ace", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: create asNode/mkNode abstraction for DiscrTree (#14911)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/b9c9eb9a3acefaa242c1da2a31e3723e94fde3a5" }, { "age_days": 2, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:8c07c8f7c1c4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add strong (co)induction principles for lattice-theoretic predicates (#14855)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/8c07c8f7c1c475db22594bc7595472daa0c438b2" }, { "age_days": 2, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:e276422fda5c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add hint to transitive `deprecated` usage warning (#14841)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/e276422fda5ca6cff5999766b98291ffa274d919" }, { "age_days": 2, "authors": [ "Julien Cretin" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:f06ec8bb53ba", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix typo in example of SourceInfo.synthetic (#14756)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/f06ec8bb53ba5a807765534b5e8d583349c2ba70" }, { "age_days": 2, "authors": [ "Julien Cretin" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:21eb84ff5bd6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix typo in Init.Data.Repr (#14750)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/21eb84ff5bd6b7b2969796d5b8853ac5afe683a4" }, { "age_days": 2, "authors": [ "Julien Cretin" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:174754bba994", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix imprecision in IO.FS.Stream.getLine and IO.FS.Handle.getLine (#14754)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/174754bba9943a578ce980d59a0f5e7f05749182" }, { "age_days": 2, "authors": [ "Eric Wieser" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "github:leanprover/lean4:fec54a0941cf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: golf two DerivingHelper proofs (#14867)", "updated": "2026-08-25", "url": "https://github.com/leanprover/lean4/commit/fec54a0941cfb51c4e49a13825adfbd1ca6ccbaa" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "github:leanprover/lean4:7169e0500dda", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: reduce aggressiveness of BitVec e-matching (#14905)", "updated": "2026-08-24", "url": "https://github.com/leanprover/lean4/commit/7169e0500ddaf19c1f0d79b2b4c23c854cf50d43" }, { "age_days": 3, "authors": [ "Mac Malone" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "github:leanprover/lean4:dd9cb93def1f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: sync `--fail-fast` test via job dependencies (#14907)", "updated": "2026-08-24", "url": "https://github.com/leanprover/lean4/commit/dd9cb93def1f4678434f84afb72ee8378c0800e4" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "github:leanprover/lean4:5c6bce120d03", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add ground evaluation Nat.log2 support (#14915)", "updated": "2026-08-24", "url": "https://github.com/leanprover/lean4/commit/5c6bce120d03401245d25ae79a4bb0d6654a5df8" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "github:leanprover/lean4:1dbcfb17854f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add BitVec.ofNatClamp (#14916)", "updated": "2026-08-24", "url": "https://github.com/leanprover/lean4/commit/1dbcfb17854ffb313419ef05578c95fbd4136859" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "github:leanprover/lean4:923390e2f934", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: reuse the Lake artifact cache in non-release builds (#14665)", "updated": "2026-08-24", "url": "https://github.com/leanprover/lean4/commit/923390e2f93471c98ac318f986f6a07186255f99" }, { "age_days": 2, "arxiv_id": "2608.25220", "authors": [ "Henry Robbins", "Connor Lawless", "Madeleine Udell", "Ellen Vitercik" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.25220", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Mixed-Integer Linear Programming (MILP) is a fundamental tool for combinatorial optimization with extensive real-world applications. A central challenge is designing computationally efficient MILP formulations. Large Language Models (LLMs) offer new opportunities to automate the modeling process, from deriving formulations to strengthening them. Reliable automation requires robust methods for verifying that proposed formulations preserve the underlying optimization problem. However, existing approaches evaluate formulations numerically and fail to reason about general problem instances. We resolve this limitation by introducing a constructive definition of MILP reformulation that can be formalized in Lean and machine-checked. We develop FLARE (Formulation-Level Automated Reformulation Evaluation), a method that uses an LLM-based agent and the Lean proof assistant to verify proposed reformulations against a reference formulation. To evaluate our approach, we introduce FormulationBench, a challenging dataset of 20 problems and 109 formulations. FLARE outperforms existing methods, with 100% accuracy on the NP-hard subset of FormulationBench. Furthermore, FLARE produces a machine-checkable certificate for every reformulation it accepts. For cases where formal guarantees are not necessary, we introduce FLARE-NL, a fast and cheap LLM proxy that matches FLARE's accuracy but produces no certificate. These methods enable reliable verification in automated optimization modeling.", "title": "FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.25220" }, { "age_days": 2, "arxiv_id": "2608.24964", "authors": [ "Yiheng Feng" ], "content_date": "2026-08-25", "freshness": "fresh", "id": "arxiv:2608.24964", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "This note studies the geometry of full conformal prediction (FullCP) regions generated by an empirical energy-form pairwise score. Candidate-score convexity alone does not guarantee connected FullCP regions, even when the candidate score is an empirical average of a loss convex in its first argument. Direct expansion of the leave-one-out scores shows that each training-point comparison for the energy-form score is exactly a pairwise-dissimilarity sublevel condition. Under symmetry, a constant diagonal, a diagonal lower bound, and attainment of the associated Fréchet-type objective, every comparison region contains a common minimizer; when the comparison regions are convex, the nontrivial exact conformal region is therefore star-shaped about that same point. For power distances $ρ_β(x,y)=\\|x-y\\|^β$, this deterministic geometry holds for $β\\ge1$, while the conventional energy score is strictly proper for $0<β<2$. In the univariate $β=1$ specialization, every nontrivial empirical-CRPS FullCP region is a nonempty closed interval, possibly $\\mathbb R$ in the $m=1$ degeneracy. On the unconditional reconstruction range $1<β<2$ and $m\\ge2$, explicit data-checkable derivative bounds yield Lipschitz control of the comparison-set radial exits and hence of the exact conformal radial function. These score-specific bounds permit existing directional root-search ideas and classical Lipschitz-extension machinery to yield certified inner and outer radial envelopes with width at most $δ+2Lh_{\\mathcal U}$ and corresponding same-ray Hausdorff guarantees. An analytic two-dimensional example shows why retaining star-shaped but nonconvex geometry can matter. The resulting reconstruction perspective is intended for low-dimensional multivariate outputs rather than high-dimensional scaling or runtime improvement.", "title": "Common-Center Geometry and Certified Radial Reconstruction for Energy-Form Full Conformal Regions", "updated": "2026-08-25", "url": "https://arxiv.org/abs/2608.24964" }, { "age_days": 3, "arxiv_id": "2608.22928", "authors": [ "Yusheng Zheng", "Xiaoyu Song", "Yanpeng Hu", "Lebin Cheng", "Yuxi Huang", "Wei Zhang" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.22928", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-24", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Agent runtimes can Checkpoint an execution, Fork it, Restore a checkpoint, or Merge branches without restarting a task. We call these operations execution edits, with Checkpoint recording the current execution for later use and Fork, Restore, and Merge changing what the Agent will do next. An execution edit cannot undo an earlier authorization or a tool request already sent. An unsafe edit can therefore authorize the same tool action twice, discard a result the task still requires, or conflict with a call that began before the edit. The Agent is untrusted, so the runtime uses its execution record to determine which past actions an edit must account for and which required results it must preserve to keep the subsequent execution safe. Yet existing Agent systems support such operations without deriving what each edit must preserve from the running execution, whereas prior methods for computing safe behavior take that requirement as input. We give an algorithm that decides exactly whether an edit is safe. It returns all safe ways to continue, or proves that none exists. To make this decision, the algorithm lists every way the task can finish without violating policy. It removes any way that could make a still-required result impossible to finish later. If none remain, it returns a checkable proof that no safe implementation exists. Otherwise, the remaining ways describe exactly what the runtime may allow. Our formal results cover Checkpoint and the six forms of Fork, Restore, and Merge, together with extensions, atomic enforcement, and the information every exact checker needs. Lean mechanizes the finite checker and runtime invariant, and tests validate all six edit forms. The source code, Lean proofs, and executable tests are available in the public GitHub repository at https://github.com/eunomia-bpf/agent-check-restore-safety.", "title": "When Can Agents Safely Checkpoint, Fork, Restore, and Merge? Exact Checking for Execution Edits", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.22928" }, { "age_days": 3, "arxiv_id": "2608.23721", "authors": [ "Daniel Carranza", "Chunyi Liu", "Emily Riehl", "Egbert Rijke" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23721", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-24", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We report our findings and the results of our experiment of autoformalizing the homotopy type theoretic computation of $π_3(S^2)$ in agda-unimath using Codex.", "title": "Autoformalizing the calculation of $π_3(S^2)$", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23721" }, { "age_days": 3, "arxiv_id": "2608.23413", "authors": [ "Seiichiro Kusuoka", "Shuta Nakajima" ], "content_date": "2026-08-24", "freshness": "fresh", "id": "arxiv:2608.23413", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-24", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We consider the Sherrington--Kirkpatrick model with inverse temperature $β>0$ and deterministic external field $h>0$. Let $q$ be the replica-symmetric fixed point: $q=\\mathbb E{\\rm tanh}^2 (h+β\\sqrt q\\,Z)$, where $Z$ is a standard normal. We prove that, uniformly on compact subsets of the strict de Almeida--Thouless region: $β^2\\mathbb E{\\rm sech}^4(h+β\\sqrt{q} Z) <1,$ the overlap satisfies the concentration: $$ \\mathbb E\\langle (R_{12}-q)^2\\rangle=O(N^{-1}). $$ The result of the present paper provides an alternative proof of the replica-symmetric free energy formula in de Almeida--Thouless region recently established by Lopatto [arXiv:2604.11921]. Moreover, our approach yields the stronger conclusion of an explicit quantitative bound. As a consequence, we obtain an $O(N^{-1})$ replica-symmetric free-energy correction and identify the finite-volume replicon susceptibility. Our proof is self-contained and does not use the identification of the limiting free energy with the Parisi variational formula. The main result supersedes the corresponding result in our recent preprint arXiv:2607.23427, extending the replica-symmetric bounds to the strict de Almeida-Thouless region. However, we keep the previous preprint, since its argument is different and substantially simpler than the one given here.", "title": "A quantitative replica-symmetric bound of Sherrington--Kirkpatrick model in the entire de Almeida--Thouless region", "updated": "2026-08-24", "url": "https://arxiv.org/abs/2608.23413" }, { "age_days": 4, "arxiv_id": "2608.22550", "authors": [ "Jan Snellman" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "arxiv:2608.22550", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-23", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We consider families of lines that cover every point of the integer lattice $\\mathbf{Z}^2$ in the plane, subject to the constraint that no two lines of different direction in the family meet at a lattice point. Restricting to \\emph{lattice lines} (lines containing at least two, hence infinitely many, lattice points, equivalently of rational direction), we show that the set of directions occurring in such a covering can be made dense in the space of line directions. The construction is a recursive splitting of $\\mathbf{Z}^2$ into nested rank-2 sublattice cosets, each handed off to a freshly chosen direction; the key technical point is a steering lemma showing that at every stage of the recursion a new direction arbitrarily close to any prescribed target can still be realized, via an elementary sieve bound.", "title": "On the directions occurring in lattice-line coverings of the integer plane", "updated": "2026-08-23", "url": "https://arxiv.org/abs/2608.22550" }, { "age_days": 5, "arxiv_id": "2608.22117", "authors": [ "Joshua Nunley" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "arxiv:2608.22117", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A standard Transformer block separates cross-token interaction in self-attention from a nonlinear feed-forward network applied independently at each position. We introduce the TANGO model (Token-Aggregated Nonlinear Gating Operators), which replaces these two sublayers with one cross-token gated residual update. Each source token produces a SwiGLU gate vector. Query-key similarities determine a weighted average of source gates for each destination, and the resulting gate rescales projected destination features. TANGO assigns a separate weight to every causally visible source and is quadratic in sequence length. The WANGO model (Windowed Aggregation of Nonlinear Gating Operators) retains the same unnormalized scores within a recent window and uses positive feature-map prefix statistics for older sources, giving linear sequence-length complexity for fixed window and feature dimensions. We compare TANGO and WANGO with Recurrent and Untied Transformer++, full-attention GAU, and FLASH. All models have approximately 44.3M nonembedding parameters and are trained in three matched runs. TANGO, WANGO, and Recurrent Transformer++ apply one shared block four times; the other architectures use four independent blocks. TANGO obtains the lowest mean validation negative log-likelihood on FineWeb-Edu, Lean, and DeepMind Mathematics, although it has the largest analytical forward-pass operation count. WANGO obtains the lowest mean FineWeb-Edu NLL among the architectures with computation linear in sequence length and outperforms Recurrent Transformer++ at nearly the same analytical forward-pass multiply-accumulate count.", "title": "TANGO: Token-Aggregated Nonlinear Gating Operators for Natural and Formal Language Modeling", "updated": "2026-08-22", "url": "https://arxiv.org/abs/2608.22117" }, { "age_days": 6, "arxiv_id": "2608.21502", "authors": [ "Bennett Chow", "Yuan Liao", "Ziyang Qin" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "arxiv:2608.21502", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-21", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We describe a Lean formalization of Hamilton's 1982 theorem on closed, connected three-manifolds with positive Ricci curvature. The development contains a short-time existence theorem for Ricci flow and substantial geometric-analysis infrastructure: Riemannian tensor calculus, the Levi--Civita connection, Ricci-flow evolution equations, scalar and tensor maximum principles, three-dimensional curvature algebra, preservation of Ricci pinching, and Hamilton's improved pinching estimate. The formalization follows an alternative blow-up route, rather than Hamilton's original normalized-flow proof. Its time-uniform short-time existence, maximal continuation, no-local-collapsing, and Cheeger--Gromov--Hamilton compactness pipelines have been formalized and are included in the artifact, while we give only a brief account of these companion developments and record the interfaces and consequences used by the Hamilton argument; a detailed exposition of their full constructions is deferred to the second author's forthcoming thesis. We interweave representative Lean declarations with their mathematical meaning and record the status and provenance of every major component. All source-level status claims are tied to the source release identified below.", "title": "A Lean Formalization of Hamilton's Three-Manifold Theorem", "updated": "2026-08-21", "url": "https://arxiv.org/abs/2608.21502" }, { "age_days": 7, "arxiv_id": "2608.21458", "authors": [ "Hiroyuki Nakahata" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.21458", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In a software architecture, each service can obey its own conventions and each handoff between adjacent services can hold, and yet a semantic inconsistency may remain that appears only on a full traversal of the system. This paper independently constructs two cohomologies measuring this gap between local and global correctness, and proves that they agree. The first construction speaks the language of repair: from the semantic repair options admitted in each local context and their equivalence relation, it generates the coefficient $M_{\\mathrm{sem}}$. The second speaks the language of equations: it organizes the constraints of the architecture as a simultaneous equation system and generates the quotient coefficient $Q_E$ by its obstruction ideal. Over a selected finite cover $U$ in Algebraic Architecture Theory (AAT), which constructs software architecture as algebraic geometry, and under finitely many selection conditions matching the local data, the comparison map induces the isomorphism $H^1_{\\mathrm{sem}}(U) \\cong \\check{H}^1(U, Q_E)$ together with a correspondence of residual classes. We call this the SAGA comparison theorem. The obstructions measured in the two languages are the same cohomology class, so semantic diagnosis and geometric computation translate into each other. Moreover, when the family of repair states satisfies the sheaf condition, a global repair exists if and only if the obstruction class vanishes on both sides. The paper presents this result in three layers: the mathematical proof; the Lean formalization status at release time; and a diagnosis in which the measurement tool ArchSig, on a real open-source microservice system, reproducibly walks the full circle from a measured nonzero obstruction to its disappearance after repair. The three layers refer to the same release identity, and each claim is connected to primary evidence.", "title": "SAGA: A Comparison Theorem for Local-to-Global Software Architecture - From Semantic Repair Cohomology to Algebraic-Geometric Descent", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.21458" }, { "age_days": 7, "arxiv_id": "2608.23237", "authors": [ "Simon Daniel", "Timon Böhler", "David Richter", "Pascal Weisenburger", "Mira Mezini" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.23237", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "With growing complexity, distributed software systems become increasingly challenging to maintain and reason about. When implementing a distributed protocol, developers must ensure manually that the different components fit together. Choreographic programming addresses this challenge by specifying global protocols in a single program and projecting them into communicating processes, so-called endpoints. Recent choreographic approaches are designed as programming libraries that embed this paradigm into a host language like Haskell or Rust. In these designs, we observe common cases of partiality: unreachable branches in endpoint projection (EPP) and located-value access can trigger runtime errors or undefined behavior, relying on manual discipline of library maintainers rather than being statically type-checked. Also, some programs require users to write down dummy branches that should not be reachable, for example when branching on sum types. To close this gap, we use the dependently typed Lean programming language to implement a similar choreographic library. We show how we are able to move from a partial EPP to a total EPP function, and also eliminate cases of partiality in user-written code with pattern matching on sum types. ChorLean ensures total EPP and safe value access via proof-carrying located values, passing Lean's totality checker without undefined cases, while supporting the same feature set as libraries like MultiChor.", "title": "On Eliminating the Impossible with Dependent Types: Choreographic Libraries with Proof-Carrying Located Values", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.23237" }, { "age_days": 7, "arxiv_id": "2608.19844", "authors": [ "Liyan Wang" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.19844", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "For $n\\geq 4$, let $c(n)$ be the minimum number of distinct circles containing at least three points of an $n$-point set in the Euclidean plane, where the set is neither collinear nor concyclic. Put[F(n)=1+\\binom{n-1}{2}-\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor.]We determine $c(n)$ for every $n\\geq 4$: it equals $F(n)$ apart from three exceptional orders. We also solve the variant in which no three points are collinear; that variant has a single exceptional order. The proofs and exact finite verifications were developed through a collaboration between human researchers and artificial-intelligence systems.", "title": "Circles determined by planar point sets", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.19844" }, { "age_days": 7, "arxiv_id": "2608.20589", "authors": [ "Andrey Itkin" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.20589", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The Marketron model of \\cite{HalperinItkin2025Mark} and its option pricing extension in \\cite{HalperinItkinMarketron2} suffer from structural non-identifiability: an eighteen-parameter space traps solvers in suboptimal local minima and renders economic quantities unmeasurable. By removing exact scaling gauges and sign symmetries, freezing non-financial parameters by explicit criteria, and adiabatically eliminating the fast hidden signal, we derive a robust nine-parameter reduced model. A Gauss-Newton Hessian with empty null space and a manifold-boundary analysis confirm that the reduced core carries no exact symmetry and admits no further reduction. A diffusive correlation between flow and return innovations captures the short-maturity skew. A staged calibration from the physical measure to the risk-neutral measure, illustrated on SPX options, fits the whole surface with a single parameter set. The same reduction turns the wedge between the physical and pricing values of the flow block into a well-defined market price of flow risk rather than a ridge artifact, identifiable here for the first time, though a single surface constrains its level only weakly. Finally, our analysis reveals that in the Marketron model the log-price obeys a generalized Langevin equation with a closed-form, state-modulated memory kernel, and that the memory variable itself is the exact Markovian lift of this kernel. This mapping also yields a testable condition, the equality of the signal and memory relaxation rates, which on the SPX surface come out well separated, though both weakly identified, placing the fitted market tentatively in the driven, non-equilibrium regime and turning the active-matter reading from an analogy into a falsifiable constraint.", "title": "Calibrating Inelastic Markets to Options: The Lean Marketron and the Generalized Langevin Equation", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.20589" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }