{ "counts": { "adjacent": 16, "core": 2, "errors": 0, "negative": 71, "total": 89 }, "date": "2026-08-03", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-03T17:25:48Z", "items": [ { "age_days": 5, "arxiv_id": "2607.27259", "authors": [ "Ziyi Yang", "Wenji Fang", "Chen Chen", "Zhiyao Xie", "Hongce Zhang" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "arxiv:2607.27259", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-29", "score": 12.5, "source": "arxiv-ai4math-core", "summary": "Modern integrated circuits (ICs) are becoming increasingly complex, making functional verification a major bottleneck. The dominant hardware formal verification methodology, model checking, verifies each design instance separately and exposes only pass/fail results, so the reasoning behind a proof stays locked inside solver heuristics and is repeatedly reconstructed across related designs. Interactive theorem proving instead yields explicit, reusable proof artifacts, but applying it to hardware remains largely manual, demanding expert effort for formalization, invariant discovery, and proof development. In this paper, we present CircuitProver, an agentic Lean 4-based verification framework supporting proof-accumulation and parameterized verification. CircuitProver automatically translates parameterized hardware designs and their natural language specifications into executable Lean 4 models. It then iteratively constructs machine-checked proofs through Lean feedback to establish that the hardware code complies with the specification. The proving traces and verified theorems are distilled into reusable libraries, where proving strategies guide future agent reasoning and verified lemmas support formal proof reuse across related hardware verification tasks. We further introduce the first benchmark suite for evaluating agentic hardware theorem proving, covering diverse parameterized hardware designs, specifications, proof tasks, and evaluation metrics. Across 63 tasks, CircuitProver successfully proves all benchmarks, while a vanilla agent solves 92.1% of them and requires twice as many proof rounds on average. Ablation studies show that accumulated proof knowledge reduces redundant proof construction across related verification tasks, reducing proof length by 16.3% and verification time by 23.2%.", "title": "CircuitProver: Agentic Lean 4 Theorem Proving with Reusable Circuit Proof Library for Hardware Verification", "updated": "2026-07-29", "url": "https://arxiv.org/abs/2607.27259" }, { "age_days": 4, "arxiv_id": "2607.28877", "authors": [ "Ha Trung Tran" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28877", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-30", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Verification consumes the majority of modern chip design effort, yet the formal verification tools that provide mathematical guarantees of correctness remain expensive and restrictively licensed. While large language models (LLMs) have shown promise for hardware design, existing approaches to RTL repair validate their results through simulation - which exercises only a subset of inputs - or rely on commercial tools, and few combine formal proof with an entirely open-source toolchain. In this paper, we present a multi-agent pipeline that couples an LLM with an open-source formal backend (Yosys, SymbiYosys, and Z3) to repair RTL through counterexample-guided iteration: the framework generates formal properties, verifies the design, and feeds counterexamples back to the LLM until the design is proved correct by k-induction or an iteration budget is exhausted. Through an ALU case study, we show that the pipeline can detect and repair a real functional bug with a formal proof of correctness. Across a six-benchmark suite, one design is repaired reliably, and we characterize four distinct failure modes: bounded-cover vacuity, specification ambiguity, temporal-logic bugs, and multi-property pressure. We frame this work as a feasibility study with a detailed failure analysis, and additionally report a practical limitation of the Yosys bind directive relevant to the open-source formal verification community.", "title": "Open-Source LLM-Driven Formal Verification: A Multi-Agent Pipeline for RTL Repair", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28877" }, { "age_days": 3, "arxiv_id": "2607.29349", "authors": [ "Jonathan Washburn", "Milan Zlatanović" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "arxiv:2607.29349", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-31", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Let $δ$ denote the primitive act of distinction, formally realized as the one-step extension $r \\mapsto Sr$ of a finite record. We study the inductively generated $δ$-orbit and its first-order arithmetic presentation $\\mathbb{N}_δ$. The corresponding $δ$-calculus is an intuitionistic first-order proof system over the signature $\\{0,S,+,\\cdot\\}$. Every derivation carries a ledger recording the use of the law of excluded middle, the limited principle of omniscience, Markov's principle, and induction on quantified formulas. The last entry does not affect whether a derivation is forced. If a closed formula is derivable in the forced fragment, then it is true in the standard model. Starting from $δ$, we construct a choice-free number tower $δ\\leadsto \\mathbb{N}_δ\\hookrightarrow \\mathbb{Z}_δ\\hookrightarrow \\mathbb{Q}_δ$. The metatheoretic number systems $\\mathbb{N}$, $\\mathbb{Z}$, and $\\mathbb{Q}$ each admit an explicit injection into $\\mathbb{N}_δ$. We also classify the recognition quotients of the additive monoid $(\\mathbb{N}_δ,+,0)$. Assuming the law of excluded middle, every recognizer is either injective or has a kernel congruence $\\equiv_{i,p}$, with index $i$ and period $p$, for a unique pair $i\\ge 0$, $p\\ge 1$. In the noninjective case the quotient is isomorphic to the finite monogenic monoid $M(i,p)$. We price this classification with the ledger, determining which nonconstructive principles each form requires. If the congruence is decidable and an explicit pair of distinct related elements is given, the classification is forced. If the congruence is decidable and different from equality, Markov's principle is needed. For an arbitrary congruence, the dichotomy requires the law of excluded middle. The reverse implications show that the last two prices cannot be lowered. The main results are formalized in Lean 4.", "title": "The $δ$-calculus: from distinction to arithmetic", "updated": "2026-07-31", "url": "https://arxiv.org/abs/2607.29349" }, { "age_days": 4, "arxiv_id": "2607.28699", "authors": [ "Fanzhe Wei", "Li Liu" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28699", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-30", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "KV-cache quantization is validated today by offline benchmark averages; a deployed system cannot tell whether compression is damaging the request it is serving right now. We give it a provably sound runtime meter, a \"DTrace for KV quantization\": a per-(layer, head, step) upper bound on the total variation between exact and compressed attention. The meter has two tiers: a deterministic band-norm-witness bound, sound for any cache-preserving black-box quantizer and for any query (adaptive-safe, worst-case Cauchy-Schwarz plus RoPE band-unitarity), and a tighter probabilistic certificate for a controlled subtractively-dithered INT8 quantizer under an explicit request-level failure budget (stated for non-adaptive queries; core theorems machine-checked in Lean 4). Three results. Observability: the meter enters SGLang through an environment-guarded patch, and any scheme registered as one tensor function is measured in live serving. Repair: meter-driven gating, risk-ranked where the witness is saturated and certified where it is informative, empirically restores the quality floor at benchmark scale. For example, raw-cast FP8 improves from 22.8 back to 79.7 on hard RULER tasks, with the difference from uncompressed bounded at [+0.0, +0.8] by a paired test. Analysis: aggressive schemes survive on cross-layer error cancellation, not per-step fidelity. In a 28-layer sweep, no single layer's pollution alone loses anything (0/28), and the certified INT8 cache serves 1.88 times more KV tokens at the same memory in SGLang.", "title": "WitCert: Sound Runtime Risk Observability and Gating for KV-Cache Quantization", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28699" }, { "age_days": 4, "arxiv_id": "2607.28110", "authors": [ "Ruslan Khrulev" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28110", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-30", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operation names the node it edits, so the target theorem cannot be changed. Lean checks every applied change, and an accepted repair must declare every blueprint lemma its proof uses. We also construct BlueprintTrace, a benchmark of 142 controlled failures with complete accepted and rejected repair trajectories. We compare typed edits, exact source patches, and complete module rewrites under matched source, feedback, model, and budget, one episode per state and interface. With DeepSeek-V4-Flash, the three interfaces solve almost the same number of the benchmark's localized failures. Typed repair is the cheapest per solved state (patching is 1.30x as expensive, rewriting 2.06x), and within 10,000 completion tokens per task it reaches almost all of its final coverage, while both free-form interfaces are well behind. A second model, Qwen3.6-Flash, solves fewer states but keeps typed repair cheapest, puts it ahead on the proof-authoring states, and repeats the localized pattern.", "title": "BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprints", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28110" }, { "age_days": 5, "arxiv_id": "2607.26413", "authors": [ "Shayaan Siddique", "Ibrahim Mian" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "arxiv:2607.26413", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-29", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The best known lower bound for the minimum Kochen-Specker vector system in $\\mathbb{R}^3$ -- 24 vectors -- rests on a computational proof whose combinatorial half emits DRAT proofs but whose geometric half does not: the non-embeddability of thousands of candidate graphs is established by Z3's nonlinear real arithmetic, which produces no checkable proof objects. We close this gap for the proof's blocking database. We introduce exact rational case-tree certificates of real non-embeddability, whose splits are polynomial factorizations and rational sum-of-squares decompositions and whose leaves are discharged by injectivity, ideal-membership, or Positivstellensatz-shaped positivity arguments, and we certify all 291 source lines (180 distinct graphs) of the published pipeline's order-10 to order-13 blocking lists. Certificates are replayed by two independent checkers that share no code with the generator: a pure-Python replay over exact fractions, and a total checker implemented and proved sound in Lean 4. The soundness theorem -- acceptance implies that no injective-on-rays, orthogonality-respecting assignment of nonzero real vectors realizes the graph -- is kernel-checked with axiom closure {propext, Classical.choice, Quot.sound}, and a gcd-free rational arithmetic layer makes the entire verdict computation kernel-reducible, so each per-graph non-embeddability result is a closed kernel theorem proved by decide. The formalization surfaced findings about the published pipeline, including a load-bearing injectivity side condition in its embeddability notion, hidden WLOG case obligations invisible to Z3-based workflows, and an unreproducible candidate count that we resolve against the published artifacts. All certificates, checkers, and proofs are available and replayable from a single build.", "title": "Machine-Checked Certificates for the Geometric Half of the Minimum Kochen-Specker Bound", "updated": "2026-07-29", "url": "https://arxiv.org/abs/2607.26413" }, { "age_days": 5, "arxiv_id": "2607.26997", "authors": [ "Kuldeep S. Meel", "N. V. Vinodchandran", "Sourav Chakraborty" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "arxiv:2607.26997", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-29", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We study estimating the size of the union of sets $S_1,\\dots,S_M$, where each $S_i\\subseteqΩ$ is presented implicitly and arrives in a stream. We introduce Delphic sets, a class of streaming problems in which membership, sampling, and counting queries to each set are efficient, and show that this notion captures three well-known problems: Klee's measure problem (discrete version), test coverage estimation in combinatorial testing, and model counting of DNF formulas. Our primary contribution is a simple and efficient sampling-based algorithm that outputs an $(\\varepsilon,δ)$-approximation of the cardinality of the union of Delphic sets in the streaming setting. It has space complexity $O(R\\log|Ω|)$ and update time $O(R\\log R\\cdot\\log(M/δ)\\cdot\\log|Ω|)$, where $R=O(\\log(M/δ)\\cdot\\varepsilon^{-2})$. For the streaming Klee's measure problem, this gives the first algorithm whose update time depends linearly on the dimension $d$ for $d>1$, settling an open problem of Tirthapura and Woodruff (PODS 2012), and it directly yields efficient streaming algorithms for coverage estimation and DNF model counting. We further show that the space for coverage estimation can be made near-optimal at the cost of an update procedure in $\\mathrm{P}^{\\mathrm{NP}}$, revealing a time-space trade-off. A key strength of our approach is the simplicity of both the algorithm and its analysis, which makes it amenable to practical implementation. In this revised version, the algorithm and its correctness analysis have additionally been formalized and machine-checked in Lean 4. (Shortened for Arxiv)", "title": "Estimating Size of the Union of Sets in Streaming Model", "updated": "2026-07-29", "url": "https://arxiv.org/abs/2607.26997" }, { "age_days": 5, "arxiv_id": "2607.27452", "authors": [ "Samuil Petkov" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "arxiv:2607.27452", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-29", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "WOW-284 asserts that the minimum dual degree of every connected graph of order at least three and girth at least five does not exceed the negative of its least distance eigenvalue. We refute it with exact counterexamples of orders $38,39,40,42$, and $50$, and develop a structural theory of the failure. For a connected $k$-regular graph of girth at least five and diameter three, we prove $δ^*(G)+λ_{\\min}(D(G))=2k-2-\\max_{θ\\ne k}(θ+1)^2$. Here $θ$ ranges over the nonprincipal adjacency eigenvalues. We further prove that every regular strict counterexample has degree at least six and diameter at most four, while diameter four forces degree at least ten. We solve the associated one-variable nonbacktracking linear program exactly, including optimizer rigidity. For regular strict counterexamples of diameter three, the optimizer yields a positive-semidefinite slack matrix whose integral excess gives the stronger bound $|V(G)|\\le\\left\\lfloor 3(k+2)^2(k^2+3)/(18k+41)\\right\\rfloor$; this follows from a three-to-one quantization theorem for the integral excess. The slack matrix's principal minors also recover local cycle constraints. In particular, regular degree-six counterexamples have order at most $50$, and at the degree-six, order-$50$ boundary the associated signed complement is necessarily disconnected. We determine the distance spectra of one- and two-vertex punctures of Moore graphs and establish a uniform deletion-stability bound: every deletion of at most five vertices from the Hoffman--Singleton graph remains a strict counterexample, whereas an explicit six-vertex deletion does not. All theorem-level computations use exact arithmetic. Lean 4.31 kernel-checks the explicit $50$-vertex Hoffman--Singleton counterexample at graph level, finite spectral certificates at orders $38,39,40,42$, and the analytic LP optimum and rigidity for every integer $k\\ge4$.", "title": "Counterexamples, Spectral Obstructions, and Deletion Stability for WOW-284", "updated": "2026-07-29", "url": "https://arxiv.org/abs/2607.27452" }, { "age_days": 6, "arxiv_id": "2607.25628", "authors": [ "Ibrahim Mian", "Shayaan Siddique" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.25628", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The Erdős-Selfridge odd covering problem (Erdős problem #7) asks whether a covering system of $\\mathbb{Z}$ exists whose moduli are all odd, distinct, and greater than 1. The problem is open. We present a Lean 4 formalization, checked end to end by the proof kernel, of the exclusion: any covering of $\\mathbb{Z}$ by finitely many congruence classes with distinct odd moduli > 1 has lcm of the moduli exceeding 10000. The proof composes a formalized density argument (a covering by divisors of $N$ exceeding 1 forces $2N \\le σ_1(N)$, so the lcm is abundant or perfect), a kernel-checked abundancy floor (no odd $N < 945$ qualifies), a family of Chinese-Remainder capacity certificates -- decidable per-$N$ arithmetic inequalities each refuting every covering with distinct moduli > 1 dividing that $N$ -- for all 23 odd abundant numbers below $10^4$, and a kernel-checked enumeration establishing that those 23 are the only odd non-deficient candidates. The result is transported to the official StrictCoveringSystem $\\mathbb{Z}$ formulation of Erdős #7 in google-deepmind/formal-conjectures, with a bidirectional periodicity bridge between coverings of $\\mathbb{Z}$ and finite checks over $\\mathbb{Z}/N\\mathbb{Z}$ suitable for consuming future SAT-style search output. All 63 published theorems depend on exactly propext, Classical.choice, and Quot.sound: no sorry, no native_decide, no solver in the trusted base. The mathematical content is known -- the density argument is folklore, and far larger uncertified classifications of covering numbers exist -- so the contribution is epistemic rather than mathematical: these exclusions are theorems of the Lean kernel, with an axiom gate enforced mechanically in continuous integration.", "title": "Kernel-Checked Exclusions for the Erdős-Selfridge Odd Covering Problem: Any Odd Covering of $\\mathbb{Z}$ Has lcm Exceeding 10000", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.25628" }, { "age_days": 6, "arxiv_id": "2607.26306", "authors": [ "Lefteris Lazaropoulos", "Zoe Paraskevopoulou" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.26306", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Relating low-level executable code to a high-level account of its behavior has been a central concern of programming-language research for decades. From formally verified compilers to translation validators, certifying compilers, and proof-carrying code, each approach chooses between laborious but foundational mechanized proofs and automation that costs completeness, generality, and an increased trusted base. Recently, large language models (LLMs) have begun to change the economics of formal verification. Agentic proof development is now capable of producing machine-checked proofs at a scale and speed that were previously out of reach. In this paper, we evaluate the capabilities of LLMs to produce foundational, machine-checked proofs of refinement between executable code and its high-level specification, as post hoc, per-artifact certificates. We study this in the context of the Ethereum Virtual Machine (EVM), a low-level virtual machine that executes smart contracts on the Ethereum blockchain. We build EquiVM, a foundational framework in Lean comprising an executable EVM semantics and a specification language that characterizes the intended behavior of smart contracts, but commits to no source language or compilation toolchain. In EquiVM, refinement is stated for deployed bytecode of arbitrary provenance, interaction with unknown code is part of the semantics, and each proof is a replayable, machine-checked certificate. No previous technique achieves this combination. Using frontier commercial LLMs, twenty-three real-world contracts are proved end to end with minimal human guidance, among them most of the MakerDAO stablecoin system, at up to a hundred million tokens and a hundred hours of proof time per contract. We conclude that foundational mechanized proofs can now be bought at the price of tokens, and that this shift can reshape how verification frameworks are architected.", "title": "Foundational Refinement Proofs for Deployed Bytecode, at the Price of Tokens", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.26306" }, { "age_days": 6, "arxiv_id": "2607.26230", "authors": [ "Alain Chavarri Villarello", "Sander R. Dahmen" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.26230", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Number fields, which generalize the rational numbers, are fundamental objects in number theory. Many of their key arithmetic properties are captured by invariants whose computation is among the central tasks of computational algebraic number theory and a focus of several computer algebra systems and databases. In this paper, we describe a Lean 4 formalization for certifying several of these number field invariants. Building on previous work on certifying rings of integers, we extend this certification approach to further invariants including the signature, the unit group modulo $p$-th powers, and, ultimately, the class group. We also improve discriminant certification, allowing verifications for higher-degree number fields infeasible in previous work. We introduce structures based on representations of algebraic objects suited to computation, including reusable ones for certifying ideal arithmetic. Along the way, we formalize several underlying mathematical results, for instance on real closed fields and pseudo-remainder sequences, which are of independent interest. We apply our framework to verify hundreds of entries of the $\\textit{L-functions and modular forms database}$ (LMFDB) concerning the discriminant, signature, class number, and class group structure of various number fields. To this end, we wrote a SageMath script that computes the certificates and outputs Lean proofs of the corresponding statements.", "title": "Formally certifying number field invariants", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.26230" }, { "age_days": 6, "arxiv_id": "2607.26344", "authors": [ "Xin Xu", "Siru Tao", "Kaizhen Tan" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.26344", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-28", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.", "title": "Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.26344" }, { "age_days": 7, "arxiv_id": "2607.24483", "authors": [ "Alexander Temerev", "Alessio Doria" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "arxiv:2607.24483", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-27", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We solve Bellman's lost-in-a-forest problem for the golden gnomon $G$, the isosceles triangle with equal sides $1$ and apex angle $108^\\circ$: the shortest curve guaranteed to reach the boundary of $G$ from an unknown starting position and heading is a symmetric seven-piece path of segments, circular shoulders, and tangents, of exactly determined length $C=1.282676025459\\ldots$. To our knowledge, this is the first proved exact optimum for an isosceles triangle whose base angle is below $45^\\circ$. The curve's parameters come from one isolated quartic root, and $C$ is transcendental. Equivalently, $C^{-1}G$ is the smallest homothetic golden-gnomon cover of all unit arcs. The proof introduces a balanced support calibration: one weighted family of escape inequalities, built on the linear relation among the triangle's three normals, exactly saturated by the candidate, through eighteen exact support windows, and confronting every shorter competitor at once. Aggregation along the normal fan compresses the calibration to a finite zero-sum family of supported vectors; summation by parts then bounds its total by path length whenever the running suffix balance, the ledger, stays in the unit disk. A local two-gap surgery and cyclic bitonicity force a shortest hypothetical counterexample into exactly the temporal order the ledger tolerates. Lean 4 verifies the two finite algebraic certificate families and the reusable discrete ledger identities and bounds.", "title": "The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon", "updated": "2026-07-27", "url": "https://arxiv.org/abs/2607.24483" }, { "age_days": 7, "arxiv_id": "2607.24504", "authors": [ "Cao Nguyen Pham", "Oliver Bračevac", "Yichen Xu", "Yaoyu Zhao", "Martin Odersky" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "arxiv:2607.24504", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-27", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Capture checking in Scala 3 enables lightweight and practical effect and resource tracking by recording capabilities in types. However, the system offers no way to reason about kinds of capabilities. Natural constraints such as \"retaining only the control-flow capabilities of this closure\" or \"excluding all thread-local capabilities from this argument\" become inexpressible. Both arise in the Scala 3 standard library: \"Try\" re-throws caught exceptions, so it retains only the control-flow capabilities of its body, and \"Future\" must not capture thread-local resources. The inability to state these constraints has kept parts of the library outside capture checking. We introduce capability classifiers: a tree-structured, user-extensible hierarchy of tags that classify capabilities by their semantic role. Projections filter capture sets by classifier, supporting both inclusion (\"c.only[C]\") and exclusion (\"c.except[C]\"). The tree structure enables decidable disjointness reasoning: classifiers on separate branches are guaranteed to be disjoint regardless of unknown extensions elsewhere in the hierarchy. We formalize classifiers as an extension of System Capless, a core calculus for capture checking, introducing a classifier kind algebra based on intersection, union, and subtraction of classifier subtrees. We extend the operational semantics to model exception interception and establish type safety, effect safety, and handler coverage via a big-step proof, fully mechanized in Lean 4. Classifiers are implemented in the Scala 3 capture checker, and we demonstrate their use on standard library types and real-world effect exclusion patterns.", "title": "Classifying Capabilities (Extended Version)", "updated": "2026-07-27", "url": "https://arxiv.org/abs/2607.24504" }, { "age_days": 3, "arxiv_id": "2607.29191", "authors": [ "Jinhui Li", "Beibei Xiong", "Zhengfeng Yang" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "arxiv:2607.29191", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-31", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "The Dittert conjecture states that the Dittert functional on nonnegative $n\\times n$ matrices whose entries sum to $n$ is uniquely maximized by the uniform matrix. We prove the conjecture in dimension $4$. More precisely, let $K_4$ be the simplex of nonnegative $4\\times4$ real matrices whose entries sum to $4$, let $U_4$ be the uniform matrix, and let $φ$ denote the Dittert functional. We establish $\\frac{61}{32}-φ(A)\\geq \\frac{1}{52}\\lVert A-U_4\\rVert_F^2$ for every $A\\in K_4$. Consequently, $U_4$ is the unique maximizer of $φ$ on $K_4$. The proof reduces to certifying the nonnegativity of a structured quartic polynomial in sixteen variables on a simplex. We construct an exact rational constrained sum-of-squares certificate using an agent-guided symbolic-numeric procedure that combines template selection with sequential rational recovery. The main SOS consists of $152$ positively weighted rational squares, while each of the $136$ smaller SOS blocks consists of $16$ such squares. Exact $LDL^{\\mathsf{T}}$ decompositions certify positivity, and exact coefficient comparison over $\\mathbb{Q}$ verifies the complete polynomial identity. The resulting exact certificate is formally verified using the Lean proof assistant.", "title": "A Proof of the Dittert Conjecture in Dimension 4 via an Agent-Guided Exact Sum-of-Squares Certificate", "updated": "2026-07-31", "url": "https://arxiv.org/abs/2607.29191" }, { "age_days": 4, "arxiv_id": "2607.28225", "authors": [ "Haoqing Wang", "Xingrun Xing", "Wei Xia", "Ziheng Li", "Yehui Tang" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28225", "kind": "paper", "label": "adjacent", "matched_signals": [ "negative:vision_world_models", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-07-30", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Agentic vision-language models (VLMs), which interleave textual reasoning with explicit tool calls such as cropping and code-based image manipulation, have emerged as a compelling paradigm for reliable and interpretable multimodal reasoning. However, recent studies have revealed that such models often use tools unfaithfully. Many process images are irrelevant to the question (e.g., the tool crops the wrong region or misses the queried target), yet the call still receives full credit and the model still answers correctly. Such decorative or misaligned tool calls waste computation and reveal that the model leans on prior knowledge or the original image rather than the evidence it retrieves. This may stem from two limitations of prevailing methods: the tool reward fails to distinguish useful from useless calls, and tool feedback carries no signal of usefulness. To this end, we introduce FaithEyes, a multi-agent self-judging framework. Concretely, we use a VLM to judge whether each process image helps answer the question. The judgement is injected into the reasoning context as part of the tool observation to help subsequent reasoning, and meanwhile is used to scale the tool reward by the helpful-tool ratio to suppress reward hacking. To keep judgement available at evaluation and thus ensure train-test consistency, we further design a multi-agent framework where the model itself serves as a subagent to judge the tool calls from main agent, eliminating any dependence on an external model at inference. Training via a two-stage SFT + RL pipeline on adapted open-source data, FaithEyes attains competitive or superior accuracy across visual perception and reasoning benchmarks, while markedly improving tool faithfulness. The homepage is at https://github.com/Mosi-AI/FaithEyes.", "title": "FaithEyes: Towards Faithful Tool Use via Multi-Agent Process-Image Verification", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28225" }, { "age_days": 6, "arxiv_id": "2607.27246", "authors": [ "Jun Qing" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.27246", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-28", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let G be a nonempty finite simple graph of order n, and let m(G) be the upper median of its degree sequence. We prove that the 2-domination number satisfies gamma_2(G) <= n - m(G) + 1. This proves Graffiti.pc Conjecture 387. In fact, the argument establishes the inequality for every nonempty finite simple graph, so the connectedness hypothesis in the original formulation is unnecessary. The proof uses the complement graph and a minimally linearly dependent family of polynomials encoding selected nonneighborhoods.", "title": "The 2-Domination Number and the Upper Median Degree: A Proof of Graffiti.pc Conjecture 387", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.27246" }, { "age_days": 7, "arxiv_id": "2607.25064", "authors": [ "David Victor Feldman" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "arxiv:2607.25064", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-27", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "A compact convex body $K\\subseteq\\mathbb{R}^n$ is a first-order structure in two natural languages: $L_{\\mathrm{aff}}$, with a ternary betweenness relation and convex-combination operations, and the sparser $L_B$, with betweenness alone. Isomorphism means affine equivalence in the first and, by a theorem of Shiffman, projective equivalence in the second. We ask when elementary equivalence already determines the body. Main theorem: two compact convex bodies of any dimension, with no regularity hypotheses, are elementarily equivalent in $L_{\\mathrm{aff}}$ if and only if they are affinely equivalent. The proof rests on a definable compact family of gauges: simplices stationary for barycentric coordinates, with volume bounded below via the anticomplementary simplex. For $L_B$ we develop an interior von Staudt calculus, all quantifiers ranging over the body, making harmonic conjugacy, rational cross-ratio comparisons, and cross-ratio equality first-order; only the harmonic primitive is needed, with a single interior perspectivity effecting the change of scale. Consequences: the closed unit ball is separated from $\\{\\sum x_i^4\\le 1\\}$ in $L_B$ for every $n\\ge 2$; and in the plane, projective categoricity holds outright for convex polygons and for bodies with real-analytic, positively curved, non-conic boundary, the latter via a new finite projective invariant, the conic-cluster set: the points whose every boundary arc contains six co-conic extreme points. A general reduction isolates what remains of the projective conjecture: recovery of boundary coordinates in dimension at least three, and a definable compact gauge, obstructed exactly by non-compact projective symmetry, as on the quadric. We also classify the natural noncompact examples.", "title": "Elementary equivalence of convex bodies in affine and projective languages", "updated": "2026-07-27", "url": "https://arxiv.org/abs/2607.25064" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:a2294bb6deef", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: port bv_decide to SymM (#14215)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/a2294bb6deef5984c971cfcc4f3ef0a38bf3349c" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:945e78b86645", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: lake: `builtin-lint` has a `Mode` flag (#14617)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/945e78b86645b179655123cd2fdba83d89d28d07" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:41dfb4d1563b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: keep the deletion worklist in a register in `lean_dec_ref_cold` (#14660)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/41dfb4d1563b0df66a8a12dd6047793095239b66" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:0bae3215657e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: fold `UInt*.ofNatLT` applied to literals (#14662)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/0bae3215657e2f99e2b7e7bf976fa439e0861b81" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:6ce2149e7865", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `mkTheoremFromDecl` from `SymM` (#14664)", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/6ce2149e786585ec5ac65b0930c2646702b7c2a3" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover/lean4:58408f99cb2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-08-03", "url": "https://github.com/leanprover/lean4/commit/58408f99cb2b6cdd72be94b5fbc26881e49502dc" }, { "age_days": 0, "authors": [ "Aaron Liu" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8d2ab6981b51", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(RingTheory/DedekindDomain): make `IsDedekindDomainInv` private (#42392)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/8d2ab6981b5112e5f3e7cde2f37d2996a7865e45" }, { "age_days": 0, "authors": [ "Kevin Wilson" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:93594942ef3b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Semicontinuity/Hemicontinuity): sequential characterizations of hemicontinuity (#40377)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/93594942ef3b93fae5272d7bf368676ff40f8eb1" }, { "age_days": 0, "authors": [ "Moritz Doll" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9c0c555bde5a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory): use `IsApply` for `ModularForm` etc (#41561)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/9c0c555bde5a8277cd36dc4dc6dfe2a5a77a2b11" }, { "age_days": 0, "authors": [ "Akhil Mathew" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e76b996718f2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Counterexamples): a finite free group scheme of order four not killed by four (#41748)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/e76b996718f27fb278e4f046c7e94537e033fb92" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:64e0afda5236", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(Topology): fix typo in weak space docstring (#42379)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/64e0afda5236d382ce3267152e03fe3f2ef46944" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8cbb95e6e084", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "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 2026-08-03 (#42403)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/8cbb95e6e08446476813711ab8f45e59d4fda94d" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:533312790e4c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename a lemma containing `not_unit` (#42387)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/533312790e4cb6b1a2b6e999cd48e52d7184bfb6" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c0032752b47a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `Prime.not_unit` to `Prime.not_isUnit` (#42385)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/c0032752b47af314b015a7b411123fa4ac99bbaf" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d586c71e87dd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `IsPrimePow.not_unit` to `IsPrimePow.not_isUnit` (#42389)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/d586c71e87ddf1c4fef06a739cdd3b733fd8b64d" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c10d9bc1c8e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `FiniteMultiplicity.not_unit` to `FiniteMultiplicity.not_isUnit` (#42390)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/c10d9bc1c8e481eb623c555f57897eab3a1fb24d" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:49c3708b8696", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove unused `have`/`let` (#42395)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/49c3708b8696eca37c065f6f9612d48fb53d19fd" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-08-03", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:51e6992efd06", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-03", "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-rc2 (#42401)", "updated": "2026-08-03", "url": "https://github.com/leanprover-community/mathlib4/commit/51e6992efd06126df61a496bebf8f49482a4e129" }, { "age_days": 1, "authors": [ "Kim Morrison" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:f1053b60be68", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: replace grind proofs in Vector.Algebra (#14644)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/f1053b60be68ce3149109206989f04eedb5d2239" }, { "age_days": 1, "authors": [ "Jacob Reinhold" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:cdd822aebc52", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: report a missing library root file (#14625)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/cdd822aebc524d97456a21bda1f4724bf9da05e5" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:0ccd6f74fc3d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: gracefully handle curl and IO errors during transfer (#14651)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/0ccd6f74fc3d6471d7c2c91bbd3cf2a252113590" }, { "age_days": 1, "authors": [ "Sankalp Thakur" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover/lean4:110db9cb751a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: elide redundant \"Lean exited with code 1\" after diagnostics (#14629)", "updated": "2026-08-02", "url": "https://github.com/leanprover/lean4/commit/110db9cb751afaee8b2ac344887d6c7e632f77b4" }, { "age_days": 1, "authors": [ "Dennj" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:375d54da2968", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(MeasureTheory): generalize rpow·exp and scalar-multiplication integrability lemmas (#40587)", "updated": "2026-08-02", "url": "https://github.com/leanprover-community/mathlib4/commit/375d54da29680b0a33d5b2f3281b11009e079081" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:68302e4c4fd7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/SimpleGraph/Acyclic): a nontrivial finite tree has at least two leaves (#41669)", "updated": "2026-08-02", "url": "https://github.com/leanprover-community/mathlib4/commit/68302e4c4fd7938be53021dd6fa92f4b9b44fabb" }, { "age_days": 1, "authors": [ "Emily Riehl" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ae0d973d69b7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory): initial object implies corepresentable (#41994)", "updated": "2026-08-02", "url": "https://github.com/leanprover-community/mathlib4/commit/ae0d973d69b779efa724095bd41793b8cf233831" }, { "age_days": 1, "authors": [ "Monica Omar" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:18f56bef5344", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/CStarAlgebra/Basic): `star (ball x r) = ball (star x) r` (#42309)", "updated": "2026-08-02", "url": "https://github.com/leanprover-community/mathlib4/commit/18f56bef5344cefb0563662c495e3eb3824a2589" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-08-02", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e75dd8437c8d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-02", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/HasLimit): use `to_dual` (#41017)", "updated": "2026-08-02", "url": "https://github.com/leanprover-community/mathlib4/commit/e75dd8437c8d32385c65a341f67a7cb1d82ccef1" }, { "age_days": 2, "authors": [ "Sankalp Thakur" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:05a6ddfb52c0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: error on unknown package names in `lake update` (#14630)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/05a6ddfb52c033f12967c96443a93b0ca7b8a58a" }, { "age_days": 2, "authors": [ "Robin Arnez" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:ea9fad0706f0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove deprecated `toCtorIdx` alias for `ctorIdx` (#14627)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/ea9fad0706f0b1da2467195dae75480595640670" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:393d38abb065", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: harden kernel invariants (#14632)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/393d38abb065d369a8a84b5a3da1f4da2e8517ad" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:4b7a61dfa4ff", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: check the structure name when comparing projections in the kernel (#14631)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/4b7a61dfa4ff3f29f07f0ae8ce428fbe39babd6f" }, { "age_days": 2, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover/lean4:5fa71c91416b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: check binder types before extending the local context (#14633)", "updated": "2026-08-01", "url": "https://github.com/leanprover/lean4/commit/5fa71c91416bb2eec2f8dc7b0064cdf80dda6370" }, { "age_days": 2, "authors": [ "Francesco Chotuck" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d5c40f0b6120", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(MeasureTheory): pushforward of Hausdorff measure under a homothety (#41798)", "updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/d5c40f0b612031a266692bc719fa5fef659fb7fa" }, { "age_days": 2, "authors": [ "Artie Khovanov" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:40cb31be4a51", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Dimension/Free): division version of tower law (#41488)", "updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/40cb31be4a51505f4a25060b8e0c775dcb537dac" }, { "age_days": 2, "authors": [ "Joël Riou" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:62244e5ddb2b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Homology): homotopy equivalences satisfy the two out of three property (#42321)", "updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/62244e5ddb2bb0c35e3500acb5730ad8fb4b17aa" }, { "age_days": 2, "authors": [ "Marcus Zibrowius" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:32beea3cad90", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/DirectSum): equivalence between direct sum indexed by ι₁ and double sum indexed by ι₂ and fibres of f : ι₁ → ι₂ (#39607)", "updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/32beea3cad9021f3904958d54eddddba078a6aca" }, { "age_days": 2, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:54df8a3f96ac", 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"updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/932a58b04d345d516adb54545493f5b3a59d0f33" }, { "age_days": 2, "authors": [ "Felix Pernegger" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4f85c2fcf79", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-01", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: fix various typos (#42232)", "updated": "2026-08-01", "url": "https://github.com/leanprover-community/mathlib4/commit/f4f85c2fcf7946e12ddc6ea21639d953b62d1284" }, { "age_days": 2, "authors": [ "Yaël Dillies" ], "content_date": "2026-08-01", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:294355479299", "kind": "github_update", "label": "negative", "matched_signals": [], "published": 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"2026-07-31", "url": "https://github.com/leanprover/lean4/commit/02a57df9499109bb4eec0820ece3af0fe00e3086" }, { "age_days": 3, "authors": [ "Robin Arnez" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "github:leanprover/lean4:23393b959b33", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: generalize `MonadTail (StateT σ m)` instance (#14623)", "updated": "2026-07-31", "url": "https://github.com/leanprover/lean4/commit/23393b959b33e3a8d15796b2397f8a04c315b9f4" }, { "age_days": 3, "authors": [ "Mac Malone" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "github:leanprover/lean4:552252630a8b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": 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"leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra): use `IsApply` for `QuadraticMap` (#42134)", "updated": "2026-07-31", "url": "https://github.com/leanprover-community/mathlib4/commit/ce88332a27540b49d649b17a9d1a8c1cdfb9f193" }, { "age_days": 3, "authors": [ "Thomas Browning" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4570dc2f3c8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-31", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/*): remove domain assumptions by generalizing from torsion free to faithful smul (#41379)", "updated": "2026-07-31", "url": "https://github.com/leanprover-community/mathlib4/commit/f4570dc2f3c801ed0c0edd5867f943e2b84e4dec" }, { "age_days": 4, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "github:leanprover/lean4:fd1cec3b99e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: missing `check_no_metavar_no_fvar` checks at `inductive.cpp` (#14607)", "updated": "2026-07-30", "url": "https://github.com/leanprover/lean4/commit/fd1cec3b99e4887d59c833a52691e3ba4cd5d40d" }, { "age_days": 4, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "github:leanprover/lean4:d53dcb222f81", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: mark exported stubs of `partial` definitions as unsafe (#14609)", "updated": "2026-07-30", "url": "https://github.com/leanprover/lean4/commit/d53dcb222f8122be00cfc00947e0154b9bb337c6" }, { "age_days": 4, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "github:leanprover/lean4:41056da26750", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: check universe parameters in mutual definitions (#14608)", "updated": "2026-07-30", "url": "https://github.com/leanprover/lean4/commit/41056da267503cb8d83577a689d3ade292aac8c6" }, { "age_days": 4, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "github:leanprover/lean4:a0acacbd5332", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add an `assert` do element for intrinsic verification (#14602)", "updated": "2026-07-30", "url": "https://github.com/leanprover/lean4/commit/a0acacbd53322e37aab1fb2b0c0e7f8f962fece0" }, { "age_days": 4, "authors": [ "Mac Malone" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "github:leanprover/lean4:8be365039be8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: untrace core build internal flags (#14599)", "updated": "2026-07-30", "url": "https://github.com/leanprover/lean4/commit/8be365039be84ca0b3e2a4579676892a261eee2e" }, { "age_days": 3, "arxiv_id": "2607.29681", "authors": [ "Pjotr Buys", "Sven Polak", "Jeroen Zuiddam" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "arxiv:2607.29681", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-31", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We give new lower bounds for the Shannon capacities of small odd cycles: $Θ(C_7)\\geq3.258805369885\\ldots$, $Θ(C_{11})\\geq5.294502522149\\ldots$, $Θ(C_{13})\\geq6.302455083464\\ldots$, $Θ(C_{15})\\geq7.301600534487\\ldots$, $Θ(C_{19})\\geq9.357192705918\\ldots$, $Θ(C_{21})\\geq10.342455853338\\ldots$, and $Θ(C_{23})\\geq11.328224257774\\ldots$. The bounds are obtained by an iterative procedure due to Gao (2026) which is based on a method by Itty, Rosin, Carstensen and Reichman (2026). The bounds are fully formalised in Lean.", "title": "Lean-verified lower bounds for the Shannon capacity of odd cycles", "updated": "2026-07-31", "url": "https://arxiv.org/abs/2607.29681" }, { "age_days": 3, "arxiv_id": "2607.29602", "authors": [ "Jeffrey M. Girard", "Jason Z. Zheng", "Jacqueline R. Vertino", "Antony D'Avirro", "Benjamin Peloquin" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "arxiv:2607.29602", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-31", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Reading a social situation often depends on behavior, not words alone. We introduce FriendBench, a benchmark for inferring whether two people are already familiar or are meeting as strangers, from a 20-second clip of a dyadic ice-breaker conversation. Every pair answers the same type of prompt, so only the manner of interaction can reveal the answer. Across text, audio, and video, we compare 26 models from seven companies against matched human panels over 96 balanced dyads. The best model and the human crowd are statistically indistinguishable on accuracy in every modality, but reach it differently: humans stay balanced across the two answers, while the strongest models lean toward \"stranger\"---a difference in effective prior, not discrimination. Richer channels help both unequally, and only humans gain from visible behavior on top of speech. We release the stimuli, human ratings, and model predictions.", "title": "FriendBench: Benchmarking Dyadic Familiarity Inference in Humans and Multimodal Large Language Models", "updated": "2026-07-31", "url": "https://arxiv.org/abs/2607.29602" }, { "age_days": 3, "arxiv_id": "2607.29111", "authors": [ "Damiano Testa" ], "content_date": "2026-07-31", "freshness": "fresh", "id": "arxiv:2607.29111", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-31", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We define a non-unital, generally non-associative, commutative semiring structure on the collection of normal subgroups of a group $G$. This viewpoint allows us to recast in ring-theoretic terms Fitting's classical theorem that the join of two nilpotent normal subgroups is nilpotent. From this perspective, the two key inputs are a binomial expansion in a non-associative setting and the fact that the commutator subgroup of two normal subgroups lies in each factor. The development is formalized in Lean, making essential use of Mathlib for the core definitions and results.", "title": "Fitting's Theorem and Semirings of Normal Subgroups", "updated": "2026-07-31", "url": "https://arxiv.org/abs/2607.29111" }, { "age_days": 4, "arxiv_id": "2607.28332", "authors": [ "Haewoon Kwak" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28332", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "When AI systems surpass elite human performance and settle into everyday expert practice, the question that follows is how machine judgment is made publicly intelligible and attributable. We study Korean Go commentary on YouTube, where AI systems such as KataGo became standard analytic tools after AlphaGo. Our corpus spans a decade (2016--2025) and approximately $1{,}900$ hours of footage across institutional broadcasters and creator-led channels, in four phases of AI availability. We document a widening asymmetry between visual and verbal AI presence: AI winrate graphs are visible for about $98\\%$ of late-period institutional broadcast time, yet AI-salient talk accounts for only $2.63\\%$ of sentences. What recedes is the source label, not the metric: winrate and point-gap talk persists while ``AI'' itself goes unsaid. We read this recession as the communicative signature of domestication. Our strongest evidence is a compositional shift in verbal mediation: explicit naming gives way to interface rendering, and creator-led commentary leans further toward it than institutional commentary. We develop a typology distinguishing source-foregrounding from source-receding mediation, and argue that the two preserve different hooks of contestability: discursive anchors through which audiences can recognize and question the machine source. The stakes of that difference rise in domains where AI is less reliable than in Go.", "title": "When AI Becomes Routine: A Decade of Public AI Mediation in Korean Go Commentary", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28332" }, { "age_days": 4, "arxiv_id": "2607.28778", "authors": [ "Nils Küchenmeister", "Alex Ivliev", "Dörthe Arndt", "Markus Krötzsch" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28778", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Combining RDF rule languages, such as N3 or SHACL Rules, with default negation is challenging. Existing methods to stratify negation often fail for RDF rules, since individual triples do not carry enough information to meaningfully restrict potential dependencies. Blank nodes in rule heads further complicate the matter, since the order of rule applications may determine whether new values are created, which in turn can change the applicability of rules with negation. To solve these open problems, we propose chain stratification as a robust new condition that guarantees a well-behaved semantics for RDF rules with negation, and existential rules in general. Our condition combines an elaborate analysis of potential multistep derivations with a mechanism for using integrity constraints to discard impossible cases. Applying rules in any order that respects chain stratification is guaranteed to derive an RDF graph that is unique, lean, and justified under the usual negation-as-failure semantics. To show the practicality, we also provide a prototype implementation.", "title": "Stratified Negation in RDF Rules: A Correct Approach (Extended Version)", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28778" }, { "age_days": 4, "arxiv_id": "2607.28459", "authors": [ "Pablo Manrique", "Stefan Szeider" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28459", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Constraint programming is a core technology for solving complex combinatorial problems in scheduling, planning, configuration, and verification. Trusting its results therefore demands guarantees at two levels: that reformulations applied beforehand are semantics-preserving, and that solvers produce correct answers. In this work, we introduce a framework that addresses both verification levels in the Lean theorem prover: it can be used to prove formulation-level properties, such as equivalence, equisatisfiability, and the correctness of symmetry-breaking constraints, parametrically for entire problem families; and to check solver-produced certificates for individual instances via translation backends to external formats such as MiniZinc, SMT-LIB, and OPB. Combining both levels yields an end-to-end workflow that establishes the satisfiability or unsatisfiability of a constraint problem without trusting the external solver. Experimental results show that our framework's verified symmetry breaking also pays off in practice: a single parametric proof per problem family, reused across all instance sizes, reduces solver search effort by a factor of up to 2x10^7, while the entire in-Lean certification stays affordable, taking at most a few minutes for our largest instances.", "title": "LeanCSP: A Framework for Certifying Constraint Reformulation and Solving in Lean", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28459" }, { "age_days": 4, "arxiv_id": "2607.28133", "authors": [ "John Conlon", "Peter Schwardmann" ], "content_date": "2026-07-30", "freshness": "fresh", "id": "arxiv:2607.28133", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We examine whether sycophantic AI advice distorts decisions. Our experiment involves 1,500 participants in 30 decision environments spanning core domains in economics and the social sciences. Contrary to the vast majority of predictions in an expert survey we conduct, we find that AI advice depolarizes choices on average, moving participants away from their initial leanings. This depolarization arises despite the LLM being measurably sycophantic: it disproportionately offers considerations that support users' initial leanings and uses agreeable and flattering language. Depolarization occurs across moral and non-moral, objective and subjective, strategic and non-strategic, and complex and simple tasks. Increasing sycophancy weakens depolarization, showing that sycophancy is behaviorally relevant, even if it is generally outweighed by the informativeness of AI advice. Finally, several results mitigate the concern that market forces will generate greater polarizing effects outside the experiment or in the future. On the supply side, our baseline AI's level of sycophancy is typical of leading models, and these models are not becoming more sycophantic over time. On the demand side, participants do not prefer greater sycophancy, do not select into AI advice in tasks where it is more polarizing, and exhibit greater depolarizing effects when they are more frequent AI users outside the experiment.", "title": "AI Sycophancy and Decisions", "updated": "2026-07-30", "url": "https://arxiv.org/abs/2607.28133" }, { "age_days": 5, "arxiv_id": "2607.27298", "authors": [ "Shuo Deng", "Kenneth W. Shum" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "arxiv:2607.27298", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-29", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "As large language models become increasingly capable of generating mathematical arguments, mathematics is likely to face not a scarcity of proofs but an abundance of plausible ones. In such an environment, verification, exposition, and incorporation into reusable mathematical infrastructure become central tasks. We report on an ongoing Lean formalization of \"Measure-Theoretic Probability: With Applications to Statistics, Finance, and Engineering\", a fourteen-chapter upper-level undergraduate textbook covering topics from Riemann--Stieltjes integration to martingales and limit theorems. The project produces a machine-checked companion to the textbook and contributes reusable infrastructure for future formalizations involving probability theory. A Lean formalization provides computer-checked statements and proofs, makes hypotheses explicit, and allows readers to inspect the precise logical content of textbook results. A central challenge is to bridge textbook-facing statements with Mathlib's more general measure-theoretic interfaces. We reuse Mathlib results when possible and introduce reviewable interface lemmas when the textbook formulation and library abstraction differ. The project illustrates how formalized textbooks can support teaching, clarify mathematical assumptions, and help build the formal foundations needed for reliable AI-assisted mathematics.", "title": "From Lecture Notes to Lean: Formalizing a Textbook on Probability Theory", "updated": "2026-07-29", "url": "https://arxiv.org/abs/2607.27298" }, { "age_days": 6, "arxiv_id": "2607.25262", "authors": [ "Wenhua Li", "Darius Foo", "Quang Trung Ta", "Wei-Ngan Chin" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.25262", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-28", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Type safety has traditionally rested on carefully crafted type systems, under the motto \"well-typed programs cannot go wrong\". Modern demands push type systems past this basic guarantee: toward memory safety (e.g., Rust), stronger data-structure invariants (e.g., GADTs), and broader typability (e.g., MLstruct). The motto absorbs each such property by enlarging the set of states deemed \"wrong\", but collapses them into one binary verdict: heap ownership, flow-sensitive changes to a variable's type, and the gap between a recoverable and a fatal error are relational, stateful facts about intermediate states that one verdict cannot tell apart. Worse, each demand typically brings its own extension, making it hard to say what each guarantees or how they combine. Floyd-Hoare logic supplies a unified foundation. We present a framework for type-safety verification built from four ingredients: (i) case specifications for path-sensitive typing; (ii) separation types, inspired by separation logic, for flow-sensitive type mutation and must-aliasing; (iii) a disciplined distinction between Err (runtime error values our types track) and Abrt (compile-time errors), yielding the refined motto well-typed programs must never abort; and (iv) type predicates for data-structure invariants. Since all four are ordinary types in one Boolean algebra rather than separate extensions, the framework subsumes both GADTs and liquid types within one type logic, spanning weak specifications that tolerate Err to strong ones that eliminate it. Subtyping reduces to one decidable emptiness test, so a single lightweight procedure serves the whole framework with no SMT oracle in its trusted base. We formalise the Hoare rules and prove soundness in a machine-checked Lean mechanisation; by proof reflection it yields a self-certifying type-checker, evaluated on a benchmark suite.", "title": "Type Safety via Hoare Logic with Separation and Pure Types", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.25262" }, { "age_days": 6, "arxiv_id": "2607.26297", "authors": [ "Adam Y Shavit" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.26297", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-28", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Patient-reported pain location is diagnostically decisive for some presentations and nearly uninformative for others. The prevailing account treats this as a single gradient of diagnostic utility governed by anatomical complexity. That explanation conflates three epistemically distinct failures of localization, each with its own mathematical structure, optimal instrument, and public-health consequence. In anatomical multiplexing (a), many structures share one location: a non-identifiable inverse problem. In delocalized amplification (b) --- clinically, central sensitization or nociplastic pain --- a centrally driven pain-behaviour pattern replaces the peripheral generator: a change of generative model. In referred/atypical displacement (c), location shifts in a systematic, person-dependent way, as in referred pain and in atypical presentations: a covariate-dependent bias. The three behave differently under inverse-problem, information-theoretic, decision-theoretic, and neural-field models, and demand different remedies. A single principle unifies them: they are one Bayesian inference problem failing at different nodes, meaning different points in one generative model: the likelihood, the model class, and the prior and loss. Observation over time increases the recoverable information. A fourth node, the report itself, carries this paper's main formal contribution --- a spatial Bayesian model of where pain is said to be, distinct from where it is felt. Re-examination further finds that the published \"high-utility\" accuracy band leans on overstated specificity, so the gradient is real but flatter than drawn. The account sits on a \"why-location-fails\" axis, a synthesis distinct from the nociceptive/neuropathic/nociplastic taxonomy (Kosek et al., 2016).", "title": "Three Failures of Pain Location: Why the Diagnostic Utility of Symptom Localization Is Not One Thing", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.26297" }, { "age_days": 6, "arxiv_id": "2607.26331", "authors": [ "Kazuki Ikeda" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "arxiv:2607.26331", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-28", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit completely positive family with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove $O(N^{-1/2})$ convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large $N$. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.", "title": "Quantum Turing Patterns", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.26331" }, { "age_days": 7, "arxiv_id": "2607.24893", "authors": [ "Diego Fernandez Arias", "Dev Prashant Mistry", "Ren Wang", "Yibo Hu" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "arxiv:2607.24893", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-27", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Multi-agent LLM systems can be attacked by a payload that no single agent ever holds in full: a poisoned tool hides encrypted fragments in its observations, spreads them across several agents, and an external step reassembles and executes them after the run. Per-step safety checks that judge each action in isolation may fail to recognize the complete distributed payload. We investigate how early such an attack can be detected while the run is still unfolding, and how robustly it can be caught once its most obvious cues are stripped away. We build a working instance on a hierarchical multi-agent system, run it under benign and attacked conditions across five language models and two task domains, and record when each fragment is injected and when the payload is assembled and executed. Detection is a race against assembly. Before the first fragment is injected, attacked and benign runs are indistinguishable; once injection begins, a prefix detector flags $99.3\\%$ of successful attacks with a median of five steps remaining and a $10.3\\%$ safe-run false-positive rate. Because assembly occurs only after the run, these alarms arrive in time to abort nearly every successful attack. We then measure how much of that warning rests on removable surface cues of the attack rather than on its distributed structure. Generic zero-shot and behavior-trained detectors provide almost no warning at all; the detectors that do work lean in part on removable surface cues, chiefly the ciphertext's length and entropy, and once the entropy cue is removed from the payload and the length features from the detector, detection arrives later and transfers poorly across domains, though a fine-tuned model recovers some of the loss.", "title": "Early Detection of Distributed Backdoors in Multi-Agent LLM Systems: A Characterization Study", "updated": "2026-07-27", "url": "https://arxiv.org/abs/2607.24893" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }