{ "counts": { "adjacent": 19, "core": 3, "errors": 0, "negative": 65, "total": 87 }, "date": "2026-07-29", "errors": [], "fresh_content_days": 21, "generated_at": "2026-07-29T16:50:49Z", "items": [ { "age_days": 5, "arxiv_id": "2607.22511", "authors": [ "Jiyuan Tan", "Vasilis Syrgkanis" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "arxiv:2607.22511", "kind": "paper", "label": "core", "matched_signals": [ "mathlib_retrieval", "tool_use_agents", "verifier_guided_reasoning" ], "published": "2026-07-24", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Automating theoretical research is constrained not only by the generation of candidate results, but also by their reliable evaluation. A common approach is to close the research loop with a large language model (LLM) reviewer. However, such reviewers remain empirically unreliable: they may accept fabricated papers and detect them at rates close to chance (Bad Scientist, 2025). We present CausalForge, a framework for automated theoretical research in causal inference grounded in the Lean proof assistant. CausalForge combines Causalean, a foundational Lean library for causal inference containing 7,035 machine-checked declarations developed with language-model assistance under human design and review, with CausalSmith, a self-improving agentic pipeline that selects research topics, proposes results, formalizes statements, constructs proofs, and presents the resulting artifacts for human inspection. Because a machine-checked proof establishes only that a formal statement follows from its assumptions, not that the statement faithfully captures the intended scientific claim, the pipeline augments kernel verification with a statement audit that compares each formal theorem against the informal claim it is intended to express. We evaluate the system using artifacts produced by completed autonomous research runs. The source code, formal library, and run records are available at https://github.com/Jiyuan-Tan/CausalForge.", "title": "CausalForge: A Formally Grounded, Self-Improving Agentic Framework for Automated Research in Causal Inference", "updated": "2026-07-24", "url": "https://arxiv.org/abs/2607.22511" }, { "age_days": 4, "arxiv_id": "2607.23390", "authors": [ "Mojtaba Soltanalian" ], "content_date": "2026-07-25", "freshness": "fresh", "id": "arxiv:2607.23390", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-25", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "When can additional low-bit residual computation replace missing numerical precision for a fixed input-output map? We model a quantized residual system over a fixed horizon as a pure schedule selecting fields from a declared low-bit operation library, and use relaxed controls to characterize its infinite-depth limit. The distance from the target to the closed relaxed reachable set is the exact structural floor: no increase in depth can remove it for that library. Pure schedules approach the relaxed class at rate $O(D^{-1})$ under bounded-variation time dependence and $O(D^{-\\vartheta}+D^{-1})$ under Holder dependence of exponent $\\vartheta$. Execution arithmetic can reverse this conclusion: full-state write-back introduces a $Dρ_z$ penalty and can freeze residual updates, whereas increment error feedback replaces this growth by a bounded carry term and obeys an exact common-lattice conservation law. A fixed-teacher converse makes this rate sharp: for coherent depth-$L$ first-order high-precision comparators, accuracy matching requires $D=Θ(L)$. Learned codebooks add a metadata resource, while state-dependent routing introduces hybrid event conditions. Verified primal and dual bounds yield feasible, impossible, or unresolved decisions before training. Companion software implements the workflow, and Lean 4 machine-checks the exact discrete core. Depth replaces precision only relative to a declared library, horizon, execution semantics, and routing model.", "title": "When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation", "updated": "2026-07-25", "url": "https://arxiv.org/abs/2607.23390" }, { "age_days": 6, "arxiv_id": "2607.21533", "authors": [ "Lei Zhang", "Yusheng Zhao", "Yimeng Cao", "Ranyiliu Chen", "Mingrui Jing", "Jizhe Lai", "Ziao Tang", "Jingu Xie", "Hongshun Yao", "Xuanqiang Zhao", "Guocheng Zhen", "Chengkai Zhu", "Xin Wang" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "arxiv:2607.21533", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-07-23", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Formal verification is becoming increasingly practical for quantum computing, yet the ability of AI agents to construct machine-checkable proofs in this domain remains unmeasured. We introduce Lean-QuantumAlg-Bench and Lean-QIT-Bench, two Lean 4 benchmarks containing 36 and 40 theorem-completion tasks for quantum algorithms and quantum information theory, respectively. Every task compiles in a fixed environment and is evaluated by deterministic proof checking and targeted semantic review, with difficulty weights assigned before model execution. We evaluate four models-GPT-5.5, Kimi K3, DeepSeek V4-Pro, and MiniMax M3-within a common theorem-proving framework under two settings: a task-only baseline and library-augmented deduction (LAD), which additionally provides access to a verified domain library. The highest difficulty-weighted scores are 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark. LAD improves both score and completion rate in all eight model-benchmark comparisons, with gains of up to 15.9 points, providing evidence that verified libraries can strengthen domain-specific proof agents. The results reveal recurring weaknesses of agentic proving in areas such as quantum simulation, quantum learning, quantum information measures, and entanglement theory. Monetary and wall-clock costs per score point also vary substantially across models, highlighting important capability-efficiency trade-offs. We expect these benchmarks to establish a reproducible baseline for developing more capable and reliable proof agents, and to pave the way toward self-evolving AI scientists for advancing quantum information science.", "title": "Benchmarking Agents for Proving Theorems in Quantum Algorithms and Quantum Information", "updated": "2026-07-23", "url": "https://arxiv.org/abs/2607.21533" }, { "age_days": 3, "arxiv_id": "2607.23664", "authors": [ "Mikko Fischer" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23664", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-07-26", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We exhibit a connected graph on 24 vertices with maximum degree 3, independence number 9 and zero forcing number 11, refuting a 2017 conjecture of TxGraffiti recorded as Conjecture 2 of the survey of Davila, Brimkov and Pepper. The same construction with a different gadget gives a connected cubic graph on 36 vertices with independence number 15 and zero forcing number 17; the conjecture therefore fails also in the cubic form in which the survey's Lean 4 appendix states it. In particular Z <= alpha + 1 is not a universal bound for connected cubic graphs, and the value Z = alpha + 2 is attained.", "title": "A counterexample to the zero forcing versus independence conjecture for cubic and subcubic graphs", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23664" }, { "age_days": 1, "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": 2, "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": 2, "arxiv_id": "2607.24095", "authors": [ "Ivan Klianev" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "arxiv:2607.24095", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-27", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In this paper, we resolve the apparent contradiction between the proven possibility of deterministic crash-tolerant consensus in a fully asynchronous environment and the reconfirmation of the FLP impossibility result by Attiya, Castañeda, and Rajsbaum. With the use of a strictly formal framework that extends their reasoning, we close this fundamental gap in theory. Specifically, we demonstrate that a single protocol phase separates their findings from reaching the exact opposite conclusion. Another important outcome is a novel algorithm with ability to tolerate multiple crash faults. We provide a rigorous, strictly formal proof of correctness to validate our results.", "title": "Consensus In Asynchrony: Strictly Formal", "updated": "2026-07-27", "url": "https://arxiv.org/abs/2607.24095" }, { "age_days": 2, "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": "2607.23715", "authors": [ "Shuqing Zhao" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23715", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-26", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We report the design and end-to-end verification of first-class IEEE-754 binary32 (FP32) and bfloat16 (BF16) arithmetic for ARCH, a hardware description language intended to be generated by language models. Every operator - comparisons, conversions, add, sub, mul, and fused multiply-add (FMA) - is described once against a single bit-vector IR and rendered three ways from one source: synthesizable SystemVerilog, an SMT-LIB model, and a Lean 4 proof model. The three artifacts cannot drift apart structurally, and the residual per-node printer correspondence is machine-checked: a Yosys-to-SMT miter proves the emitted SystemVerilog equivalent to the SMT model for all 24 operators. Verification splits at the solver-tractability frontier: multiplier-free operators (comparisons, add/sub over all 2^64 inputs, conversions, and all binary BF16 arithmetic) are proved exhaustively equivalent to the SMT-LIB FloatingPoint theory; the SAT-hard multiplier-bearing operators (FP32 mul and FMA) are proved correctly rounded in Lean, sorry-free, against a value-level round-to-nearest-even specification over exact dyadic values. Physical characterization exposed the FMA as the timing outlier: its exact-wide 470-bit datapath does not pipeline in our flow. We reimplemented it as a bounded 98-bit guard/round/sticky datapath that pipelines to 268 MHz on Nangate45, and proved, in Lean and over all 2^96 inputs, that it is bit-identical to the exact-wide reference, so it inherits the reference's proven correct rounding. The equivalence is tractable precisely because the shared multiplier appears on both sides and cancels: neither a SAT solver nor the proof ever solves a multiplier equivalence. (The BF16 FMA is deliberately an FP32-accumulating fusion, characterized as exactly that.) All machine-checked claims are pinned to a tagged open-source release.", "title": "Formally Verified Synthesizable Floating-Point Data Types in ARCH HDL", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23715" }, { "age_days": 3, "arxiv_id": "2607.23806", "authors": [ "Sietse Schelpe" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23806", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-26", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Improving a language model today means retraining it: enormous compute, a new opaque model each cycle, non-deterministic output. We take the opposite path: the model stays frozen, and a persistent memory of verified solutions grows beside it. Once a problem family is solved and has passed an independent verification step that never consults the answer key, every new instance of that family is answered at zero generation tokens, bit-exact, deterministically. Across 180 fresh instances spanning nine problem families, four architectures from four vendors - dense and mixture-of-experts - each score 180/180 at zero generation tokens per answer: execution-bound capability decoupled from parameter scaling. A negative control attributes the capability fully to the memory: emptied, it solves nothing. The same verify-before-store contract holds for open-ended reasoning: 88/88 consistency-gated acceptances across all four models, machine-checked formal proof, and reasoning-method transfer at 77/80. Memory selection takes 1.4 microseconds; a full reuse completes in 6-23 ms at 36 mWh. Approximate similarity retrieval selects the wrong item 94.3% of the time on a 4,500-item verified store where exact addressing makes zero errors. The store also serves as working context at a scale no shipped engine matches: a 6,000,000-token movable window on a single 46 GB GPU at flat memory, where vLLM stops at 30,399 tokens and SGLang silently truncates past 32,000. On published benchmarks, frontier models remain far ahead of any 12B at raw from-scratch reasoning; on everything this system has solved and verified, the comparison inverts: a frontier API call pays a fresh generation pass on every query, forever, while verified reuse costs zero tokens and returns the identical bits every time. A public testbench with free, rate-limited access accompanies this report: https://corbenic-galahad-bench.hf.space", "title": "A Frozen 12B Beats Frontier Models on Verified Work: 100% Accuracy, 0 Tokens, Bit-Exact, Forever", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23806" }, { "age_days": 4, "arxiv_id": "2607.22972", "authors": [ "Evan Wang", "Simon Chess", "Sophie Szeto", "Theodore Meek" ], "content_date": "2026-07-25", "freshness": "fresh", "id": "arxiv:2607.22972", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Lean 4's grind tactic combines congruence closure, E-matching, and case-splitting into a single automated solver, and like any such solver, it relies on hand-tuned heuristics to decide what to instantiate and where to case-split. These heuristics are tempting targets for learning, but there is a catch: because grind's search is non-monotone, a learned heuristic that helps one proof can break another, and an always-on replacement usually nets out near zero. We avoid this by invoking a learned intervention only after stock grind has already failed: a failure-triggered cascade that, by construction, cannot lose a proof grind already had. We apply it to two of grind's internal decisions. A cost-aware E-matching filter solves slightly more problems and runs about 5% faster. A lookahead step proves five theorems it otherwise times out on. We also report the negative result that motivated the design: across four feature-based models, statically predicting the correct case split is no better than random, because whether a split explodes is a runtime property that the features do not capture. Our results suggest that learning within theorem-proving tactics is most effective as a mechanism for deciding when and how to spend bounded search, backed by a reliable symbolic fallback.", "title": "Learned Interventions in Lean 4 grind", "updated": "2026-07-28", "url": "https://arxiv.org/abs/2607.22972" }, { "age_days": 5, "arxiv_id": "2607.22524", "authors": [ "Junye Ji" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "arxiv:2607.22524", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We formalize in Lean 4 the Kannan-Bachem Smith normal form algorithm for nonsingular square integer matrices. The program returns $S,U,U^{-1},V,V^{-1}$ and proves $UAV=S$, $U^{-1}SV^{-1}=A$, four inverse identities, the Smith divisibility conditions, and equality of $S$ with a canonical reference matrix. Stabilization terminates because each recursive pass strictly decreases the binary size of the active pivot; the outer algorithm recurses on the lower-right block. The computation also emits a flat trace of designated sign-magnitude arithmetic leaves. Branch conditions, quotients, Bezout data, and matrix entries are taken from the recorded primitive runs. Composite phases form their traces by concatenating the charge lists returned by the executed children. Verified self-delimiting codecs define the input and output sizes. Coefficient and work recurrences, closed by a kernel-checked polynomial-envelope calculus, give fixed polynomial bounds for both trace cost and the encoded length of the five output matrices. The theorem concerns these arithmetic primitives; structural operations and compiled Lean runtime are outside the model.", "title": "Machine-Checked Arithmetic Bit Complexity of the Kannan-Bachem Smith Normal Form in Lean 4", "updated": "2026-07-24", "url": "https://arxiv.org/abs/2607.22524" }, { "age_days": 6, "arxiv_id": "2607.20816", "authors": [ "Eric Hou" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "arxiv:2607.20816", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-23", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We construct a nonzero transcendental entire function such that every nonempty open subset of the complex plane contains a zero of every sufficiently high derivative; equivalently, the union of the zero sets along every infinite increasing sequence of derivative orders is dense. The construction is probabilistic and uses a bounded-coefficient Fock series. A saddle estimate, a one-coordinate small-ball bound, and Jensen's formula give summable outer probabilities for zero-free disks. The resulting function satisfies the explicit growth bound $|f(z)|\\leq\\sqrt2\\exp(|z|^2)$ and therefore also supplies a counterexample to a 1973 theorem of Boas and Reddy as printed. A machine-checked Lean 4 formalization verifies the existence theorem, the growth bound, and their supporting lemmas.", "title": "Cofinite Zeros of High Derivatives", "updated": "2026-07-23", "url": "https://arxiv.org/abs/2607.20816" }, { "age_days": 6, "arxiv_id": "2607.21187", "authors": [ "Fred Mesnard", "Étienne Payet", "Wim Vanhoof" ], "content_date": "2026-07-23", "freshness": "fresh", "id": "arxiv:2607.21187", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-23", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP (Logic Program Theorem Prover) system for stating and proving properties about logic programs. As the proof language of LPTP is based on natural deduction, the proofs are human readable. In our case study, we sketch in LPTP the usual proof showing the irrationality of the square root of 2. Then we describe the interactions we had with the LLM. We end up with a complete formal proof, partially generated by an LLM and fully proof-checked by LPTP.", "title": "Case study: proving sqrt(2) irrational with LPTP and an LLM", "updated": "2026-07-23", "url": "https://arxiv.org/abs/2607.21187" }, { "age_days": 7, "arxiv_id": "2607.20418", "authors": [ "Jack Fitzsimons" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20418", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Nikolov and Ullman asked whether k statistical queries on a universe of size T can be released under pure differential privacy with expected worst-coordinate error at the square-root rate suggested by known lower bounds. We prove their conjectured upper bound. For every database size n and privacy parameter $\\varepsilon>0$, there is an $\\varepsilon$-differentially private mechanism with expected error $O(\\min\\{1,\\sqrt{\\log(2T)\\log(2k)/(\\varepsilon n)}\\})$. This matches the lower-bound dependence in the standard high-dimensional regimes where those bounds apply; the shifted logarithms and outer minimum make the upper bound valid without additional parameter assumptions. The construction starts from a selection-only private multiplicative weights transcript, then replaces its probability mass function by a distance-penalized likelihood envelope. To prove that the modification preserves accuracy, a likelihood-level Maurey argument upper-bounds each Hamming-ball maximum by a small family of auxiliary PMW laws. Renyi moment bounds control nearby balls, a direct mixture bound controls distant balls, and grouping radii at the privacy scale prevents an additional $1/\\varepsilon$ factor in the error. The mechanism is information-theoretic. A companion Lean 4 development machine-checks the finite construction, pure privacy after deterministic decoding, and the displayed all-regimes upper bound.", "title": "Pure-DP Statistical Query Release at the Conjectured Square-Root Rate", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20418" }, { "age_days": 7, "arxiv_id": "2607.20186", "authors": [ "Lorenzo Saraiva", "Edward Hermann Haeusler" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20186", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In this article, we present a method for encoding Dag-Like Derivability Structures (DLDS), obtained via horizontal compression of Natural Deduction proofs in purely implicational minimal logic, as Boolean circuits. These DLDS compress Natural Deduction tree-like proofs into directed acyclic graphs, preserving logical correctness while reducing redundancy. We formally define the circuit construction process and establish its pointwise correctness, showing that, for any fixed path assignment, the resulting Boolean circuit agrees with the intended dependency-propagation semantics. A Lean formalization establishes machine-checked guarantees for the circuit evaluator and includes a restricted bridge for the uncompressed simple-tree fragment, connecting valid DLDS instances in that fragment to genuine circuit acceptance of their extracted paths under the route and discharge conditions formalized in Lean. This approach opens new perspectives for automated theorem proving and formal certification.", "title": "From Dag-Like Proofs to Boolean Circuits in Lean", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20186" }, { "age_days": 7, "arxiv_id": "2607.20188", "authors": [ "Sebastián Urciuoli" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20188", "kind": "paper", "label": "adjacent", "matched_signals": [ "verifier_guided_reasoning" ], "published": "2026-07-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "In this paper we continue assessing the feasibility of the approach to the mechanization of type theory by using classical syntax and Stoughton's multiple substitutions and report some substantial progress. We present formal proofs of confluence for beta-reduction and by using Takahashi's revision of Tait and Martin-Löf's proof, subject reduction for the entire family of the Pure Type Systems and consistency for some impredicative subclass, assuming normalization. As to the proof of confluence, we also develop a theory of alpha-commutative relations which, in our view, entails a clearer presentation and treatment of the problem than in similar developments. Finally, we assess general merits and drawbacks of the approach. The whole development has been machine-checked using Agda.", "title": "A Machine-checked Proof of Consistency for Impredicative Pure Type Systems", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20188" }, { "age_days": 8, "arxiv_id": "2607.19263", "authors": [ "Cameron Khanpour", "Samuel Talkington" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.19263", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-07-21", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth, making recent empirical observations rigorous. The bounds also hold with overwhelming probability for arbitrary bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified with accompanying Lean 4 source code.", "title": "The Limits of Quantum Computers for Power Flow", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.19263" }, { "age_days": 2, "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": 3, "arxiv_id": "2607.23828", "authors": [ "Thien Le", "Melanie Weber" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23828", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-07-26", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "We prove a conjecture of Monical, Tokcan, and Yong that every fixed positive power of the Vandermonde determinant is non-SNP in all sufficiently many variables, where a polynomial is non-SNP if there is a lattice point in its Newton polytope that does not appear with nonzero coefficient. This means our result proves that for every even power $k\\geq4$, there is always such a missing lattice monomial in large enough dimensions. The odd case follows from alternation, and the quadratic case was previously known. For every even power $k\\geq4$, we exhibit an explicit lattice point in the Newton polytope of $a_{δ_k}^k$ whose coefficient vanishes. The vanishing is obtained from a Dyson constant-term identity, proved using the finite-variable Jack scalar product and Macdonald's specialization formula. The key even-power construction and proof strategy arose from prompting with OpenAI Codex (GPT Sol 5.6 Extra High), a large language model; the complete transcript appears in the appendix. The authors subsequently checked and organized the argument. The accompanying Lean formalization is available at https://github.com/steven-le-thien/vandermonde-snp.", "title": "Powers of the Vandermonde determinant are eventually non-SNP", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23828" }, { "age_days": 7, "arxiv_id": "2607.21653", "authors": [ "Jian Hu", "Huiying Li", "Hao Zhang", "Binfeng Xu", "Yifan Zhang", "Shaokun Zhang", "Hemil Desai", "Michael Demoret", "Pavlo Molchanov", "Jan Kautz", "Yi Dong" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.21653", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-07-22", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Agentic reinforcement learning research is constant algorithm modification, new estimators, new pipeline stages, new rollout schemes, and in mainstream frameworks each change threads through layers of trainer, distributed backend, and rollout glue: the cost lands on the researcher at every iteration. Molt is a PyTorch-native training framework built to keep that cost small: a codebase compact and clean enough for a researcher to hold in their head, and for an AI coding assistant to read and reason about in its entirety, so the algorithm flow can be traced and changed end to end. The agent is an ordinary program, and one asynchronous loop trains multimodal and mixture-of-experts policies while never training on a token it did not generate, consistent in tokens, policy versions, and model semantics. Leanness does not cost performance: under a matched, fully asynchronous protocol, Molt is statistically comparable to a state-of-the-art Megatron-based stack. Molt is open source and provides recipes and containers at https://github.com/NVIDIA-NeMo/labs-molt.", "title": "Molt: A Scalable PyTorch-Native Training Framework for Agentic Reinforcement Learning", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.21653" }, { "age_days": 8, "arxiv_id": "2607.19281", "authors": [ "Philip John", "Eloghosa Ikponmwoba", "Pinaki Pal", "Opeoluwa Owoyele" ], "content_date": "2026-07-21", "freshness": "fresh", "id": "arxiv:2607.19281", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-07-21", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "This study introduces a reinforcement learning (RL) framework for generating optimal liquid-fueled reactors to improve lean blowout (LBO) predictions in gas turbine combustors. Existing approaches for determining cluster boundaries rely on manual heuristics or distance-based metrics in the input space. In contrast, the proposed method is goal-oriented, explicitly accounting for the target metric (e.g., LBO prediction accuracy) during cluster formation. The framework employs a multi-stage clustering--classification strategy: an initial clustering step (e.g., $k$-means clustering) generates a large set of homogeneous micro-clusters, followed by an actor-critic RL agent that merges them into optimal reactor zones. The validation study, performed using a Jet-A mechanism (119 species, 841 reactions), shows the RL framework offers improved predictive fidelity compared to $k$-means and captures the correct LBO trends, while achieving substantial speedups relative to the high-fidelity computational model. Overall, the RL-driven approach demonstrates strong potential as a computationally efficient reduced-order modeling technique that can complement high-fidelity simulations for rapid design-space exploration.", "title": "A Reinforcement-Learning-Augmented Liquid-Fueled Reactor Network Model for Predicting Lean Blowout in Gas Turbine Combustors", "updated": "2026-07-21", "url": "https://arxiv.org/abs/2607.19281" }, { "age_days": 0, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover/lean4:9bda38743059", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: remove `cbv at` due to breaking `SymM` invariants (#14580)", "updated": "2026-07-29", "url": "https://github.com/leanprover/lean4/commit/9bda387430591fd32a6cdfadb8807db9fb3db1df" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover/lean4:7830144a18ea", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: generalize withSetOptionIn to arbitrary result types (#14581)", "updated": "2026-07-29", "url": "https://github.com/leanprover/lean4/commit/7830144a18ea15cb4ec754508a87d259a4090f9c" }, { "age_days": 0, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover/lean4:9f011df29fa9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `where finally | spec` sections discharge residual contract verification conditions (#14579)", "updated": "2026-07-29", "url": "https://github.com/leanprover/lean4/commit/9f011df29fa925487af67848f9b3a2b900dbb17a" }, { "age_days": 0, "authors": [ "Weiyi Wang" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:be4fe8f18dc3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(LinearAlgebra/Matrix): make accidental private instance public (#42212)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/be4fe8f18dc36f2938ae3ec16af35008bd0d6224" }, { "age_days": 0, "authors": [ "Salvatore Mercuri" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:21da9fc40346", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: notation for adele rings (#40535)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/21da9fc40346c3663f0ecad16e2198748a5ba1ca" }, { "age_days": 0, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e91869b3f7e4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: lemmas about the `smallInductiveDimension` (#40879)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/e91869b3f7e43297eb8ecae06142b0e1c163a475" }, { "age_days": 0, "authors": [ "Noah Walker" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:12ab8e82f844", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Order/Basic): add `isOpen_Ioo'` (#42114)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/12ab8e82f8447fa639dabe9ffeda74436b72be31" }, { "age_days": 0, "authors": [ "Richard Osborn" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:69538871db6b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(SetTheory/Cardinal): strong induction on Nat.card for finite types (#41978)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/69538871db6b37033c369f63feadb1559ab1f2d8" }, { "age_days": 0, "authors": [ "Fabrizio Barroero" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3edb3c0658f6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/GroupWithZero/WithZero): `toAdd_unzero_eq_log` and simplify proofs (#42149)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/3edb3c0658f69f197b1e501b1f7623f3f7b3898c" }, { "age_days": 0, "authors": [ "damiano" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:53a560fefea0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `QuotientAddGroup.mk_out_eq_mul` to `mk_out_eq_add` (#41654)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/53a560fefea0a9525485d49d9f1c811ed89ae6f0" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6d8afdba83d1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove some (triple) underscore soup (#42208)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/6d8afdba83d18ca3e6c8a5838ef7d5d5d548cb09" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:edc39bf7bcc7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(NumberTheory/RamificationInertia/Basic): deprecate file (#41248)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/edc39bf7bcc706ba243ae824adaa60fff00416db" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e631b64438d2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Combinatorics/SimpleGraph/StronglyRegular): fix statement of `conway_99` (#42233)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/e631b64438d263de54e682d9ee63d84dbb010473" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d160677fd383", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Archive): convert to the module system (#42010)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/d160677fd383cf76893d1cba56bf84f251052956" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-29", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7630dcddf054", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-29", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(AlgebraicTopology/SimplexCategory): delete synthesizable instances (#42222)", "updated": "2026-07-29", "url": "https://github.com/leanprover-community/mathlib4/commit/7630dcddf054c350d73150d536390a15dbd1afc7" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover/lean4:a39eab69e1ee", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: missing check at kernel inductive declaration (#14577)", "updated": "2026-07-28", "url": "https://github.com/leanprover/lean4/commit/a39eab69e1eee9ad38f4efe507907b1026a77808" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover/lean4:aa89d2777fb4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: ci: early exit rebootstrap on no change to stage0 (#14575)", "updated": "2026-07-28", "url": "https://github.com/leanprover/lean4/commit/aa89d2777fb4342ff3084502e8f2d5a01aa17222" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover/lean4:b1722adad3d0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: handle stacked dependent projections in `cbv` that compose into dependent projection (#14567)", "updated": "2026-07-28", "url": "https://github.com/leanprover/lean4/commit/b1722adad3d00ad4443a08709b1efb93a78b477c" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover/lean4:7f7ecd721147", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: do not show deprecated syntax warnings inside of deprecated definitions (#14533)", "updated": "2026-07-28", "url": "https://github.com/leanprover/lean4/commit/7f7ecd721147fb5f61f46825a859b8721aa8fa7b" }, { "age_days": 1, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover/lean4:dfeeb611bc5a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: add basic code quality infrastructure data types (#14568)", "updated": "2026-07-28", "url": "https://github.com/leanprover/lean4/commit/dfeeb611bc5a352e49670c888b26a9ce12fe8ecc" }, { "age_days": 1, "authors": [ "Yi.Yuan" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:af9aa73bb322", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(RingTheory): use `Submodule.localized'` and kill TODO (#42174)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/af9aa73bb32239930d95e21a424be73477c6d440" }, { "age_days": 1, "authors": [ "Kevin Buzzard" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cdc4a098a5e8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf: golf Ideal.powQuotSuccInclusion_injective (#41701)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/cdc4a098a5e8c3b234f61f1529f752cfb7df8714" }, { "age_days": 1, "authors": [ "Chris Henson" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5eec30bc56ed", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf(LinearAlgebra/Pi): golf `Matrix.ker_diagonal_toLin'` (#42199)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/5eec30bc56ed5a23be2e27c544a949ba0bceddeb" }, { "age_days": 1, "authors": [ "Marcelo Lynch" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9e47bf70e265", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(cache): carry decompression pipeline state across download rounds (#41707)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/9e47bf70e26518025a5db9598f5368c23360150e" }, { "age_days": 1, "authors": [ "Floris van Doorn" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fb2c2f59cbbf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: tag lemmas with compactness and closedness (#39371)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/fb2c2f59cbbf1a6118b401fe85bcfbf849f4bdda" }, { "age_days": 1, "authors": [ "Anatole Dedecker" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c7202db459de", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: define Fredholm operators between TVSs (#41189)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/c7202db459de001e1f4dcbe9cc244a2be198010f" }, { "age_days": 1, "authors": [ "Floris van Doorn" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:06b6563c29f7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add assume tactic (#39026)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/06b6563c29f7cdb3d910b1703a6deaca0c634fd6" }, { "age_days": 1, "authors": [ "Leonid Ryvkin" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4660688d529f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: Transferring Lie Algebra structures along Equivalences (#39818)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/4660688d529f8b813a214daf3845e6c3a970d455" }, { "age_days": 1, "authors": [ "Attila Gáspár" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b56bbad0d952", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Tactic/Translate): warn when adding a docstring to an existing declaration (#41883)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/b56bbad0d9523068b60cf470df47d73e04a9a3c1" }, { "age_days": 1, "authors": [ "Chris Birkbeck" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e011717410c1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/MvPolynomial/WeightedHomogeneous): sub, eq_zero_of_no_monomials, eq_monomial_of_unique_weight (#38909)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/e011717410c13033a6fe4bebafe078835d9d3b30" }, { "age_days": 1, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0ce898f5af28", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory): bialgebra homs `R[G] → R[H]` are in bijection with group homs `G → H` (#41995)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/0ce898f5af28a9a72054a68b7f6331224e7dc767" }, { "age_days": 1, "authors": [ "Alain Chavarri" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9d302fc708aa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FieldTheory/Finite): irreducible polynomial divides X^q^n - X iff degree divides n (#39239)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/9d302fc708aa85d820df824fccefbb90d9b3e567" }, { "age_days": 1, "authors": [ "Abhishek Shivakumar" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1908d50c60ab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Spectrum): add the second resolvent identity (#39269)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/1908d50c60ab1867a250ef2d4c7263dfd6e7ed81" }, { "age_days": 1, "authors": [ "Moritz Doll" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5b20aff7a4c3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Lie): use `IsApply` for `Weight` (#42129)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/5b20aff7a4c34e27374611707081e3586186769d" }, { "age_days": 1, "authors": [ "Nailin Guan" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c9a84caef3d6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra): `Hom` commute with flat base change (#31222)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/c9a84caef3d682b3e8403b5555e1c90eaa06c400" }, { "age_days": 1, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5b1613e1dad7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: reduce the abuse of the defeq `Set α := α → Prop` (#42169)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/5b1613e1dad7f22558b292d8accde4f7800362f7" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:01cceef4309e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: make `ModelProd` and `ModelPi` implicit_reducible (#42038)", "updated": "2026-07-28", "url": "https://github.com/leanprover-community/mathlib4/commit/01cceef4309e0b28bde5dd951c72960f5282a1ac" }, { "age_days": 1, "authors": [ "Yaël Dillies" ], "content_date": "2026-07-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b595917dfbac", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Pi): use `Codisjoint`, `IsCompl` (#42173)", "updated": "2026-07-28", "url": 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"source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: compare `forbiddenTks` by pointer first in parser cache keys (#14562)", "updated": "2026-07-27", "url": "https://github.com/leanprover/lean4/commit/9ec149eff60a8012285622ea52c8adb6dfc00c2f" }, { "age_days": 2, "authors": [ "Wojciech Różowski" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "github:leanprover/lean4:76e5ec53d211", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support code actions in linters (#14402)", "updated": "2026-07-27", "url": "https://github.com/leanprover/lean4/commit/76e5ec53d211e9c6d8aec071bb427bc482515d3d" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-27", "freshness": "fresh", "id": 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"title": "leanprover/lean4: chore: reenable check for `since` field in deprecations (#14572)", "updated": "2026-07-27", "url": "https://github.com/leanprover/lean4/commit/889846da643a12e3ee2cbb0edf7f36ddd62b9e10" }, { "age_days": 2, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "github:leanprover/lean4:779f04e73e55", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: disable check for `since` field in deprecations (#14566)", "updated": "2026-07-27", "url": "https://github.com/leanprover/lean4/commit/779f04e73e553583f9496558a991ab90911acce5" }, { "age_days": 2, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-27", "freshness": "fresh", "id": "github:leanprover/lean4:e422bfd29662", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: `typeChanced` syntax for deprecated attribute (#14570)", "updated": "2026-07-27", "url": "https://github.com/leanprover/lean4/commit/e422bfd29662fe7ef890f90558725f8b8b708cee" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "github:leanprover/lean4:0bfc3acaef4e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: ensure `lean_initialize` is called when `Lean` is only privately imported (#14505)", "updated": "2026-07-26", "url": "https://github.com/leanprover/lean4/commit/0bfc3acaef4ed0576307a77fbaa0c6e1a5dca402" }, { "age_days": 3, "authors": [ "Mac Malone" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "github:leanprover/lean4:3b7f37725bc3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-26", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: lake: overhaul benchmarks & add precompile variants (#14509)", "updated": "2026-07-26", "url": "https://github.com/leanprover/lean4/commit/3b7f37725bc34d8903342666fc4a400f723d78a1" }, { "age_days": 4, "authors": [ "Wojciech Nawrocki" ], "content_date": "2026-07-25", "freshness": "fresh", "id": "github:leanprover/lean4:b4fb9a75e9e1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add SONAMEs to shared libraries (#14332)", "updated": "2026-07-25", "url": "https://github.com/leanprover/lean4/commit/b4fb9a75e9e1cfc8d936ee6a574a8b537662698b" }, { "age_days": 4, "authors": [ "Mac Malone" ], "content_date": "2026-07-25", "freshness": "fresh", "id": "github:leanprover/lean4:fed67d987430", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-25", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: ci: no `continue-on-error` for \"Upload Lake Cache\" (#14544)", "updated": "2026-07-25", "url": "https://github.com/leanprover/lean4/commit/fed67d987430595cddf0ee209f0b12dc69f182b5" }, { "age_days": 5, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:8d96b70a05ef", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: vcgen equation specs for deep-embedding program types (#14530)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/8d96b70a05ef229a0fe557ff9844360ef866ef61" }, { "age_days": 5, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:366c0a8ba4f6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: rank a vcgen call's unfoldings below a named or starred spec (#14535)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/366c0a8ba4f6d6445c8f9383c4fab0a4be1cbc9d" }, { "age_days": 5, "authors": [ "Sebastian Graf" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:952e337636d6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make Hoare `Triple` universe-polymorphic in its assertion type (#14168)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/952e337636d6152a68c5ec83f33d05c56a6fdbb7" }, { "age_days": 5, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:7fc313596478", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: prefer `dite` over `dif` in identifiers (#14501)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/7fc3135964788ce99a700906daf7e538e34cd63d" }, { "age_days": 5, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:a2c74ef85a82", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: move some `Bool` functions (#14538)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/a2c74ef85a8212503551663871b90d0d51b7417f" }, { "age_days": 5, "authors": [ "Garmelon" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "github:leanprover/lean4:7ebffd93253f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-07-24", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: update adaptation PR labels (#14534)", "updated": "2026-07-24", "url": "https://github.com/leanprover/lean4/commit/7ebffd93253f0fc50464bb89ed4c1c66a2e12fa0" }, { "age_days": 1, "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": 2, "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" }, { "age_days": 3, "arxiv_id": "2607.23500", "authors": [ "Gyeongwon Jeong", "Seonghun Park", "Jihoon Hyun", "Sang-il Oum", "Hongseok Yang" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23500", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-26", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming. We present a machine-checked formalization of the method for finite simple graphs, together with a certificate-to-proof compiler that turns externally generated certificate data into algebraic proofs checked by Lean. The formalization covers the foundations of the method: partially labeled graphs, their densities in large graphs, the quotient algebra of density expressions, graph-limit semantics through positive homomorphisms, and the downward operators used to average out labels. The compiler treats the external semidefinite programming output as candidate data rather than trusted input: Lean independently computes the required density and multiplication facts, verifies positive semidefiniteness exactly over $\\mathbb{Q}$, and carries out the algebraic normalization steps of flag-algebra proofs. Our case studies yield formal proofs of seven Turán-type upper bounds, including Mantel's theorem and the Erdős pentagon theorem, a $C_4$-density bound for triangle-free graphs, and edge-density bounds for $K_4$-free, $K_5$-free, and $C_5$-free graphs. Independently of the compiler, we formalize the matching constructions that complete the exact Turán densities of Mantel's theorem and the Erdős pentagon theorem, and prove two inequalities of Goodman. Our constrained semantics also prompted a meta-theoretic comparison of two ways of imposing graph constraints: building a hereditary constraint into the flag algebra from the start, or testing inequalities afterward on constrained graph limits with labels chosen at random. We state the resulting root-plantability criterion characterizing when the two approaches agree; a forthcoming paper will present the complete account.", "title": "Formalizing Flag Algebras in Lean", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23500" }, { "age_days": 3, "arxiv_id": "2607.23427", "authors": [ "Seiichiro Kusuoka", "Shuta Nakajima" ], "content_date": "2026-07-26", "freshness": "fresh", "id": "arxiv:2607.23427", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-26", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In this note, we consider the Sherrington--Kirkpatrick model with deterministic external field. Let $q=q(β,h)$ denote the solution of the replica-symmetric self-consistency equation \\[ q=\\mathbb E\\tanh^2\\!\\left(h+β\\sqrt q\\,Z\\right), \\qquad Z\\sim N(0,1), \\] where $β$ and $h$ are inverse temperature and external field, respectively. By refining Lata\\la' s argument, previously limited to \\(β< \\frac{1}{2}\\), and using the Kearns--Saul inequality, we prove overlap concentration and convergence of the free energy to the replica symmetric formula with error \\(O(N^{-1})\\) whenever \\[ β^2\\frac{q}{{\\rm arctanh}q}<1. \\] Note that for any $β<1$ and $h\\in \\mathbb R$, the condition above is satisfied. Moreover, for every nonzero $h$, this region contains a nonempty interval with $β>1$.", "title": "A note on Lata\\la's argument in SK model", "updated": "2026-07-26", "url": "https://arxiv.org/abs/2607.23427" }, { "age_days": 7, "arxiv_id": "2607.19811", "authors": [ "Xudong Ouyang", "Wenlun Zhang", "Yimin Xu", "Huazhong Liu", "Yunshan Zhong" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.19811", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The Segment Anything Model 2 (SAM2) has advanced temporal promptable segmentation, yet its deployment remains hindered by heavy memory cross-attention overhead and redundant full-frame visual feature extraction. While recent methods explore efficiency via heuristic memory pruning and window-based sparse routing, they typically suffer from catastrophic performance degradation in complex segmentation scenarios replete with occlusions and distractors. To resolve these limitations, we propose \\textbf{Lean-SAM2}, a holistic lightweight framework designed to address the above vulnerabilities while systematically eliminating computational redundancies. Specifically, Lean-SAM2 integrates three collaborative mechanisms: (1) Target-Anchored Memory Pruning (TAMP) safeguards target tokens against deceptive attention by modulating raw attention significance with semantic consistency against prompt-derived foreground anchors; (2) Temporal Condensation with Insurance Memory (TCIM) condenses historical context via a visibility-gated fusion while conditionally archiving high-confidence entries in a parallel insurance bank; and (3) Target-Anchored Risk-Aware Routing (TARR) selectively activates the heavy image encoder for target-related windows based on anchor similarity, utilizing a risk-aware fallback policy to trigger full-frame refreshes during volatile transitions. Extensive evaluations across multiple challenging benchmarks demonstrate that Lean-SAM2 establishes a superior balance between accuracy and efficiency. For example, on the LVOSv2 validation dataset, Lean-SAM2 achieves overall inference speedups of $1.412\\times$ and $1.417\\times$ on the SAM2.1-Large and SAM2.1-Base+, respectively, significantly outperforming Efficient-SAM2 while boosting the corresponding $\\mathcal{J}\\&\\mathcal{F}$ scores by $5.0\\%$ and $3.6\\%$. Code is available at https://github.com/DeawhaleQwQ/Lean-SAM2.", "title": "Lean-SAM2: Target-Anchored Memory and Encoder Acceleration for SAM2", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.19811" }, { "age_days": 7, "arxiv_id": "2607.19727", "authors": [ "Moritz Doll", "Iman Shames" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.19727", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We introduce an open-source library for machine-checked control theory in the interactive proof assistant Lean to lay foundations for the verification of cyber-physical systems. To this end, as representative theorems, we present formalizations of Lyapunov stability theory and the small-gain theorem. First, the machinery employed for formalizing Lyapunov stability, i.e., neighborhood filters, allows stating a Lyapunov theorem that covers both points and sets and applies to continuous, discrete, and hybrid systems. Second, the small-gain theorem is proved via stating input-output systems as relations without the usual well-posedness assumption. The Lean formalization of each of these theorems is then presented. We conclude by discussing the library architecture and mentioning some of the other system theoretic results that are formalized in the library along with future plans.", "title": "Foundations of Machine-Checked Control Theory in Lean", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.19727" }, { "age_days": 7, "arxiv_id": "2607.20382", "authors": [ "Eva McCord", "Ernest Pedapati", "Zag ElSayed" ], "content_date": "2026-07-22", "freshness": "fresh", "id": "arxiv:2607.20382", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-07-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Clinical biomarker workflows in translational research settings often rely on spreadsheet-driven tracking, manual quality control (QC) reconciliation, and loosely integrated systems, resulting in limited state visibility, delayed reporting, and increased operational risk. These challenges are particularly pronounced in multi-day assays such as Luminex-based quantification of Fragile X Messenger Ribonucleoprotein (FMRP), where HIPAA-compliant data governance, deterministic workflow progression, and coordinated communication across laboratory and clinical teams are required. This paper presents FMRP-LEAN, a HIPAA-compliant, AI-augmented Laboratory Information Management System (LIMS) architecture that formalizes biospecimen lifecycle management through a finite-state workflow model with explicit transition guards and dwell-time observability. The system integrates a self-hosted Supabase/PostgreSQL stack deployed within hospital-controlled infrastructure, hybrid edge-internal isolation with encrypted tunneling and loopback-only services, and bi-directional REDCap synchronization. A unified MRN-UUIDv7 identifier framework with QR-based tracking ensures traceable clinical-research linkage under PHI residency constraints. FMRP-LEAN incorporates automated statistical QC pre-screening and a governance-constrained AI operations module that operates exclusively on aggregate projections, with deterministic fallback guarantees. Deployment demonstrates improved workflow observability, reduced QC latency, and enhanced cross-role transparency between laboratory technicians, research coordinators, and patient-facing teams. The architecture provides a reproducible model for secure, state-explicit, and AI-augmented clinical research workflows in regulated healthcare environments.", "title": "FMRP-LEAN: A HIPAA-Compliant AI-Augmented LIMS Architecture for End-to-End Clinical Assay Workflow Optimization", "updated": "2026-07-22", "url": "https://arxiv.org/abs/2607.20382" }, { "age_days": 5, "arxiv_id": "2607.22100", "authors": [ "Lorenzo Concina", "Seraphina Fong", "Marco Matassoni", "Alessio Brutti" ], "content_date": "2026-07-24", "freshness": "fresh", "id": "arxiv:2607.22100", "kind": "paper", "label": "negative", "matched_signals": [ "negative:generic_llm_rag" ], "published": "2026-07-24", "score": -2.5, "source": "arxiv-ai4math-core", "summary": "Lightweight projectors are an established way to connect pre-trained speech encoders with large language models (LLMs), mapping acoustic features into token-level embeddings for tasks like ASR and spoken question answering. Existing systems, however, typically only support a few languages and are often limited to English. We introduce MEUSLI, the first open-science multilingual projector family that links a Whisper encoder with open-source multilingual LLMs, enabling fully open-source end-to-end ASR in 28 European languages. MEUSLI extends prior monolingual pipelines, delivering strong results across high- and low-resource languages. Using proper continual leaning techniques, MEUSLI can be easily extended to other languages not seen in training. We further demonstrate that the MEUSLI projector can be leveraged beyond ASR, enabling multilingual speech translation and topic identification with only a few hours of task specific supervision per language. Overall, MEUSLI provides a solid foundation for multilingual speech understanding tasks, supporting scalable and inclu- sive open-source SpeechLLM", "title": "MEUSLI: a Multilingual Projector for LLM-based ASR and Beyond", "updated": "2026-07-24", "url": "https://arxiv.org/abs/2607.22100" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }