{ "counts": { "adjacent": 17, "core": 3, "errors": 0, "negative": 68, "total": 88 }, "date": "2026-09-28", "errors": [], "fresh_content_days": 21, "generated_at": "2026-09-28T21:20:32Z", "items": [ { "age_days": 4, "arxiv_id": "2609.29870", "authors": [ "Hongshu Wang", "Xinyue Zuo", "Yufan Cai", "Neeraj Kumar Singh", "Yamine Ait Ameur", "Jin Song Dong" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.29870", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "verifier_guided_reasoning" ], "published": "2026-09-24", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Formal modeling provides strong guarantees about system correctness, but developing and repairing formal models remains labor-intensive and requires substantial expertise in logic and formal reasoning. Recent LLM-based autoformalization agents seek to reduce this burden by generating candidate formal models and revising them using feedback from formal tools. However, the existing approaches follow a generate-and-repair paradigm, in which repairs are driven by verification failures of the generated model and therefore depend heavily on both the granularity of the feedback and the LLM's repair capability. As a consequence, a repair targeting one level of verification may invalidate properties at another level, which requires reasoning over the complete set of event guards. To address these limitations, we propose Proof-Sketch-Guided Formal Model Synthesis (ProGS), an autoformalization method centered on model-based proof sketches. A model-based proof sketch represents the proof structure of the target formal system as a tree. Internal nodes capture case splits and inductive reasoning steps, while leaf nodes correspond to concrete state-transition events that realize individual subgoals. ProGS uses LLMs to generate and repair these sketches, with verification failures mapped back to specific nodes and subtrees to provide structured guidance for iterative repair. Our evaluation on a benchmark of 27 formal systems shows that ProGS improves over state-of-the-art agentic formal modeling approaches in syntactic validity, deductive verifiability, and behavioral correctness, demonstrating the benefit of organizing formal model construction around hierarchical proof sketches.", "title": "Formal Model Construction Guided by Model-Based Proof Sketches", "updated": "2026-09-24", "url": "https://arxiv.org/abs/2609.29870" }, { "age_days": 5, "arxiv_id": "2609.27495", "authors": [ "Gyeongwon Jeong", "Seonghun Park", "Seonghyuk Im", "Joonkyung Lee", "Hongseok Yang" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.27495", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We prove that the Turán density of the tetrahedron $K_4^{(3)}$ satisfies $π(K_4^{(3)}) \\le 312372062889819/560000000000000 < 0.557808$, improving Baber's upper bound of $0.5615$ and closing about $62\\%$ of the gap to the conjectured value $5/9$. The proof uses an exact seven-vertex flag-algebra certificate incorporating degree-stationarity from Razborov's differential method. To find the certificate, we combine the established techniques of cutting planes and column generation to optimize jointly over flag families whose types have at most five vertices. We give a complete formal proof of this Turán density bound in Lean 4.", "title": "A New Upper Bound for the Turán Density of the Tetrahedron", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.27495" }, { "age_days": 6, "arxiv_id": "2609.26546", "authors": [ "Chris Dzoba" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.26546", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-22", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "We exhibit simple, rotationally symmetric Venn diagrams with 17 curves and with 19 curves: n Jordan curves carried to one another by rotation through 2π/n, with every one of the 2^n regions present and connected and, since the diagrams are simple, every crossing on exactly two curves. Symmetric Venn diagrams exist for every prime number of curves (Griggs, Killian and Savage, 2004), but those diagrams have many curves through a point; simple ones were known only up to 13 curves (Mamakani and Ruskey, 2014). Four 17-curve and nine 19-curve diagrams were found by a Metropolis walk on rotation-invariant quadrangulations of the sphere in which regions may temporarily be duplicated, started from the Griggs-Killian-Savage diagram with its multiple crossings resolved. Every diagram is given by a machine-checkable certificate; one certificate of each size has been verified by a formal proof in Lean 4. All of the diagrams are non-monotone, which is why the crossing-sequence searches that found the 11- and 13-curve diagrams could not have found them.", "title": "Simple symmetric Venn diagrams with 17 and 19 curves", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.26546" }, { "age_days": 5, "arxiv_id": "2609.27991", "authors": [ "Georg Pichler" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.27991", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We settle three conjectures concerning a doubly symmetric binary source $(X,Y)$ with crossover $p$. Consider Markov chains $U - X - Y - V$ with $U,V$ binary, and let $\\mathcal{A}$ be the set of rate triples $(I(U;V),I(U;X),I(Y;V))$ attainable with arbitrary binary channels $X\\to U$, $Y\\to V$, and $\\mathcal{B}$ the subset attainable with binary symmetric channels. The averaged BSC conjecture, Conjecture 5.2 of Pichler, Piantanida and Matz (2022), asserts $\\operatorname{conv}\\mathcal{A}=\\operatorname{conv}\\mathcal{B}$. We prove this for every $p\\in[0,1]$. Two conjectures of Dikshtein, Ordentlich and Shamai (2022) concern the double-sided information bottleneck at $p=0$, where $Y=X$ and the two channels see the same source: their Conjecture 1 identifies the exact maximum of $I(U;V)$ at prescribed rates $I(U;X)$ and $I(Y;V)$, and their Conjecture 2 the exact minimum. We prove both for binary $U,V$: the two extrema are attained by the same pair of Z/S-channels, in opposite orientation for the maximum and in the same orientation for the minimum. The proofs were found with substantial AI assistance, and all three theorems are formalised in Lean 4 with Mathlib, depending only on the standard axioms. The development is available at https://github.com/g-pichler/bsc-averaging . The proof of Conjecture 1 of Dikshtein, Ordentlich and Shamai (2022) contains three certified computations, a polynomial bound, an interval sweep and a polynomial positivity certificate, all of which are checked in Lean.", "title": "Three Conjectures on Binary Channels for the Doubly Symmetric Binary Source", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.27991" }, { "age_days": 5, "arxiv_id": "2609.30310", "authors": [ "Pragyaan Gaur" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.30310", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "A polyhex is an edge-connected set of n cells of the regular hexagonal tiling, where each cell has area one. We prove that the convex hull of a polyhex has area at most (1/6)*ceiling(n^2 + 14n/3), and we show that some polyhex reaches this bound for every n. This proves a conjecture of Kurz from 2008, which asked for the weaker bound (1/6)*floor(n^2 + 14n/3 + 1). The two bounds differ exactly when 3 divides n. We checked the upper bound in the Lean 4 proof assistant with the Mathlib library. We also report a computation over all polyhexes with at most 12 cells, which shows that for these sizes only one shape reaches the maximum, up to rotation and reflection.", "title": "The maximum area of the convex hull of a polyhex", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.30310" }, { "age_days": 5, "arxiv_id": "2609.28603", "authors": [ "Niket Patel", "Ahmad Rammal", "Amaury Hayat", "Remi Munos", "Julia Kempe" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28603", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Recently, Large Language Models (LLMs) have been increasingly able to solve advanced mathematical problems, including many that have been open for decades. This opens the door to expansion of mathematical knowledge at unprecedented scale. Yet, while LLMs may be able to conjecture and prove more and more theorems, it remains open whether this new mathematical knowledge is interesting or useful. We define intrinsic interestingness of a theorem as the ratio between the length of its proof and the length of its statement. We show that this correlates strongly with an extrinsic measure of the downstream utility of a theorem. We identify the difficulty of a proof conditioned on a set of premises as a useful primitive for computing these metrics, and train a 27B model that predicts proof difficulty more accurately than frontier general-purpose models. Optimizing for our metric creates a model capable of producing more interesting theorems, while also reducing substantial or full overlap with Mathlib from 91.9% to 30.6%, showcasing the creation of more out-of-distribution math. We show that our system can generate candidate theorems, select the most interesting among them, and iteratively build on a self-expanding mathematical library. These metrics provide a practical and quantifiable signal for ranking conjectures and guiding proof search within formal mathematical libraries. Our framework provides a path towards self-expanding, machine-verified mathematical libraries that can choose worthwhile statements without relying on human-supplied targets.", "title": "Learning to Discover Interesting Mathematics", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28603" }, { "age_days": 5, "arxiv_id": "2609.28447", "authors": [ "Zhou Longfei", "Haijun Zou", "Tianhao Liu" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28447", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "For a convex body $K\\subset\\mathbb{R}^n$, let $w(K)$ denote the volume of its maximum-volume inscribed ellipsoid. We prove that every closed halfspace $H$ whose boundary passes through the center of the maximizing ellipsoid satisfies \\[ w(K\\cap H)\\le\\frac{\\sqrt e}{2}\\,w(K). \\] The constant is optimal uniformly over all dimensions, as witnessed by a family of circular cones, thereby establishing Khachiyan's conjecture. The proof converts containment, maximality, and the central-cut condition into algebraic constraints on positive definite matrices. Two complementary spectral bounds from a diagonal model extend to arbitrary center displacements through a directional rank-one estimate for fractional trace powers. Concavity determines their joint optimum. We also derive finite-dimensional bounds and a necessary condition for near equality, with self-contained supporting proofs and an alternative resolvent argument. An AI language model discovered the proof in a human-directed research process. Lean 4 with mathlib verifies the main theorem, sharpness, and supporting results.", "title": "A Spectral Proof of Khachiyan's Ellipsoid Conjecture", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28447" }, { "age_days": 6, "arxiv_id": "2609.28534", "authors": [ "Polona Durcik", "Marco Fraccaroli", "Joris Roos" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.28534", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-22", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger $Φ$-entropy among all Boolean functions of the input and all one-bit statistics of the output of a noisy channel. The technical heart of the matter is an explicit inequality in three real parameters, which is proved using explicit polynomial approximations and computer-assisted positivity checks. The results are also formally verified in Lean 4.", "title": "A weak Hellinger inequality for noisy Boolean channels", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.28534" }, { "age_days": 3, "arxiv_id": "2609.31557", "authors": [ "Yuchen Yang", "Xinan Dai", "Wenhao Deng", "Yingdong Shi", "Feng Xu", "Tailin Wu" ], "content_date": "2026-09-25", "freshness": "fresh", "id": "arxiv:2609.31557", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-25", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Chambolle-Dossal acceleration guarantees $F(x_n)-F^*=o(n^{-2})$ for every fixed smooth convex loss with a minimizer. We show that this qualitative improvement admits no universal quantitative rate. For every damping parameter $α>3$ and positive nondecreasing gain $G(n)\\to\\infty$, we construct a fixed one-dimensional smooth convex loss whose exact CD orbit satisfies $\\sup_{n\\ge1} n^2G(n)\\bigl(F(x_n)-F^*\\bigr)=\\infty$. Thus no divergent gain improves the $n^{-2}$ scale for all fixed losses, even with instance-dependent constants. The construction prescribes queried gradients and realizes infinitely many slow blocks within one smooth convex objective. Under local $p$-power growth with $p>2$ and sufficiently strong damping, we also construct a fixed loss whose exact CD orbit satisfies $F(x_n)-F^*\\sim Dn^{-2p/(p-2)}$, $D>0$, establishing the sharpness of the known convergence rate. Both main results are formally verified in Lean 4.", "title": "No Universal Remainder Rate for Chambolle-Dossal Acceleration", "updated": "2026-09-25", "url": "https://arxiv.org/abs/2609.31557" }, { "age_days": 4, "arxiv_id": "2609.30163", "authors": [ "George Danezis", "Zeno De Angeli", "Philipp Jovanovic", "Lefteris Kokoris-Kogias", "Markus Legner", "Alberto Sonnino" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.30163", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Dual-mode consensus protocols are fast when the network is partially synchronous and remain live under asynchrony. We introduce Steelhead, a dual-mode mechanism that composes a partially synchronous and an asynchronous commit rule over one DAG: every k-th round is decided by the asynchronous rule, whose leader a common coin reveals after the votes, and all other rounds by the partially synchronous rule. Every interval, validators replay the committed DAG under each candidate period, adopt the one with the fewest expected message delays, and fall back to k = 1 when the output stalls; the asynchronous rule applied to the coin rounds alone keeps the protocol live. Steelhead sends no message beyond the DAG's blocks, not even to agree on the period, and opens a coin only on the rounds that need a hidden leader. It is generic over pairs of DAG commit rules that share a committee; we instantiate it with Mysticeti and Mahi-Mahi at n >= 3f+1 and with the two variants of BlueBottle at n >= 5f+1. We prove it safe and live, and provide mechanized proofs in Lean 4. In simulation, Steelhead matches the partially synchronous protocol in a healthy network, stays close to the asynchronous one when network conditions stall the partially synchronous one, and adapts quickly in both directions.", "title": "Steelhead: Interleaving Partially Synchronous and Asynchronous Commit Rules on a Shared DAG", "updated": "2026-09-24", "url": "https://arxiv.org/abs/2609.30163" }, { "age_days": 4, "arxiv_id": "2609.29296", "authors": [ "Lihan Xie", "Zhicheng Hui", "Yingjun Lan", "Zhehao Li", "Xingzhi Qi", "Siyue Huang", "Jirui Liu", "Chuxiao Zeng", "Bohan Zhao", "Qinxiang Cao" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.29296", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-24", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Existing formal mathematics benchmarks, such as miniF2F, ProofNet, and PutnamBench, primarily evaluate models on constructing complete formal proofs for challenging problems. Because success is measured at the theorem level, these benchmarks offer limited insight into models' step-level formal reasoning. Evaluating this capability separately enables finer-grained diagnosis of model limitations than theorem-level evaluation alone. To fill this evaluation gap, we introduce ProofGap, a fine-grained benchmark for step-level formal reasoning. ProofGap is constructed through a natural-language proof-processing pipeline that decomposes each reasoning step into one or more aligned proof gaps. Applying this pipeline to natural-language solutions to 3,015 exercises in B. P. Demidovich's Problems in Mathematical Analysis yields 26,116 gaps. The benchmark focuses on mathematical analysis, a domain that remains challenging for current models. By supplying the local context and target explicitly, gap completion isolates local formal proof construction from end-to-end proof composition, enabling more precise localization of model failures. Natural-language solutions serve as the provenance of these obligations, while the benchmark task itself starts from an already formalized local context and goal. Beyond benchmarking, the same pipeline may support future proof-verification systems, provided that semantic translation and sequential proof composition are handled reliably.", "title": "ProofGap: Benchmarking Step-Level Formal Reasoning with Local Obligations Derived from Natural-Language Solutions", "updated": "2026-09-24", "url": "https://arxiv.org/abs/2609.29296" }, { "age_days": 5, "arxiv_id": "2609.28341", "authors": [ "Jaume de Dios Pont", "Josef Greilhuber", "Lukas Liehr", "Mitchell A. Taylor" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28341", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that for every window $w$ of the form $w(x) = e^{-π|x|^2} h(x)$, where $h$ is a polynomial, there exists a uniformly discrete set of points $\\mathcal{S} \\subset \\mathbb R^{2d}$ such that the magnitude of the short-time Fourier transform $V_w f$ on $\\mathcal{S}$ determines every $f \\in L^2(\\mathbb R^d)$ up to a constant phase factor. The separation distance can be chosen independent of the degree of $h$ and proportional to the square root of the dimension. The proof combines a discrete norming inequality, based on a multidimensional Remez inequality and VC-dimension bounds, with tail estimates for the reproducing kernel. A formalization of our main result in Lean 4 is also provided.", "title": "Phase retrieval from a uniformly discrete point set", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28341" }, { "age_days": 5, "arxiv_id": "2609.28791", "authors": [ "Yu Jiang" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28791", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The Meir--Moser rectangle-packing problem asks whether all rectangles with side lengths \\(1/n\\) and \\(1/(n+1)\\), for \\(n\\ge1\\), can be packed into the unit square with pairwise disjoint interiors. We establish a tail version of this problem. Let \\(R_n\\) denote the rectangle with these side lengths. We prove that there exists an integer \\(m_0\\) such that, for every \\(m\\ge m_0\\), the family \\(\\{R_n:n\\ge m\\}\\) admits a packing, by translations and right-angle rotations, into a square of side length \\(m^{-1/2}\\), with pairwise disjoint interiors. The area of the square equals the sum of the areas of all the rectangles. The geometric construction recursively decomposes rectangular gaps, while local randomized quotas and random permutations assign subsequent integer indices. We separately control the total area of waiting gaps and the assignment load at each index. The proof is organized in six steps: a finite-prefix reduction, geometric row decompositions, an area bootstrap, a sharp source-load estimate, control of the actual adaptive construction, and a compactness limit. For every finite time horizon, the probability of failure has a bound that is independent of the horizon and can be made arbitrarily small. The adaptive step uses a permanent load ledger, actual fresh height queries, and a one-sided comparison with a frozen source experiment. Compactness then yields an infinite packing. The final packing statements have been checked in Lean 4. A sufficient threshold is \\(m_0=10^{1000}\\). This result applies only to sufficiently late tails and does not resolve the original Meir--Moser rectangle-packing problem for the full sequence starting at \\(n=1\\), which remains open.", "title": "Packing Tails of Reciprocal Rectangles into Squares of Equal Area", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28791" }, { "age_days": 5, "arxiv_id": "2609.28102", "authors": [ "Stefan Szeider" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28102", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-23", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "A graph is biplanar if it is the union of two planar graphs on the same vertex set. The largest chromatic number of a biplanar graph is known to lie between 9 and 12. The lower bound comes from Sulanke's graph, which has independence number 2, and a biplanar graph on 19 vertices with independence number 2 would have chromatic number at least 10. Gethner and Sulanke asked in 2009 whether such a graph exists. We show that it does not, and more generally that every biplanar graph with independence number at most 2 is 9-colorable. The proof embeds a hypothetical counterexample in the union of two sphere triangulations, enumerates with SAT modulo symmetries the 3271 graphs that pass a necessary filter for the complement of such a union, and shows with a SAT solver that none of them is such a complement; a matching argument reduces the general statement to this computation and one further case on 18 vertices. The computational part of the proof, including the completeness of the enumeration and every refutation, is checked in Lean 4, assuming three classical facts about planar graphs. The Lean development, the SAT instances, and the enumeration certificates are available on Zenodo.", "title": "Biplanar graphs with independence number two are 9-colorable", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28102" }, { "age_days": 6, "arxiv_id": "2609.27105", "authors": [ "Katharina Stein", "Chaahat Jain", "Jörg Hoffmann", "Alexander Koller" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.27105", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Generalized planning aims to compute a plan that solves all instances of a planning domain. Recent work has used LLMs to automatically generate and debug such generalized plans in the form of Python programs and achieved perfect test data coverage for several domains. However, whether these generalized plans are actually complete, i.e. solve all instances of the domain, could only be determined by manual evaluation. Here, we present an approach for automatically generating generalized plans in Lean together with proofs of their completeness relative to a specification of the domain constraints provided as input. We introduce a semantic-preserving PDDL-to-Lean conversion, and use an LLM to generate both the generalized plan and the formal proof that it solves every instance satisfying the domain constraints. The correctness of the completeness proof is determined by Lean's kernel. We evaluate our approach on 13 commonly used benchmark domains, using GPT-5.6-Sol as the LLM. For 12 of the domains we obtain generalized plans together with valid completeness proofs. This is a major advancement of the state of the art in automatic generalized-plan completeness proofs.", "title": "Provably Complete Generalized Planning with LLMs", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.27105" }, { "age_days": 6, "arxiv_id": "2609.25918", "authors": [ "Qianyu Yu", "Lefteris Kokoris-Kogias", "Alberto Sonnino" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.25918", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-22", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "DAG-based consensus protocols can achieve great throughput and the optimal three-message-delay limit for n = 3f+1 consensus. While two-delay protocols exist, they pay with reduced resilience (requiring 5f+1-style committees) or rely on fallbacks that sacrifice the DAG's high throughput. This paper introduces Hydrozoan, the first DAG protocol with a dual commit path under a hybrid fault model of f Byzantine and c crashed validators, on n = 3f+c+2p+1 validators. Leaders commit in two message delays whenever at most p validators are faulty, and in three otherwise, with no extra messages, no view changes, and multiple leaders per round. Both paths are evaluated on the same DAG, using a novel graded indirect rule to reconcile them so that every honest validator reaches the same decision. We show that under geo-distributed conditions, which path is faster is a property of geography rather than the protocol, as rounds reaching a remote region cost far more than those that do not. The (f, c, p) knobs place the fast quorum where the deployment requires it, allowing a commit in two message delays. If misconfigured, Hydrozoan can still commit in three message delays: Hydrozoan commits on whichever path fires first. We also present Optimal-Hydrozoan, a variant that tolerates one more fault on the fast path, the first construction to match the known lower bound. The safety and liveness of both protocols are machine-checked in Lean 4. Our geo-distributed evaluation shows that Hydrozoan matches Mysticeti's throughput, commits ~25% faster when the fast quorum fits fast regions, and falls back to three message delays when it does not or past p faults, where existing two-delay protocols stall.", "title": "Hydrozoan: Latency-Adaptive DAG Consensus under Mixed Byzantine and Crash Faults", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.25918" }, { "age_days": 5, "arxiv_id": "2609.28465", "authors": [ "Bin Dong", "Guoxiong Gao", "Bin Guo", "Zeming Sun", "Bin Wu", "Song-Yan Xie" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28465", "kind": "paper", "label": "adjacent", "matched_signals": [ "seed_author:Bin Dong", "seed_author:Guoxiong Gao" ], "published": "2026-09-23", "score": 2.9, "source": "arxiv-ai4math-core", "summary": "We give an algebraic proof in characteristic zero of the Miyaoka--Mori criterion: every point of a curve of negative canonical degree on a smooth projective variety lies on a rational curve. Our jet technique gives, in addition, an effective numerical decomposition of the original curve class. For each prescribed point, the decomposition contains a rational curve through that point, with a positive coefficient independent of the point and with anticanonical degree at most $\\dim X+1$. Together with BDPP cone duality, this recovers the projective uniruledness criterion over $\\mathbb C$. The main result of this paper was obtained using the Pharos system. A detailed report on the use of Pharos and on the Lean~4 formalization of the main arguments is given in the Appendix B, written by Bin Dong, Guoxiong Gao, Zeming Sun, and Bin Wu.", "title": "Constructing Rational Curves via Jets on Projective Varieties with Non-Nef Canonical Bundle", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28465" }, { "age_days": 4, "arxiv_id": "2609.30235", "authors": [ "Ziyu Neroli" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.30235", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-09-24", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "We study the moiré pattern formed by the intersection of a planar Sierpiński gasket and a copy rotated about its centre. At every resonant angle, we prove that the intersection is of finite type and compute its Hausdorff and Minkowski dimensions from an explicit finite matrix; for Lebesgue-almost every angle, we bound its upper Minkowski dimension by $\\overline{\\dim}_{\\mathrm B}(\\mathcal S_θ)\\le 2\\dim_{\\mathrm H}(S)-2$. Finally, we conjecture that both dimensions equal this bound at every non-resonant angle. Sections 2 and 3 are formalised in Lean.", "title": "Moiré Pattern of Rotated Sierpiński Gaskets", "updated": "2026-09-24", "url": "https://arxiv.org/abs/2609.30235" }, { "age_days": 5, "arxiv_id": "2609.28452", "authors": [ "Abhijeet Mulgund" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28452", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-09-23", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let $n\\ge2$, and let $X=(X_1,\\ldots,X_n)$ be a centered Gaussian vector with $\\mathrm{Var}(X_i)=1$ for every $i$. Let $Z_1,\\ldots,Z_n$ be independent standard Gaussians, and put $\\overline{Z}=(Z_1+\\cdots+Z_n)/n$. We prove $\\mathbb{P}\\{\\max_i X_i\\le t\\}\\ge\\mathbb{P}\\{\\sqrt{n/(n-1)}\\,\\max_i(Z_i-\\overline{Z})\\le t\\}$ for every $t\\in\\mathbb{R}$, and for each fixed $t>0$ equality holds only when $\\mathrm{Cov}(X_i,X_j)=-1/(n-1)$ for all $i\\ne j$. The right side is the distribution function of the maximum of the regular simplex vector. Equivalently, among all simplices containing a given centered ball, the regular simplex circumscribed about the ball has the least standard Gaussian measure, as conjectured by Balitskiy, Karasev, and Tsigler. In our preceding paper we proved this comparison after both maxima are smoothed by independent Gaussian noise of variance $1/(n-1)$, which suffices for the Weak Simplex Conjecture; here we remove the smoothing, which is what probabilities at a single threshold require. As an application we consider $n$ equally likely signals of equal energy in Gaussian noise, where the transmitter may also send nothing. At every positive false-alarm level, and for every law of a common nonnegative random amplitude not concentrated at zero, the regular simplex uniquely maximizes the average probability of correct identification whenever the signal dimension is at least $n-1$. A Lean formalization is available at https://github.com/abhmul/full-simplex-conjecture-lean.", "title": "Stochastic Domination of Gaussian Maxima by the Regular Simplex", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28452" }, { "age_days": 5, "arxiv_id": "2609.27384", "authors": [ "Jiarui Qi" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.27384", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-09-23", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "A latent severity has a bounded lower tail with density of shape alpha and scale L. It is observed only through a fixed Markov kernel K that is biased and non-additive. The relative conditional spread of K diverges at the endpoint. Our sample is i.i.d. from the marginal Q alone, with no anchoring covariate or instrument. We prove a dichotomy. The shape index alpha is identifiable: for every admissible choice of the class constants, any two observationally equivalent members of a lean class share alpha, determined by a near-endpoint expansion of Q. The rate, namely L and the fixed-scale exceedance p_tau, does not survive. There exist admissible shared class constants and two members of a smaller regularity class whose observed laws coincide exactly. Across the pair alpha agrees, whereas L and p_tau move. A degenerate Le Cam two-point bound excludes any uniformly consistent estimator of either, and pointwise consistency fails at one member. Only the rate needs an anchor. We conjecture that a known kernel family with known edge map identifies the rate fiber by fiber if and only if the family satisfies a fixed-scale injectivity clause, and we prove the sufficiency direction. In surrogate safety, uncalibrated conflict data give the shape of near-crash risk, not its absolute rate.", "title": "Shape without scale: an identifiability dichotomy for a bounded tail observed through a non-additive measurement kernel", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.27384" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:8dd5d448291e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: sharing violation in `Sym.dsimp` binder telescopes (#15389)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/8dd5d448291eb0ca0180c8ae1f9d248b2c8a2a7b" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:076b0b706600", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: canonicalize cast prefixes in the `Sym.Arith` normalizer (#15381)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/076b0b706600d1b93ee11be105227fc42cd9f501" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:16df84b16f8e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `grind` normalizer never pushed negation into implications and universal quantifiers (#15378)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/16df84b16f8e90e4f1a16b97d6d144aee48fdf22" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:fabf217ac972", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: decide trivially unsatisfiable and valid `Nat` relations in `Sym.simp` (#15380)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/fabf217ac9727b42d40765fbcdad555d35805a87" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:b45f25031de9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `lhsOnly` mode to the `Sym.Arith` relation normalizer (#15376)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/b45f25031de905288cc2ede6c5898cdc92b88517" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:327439dd9c56", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `[grind hom fallback]` rules, tried only when no other homomorphism rule applies (#15383)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/327439dd9c56437dc5ac52ec59436f69dc388e13" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:9f66b6cfc9c0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `Int` coefficient gcd, tightening, and divisibility in the `Sym.Arith` normalizer (#15382)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/9f66b6cfc9c057b20bc545f4541a423ab342b161" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:c46507e3ea83", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: explain the stop condition of the `[grind hom]` rewriter (#15379)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/c46507e3ea83834737508bc4828199be7720280a" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:56b48d816210", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/56b48d816210bc0c1b646fc76b83a43ce43d9607" }, { "age_days": 0, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover/lean4:86941be18ef3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: drop the E-matching copies of `[grind hom]` image rules (#15377)", "updated": "2026-09-28", "url": "https://github.com/leanprover/lean4/commit/86941be18ef336b765f61e4faca3207342f70b96" }, { "age_days": 0, "authors": [ "Artie Khovanov" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:baf070234674", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: style: ensure space after left-arrow in rewrites (#44250)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/baf070234674946cb9468893a2326a90565f8a8c" }, { "age_days": 0, "authors": [ "Rao Xiaojia" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4adb9e6ab129", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Tactic/Echelon): refactored denominator scaling and the computation model (#44152)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/4adb9e6ab12945a132cd9e5c08c43b790b52e215" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6e123c3c89b8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf(Analysis/Normed/Affine/Isometry): scope the V₄/P₄ and V₁'/P₁' variables to their users (#42246)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/6e123c3c89b870c447231b33425c2d17d07cb374" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a287fc1e40df", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix(ValidatePRTitle): allow file extensions like .yaml, .yml, .md in the scope (#40629)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/a287fc1e40df24937375aeb152b58e382fd86497" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a9fe97382342", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: use requiresModuleSystem in mathlib (#41950)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/a9fe97382342f5a05701a71601b7d22152babf46" }, { "age_days": 0, "authors": [ "Justus Springer" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c9c3e445b2e0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(AlgebraicCycle/Basic): improve stacks tags (#44277)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/c9c3e445b2e0c347ab2d464b00c7743791b124db" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:770f2050d68a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci: use github app (#44220)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/770f2050d68a7ce8a239d0315bb94735e2f5641a" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bfb5429837e6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci: run `cache` with the tools-branch toolchain (#44298)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/bfb5429837e60a01cf62ac6ee64bceead62182a5" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6810c450ad30", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci(cache-trust-dispatch): read inputs from `env:` (#44285)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/6810c450ad30f6c0031c8e985bd9444733b303e9" }, { "age_days": 0, "authors": [ "Bryan Gin-ge Chen" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:84cb78671991", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: ci(build_fork.yml): supersede fork CI runs by PR head sha instead of arrival order (#43955)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/84cb78671991033a817afc2e1e09670ba43a9ae0" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:de07b40da25a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: use `to_dual` for `DedekindCut` (#41548)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/de07b40da25a45a8f3da1ae7b227811fe982e753" }, { "age_days": 0, "authors": [ "David Kurniadi Angdinata" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:294c41f3048f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: rename `nnorm` to `nnnorm` in declaration names (#44290)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/294c41f3048f9eb890597905c4e78d97a46b633d" }, { "age_days": 0, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c0da404748dc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove unnecessary set_option lines (#44267)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/c0da404748dcfaa230e6ad5f6599771d01e7ae56" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0c51c7e4c52e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: remove some `backward.isDefEq.respectTransparency.instanceSearchTypes` (#44157)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/0c51c7e4c52edd30f422a10801a73437d6c92c38" }, { "age_days": 0, "authors": [ "Salvatore Mercuri" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1a547d8a48a8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: make `adicCompletion` and `Completion` print nicer (#41702)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/1a547d8a48a8fa7877d2decb69d7294723bb0187" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:87e20d7db57e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: golf proofs with `grw`/`gcongr`/`gconvert` (#44245)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/87e20d7db57e7260b31218f185fe64a4073f4605" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ec6a61cec0d8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: demote public imports that need no downstream imports (#43918)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/ec6a61cec0d8f9fda04453e9bb5761a79aa43a70" }, { "age_days": 0, "authors": [ "Jeremy Tan Jie Rui" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0989870e42ab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: delete deprecated modules to March 2026 (#44239)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/0989870e42ab2f567169a2f3742b1385cf016328" }, { "age_days": 0, "authors": [ "Marcelo Lynch" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cfe38bb6c1bf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(cache): simplify progress logging (#44164)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/cfe38bb6c1bf91ca08defc13444d0959dcc97522" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8438360df5a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Tactic/Translate): split long file (#44159)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/8438360df5a7c18eb70a7ad546fe052e62b888c4" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:eaadd7133b12", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RepresentationTheory): tidy markdown headers (#42795)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/eaadd7133b120aa8480697aa142b7cb73dab99e9" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c556e0d77deb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/Atoms): use `to_dual` (#43322)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/c556e0d77deb4e2de74629f110215292e6783cb7" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9d7edada3a20", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(LinearAlgebra): tidy markdown headers (#42748)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/9d7edada3a20b4c60dd2fe0c4752a14e7116bab3" }, { "age_days": 0, "authors": [ "Edison Xie" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6b7abb3c7686", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Preadditive/Biproducts): generalize universe and remove some set_options (#43473)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/6b7abb3c7686292736be2955bd3eb9ebf63b456a" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-28", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:913e6df6e5a5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-28", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Limits/Shapes/WidePullBacks): use `to_dual` (#42794)", "updated": "2026-09-28", "url": "https://github.com/leanprover-community/mathlib4/commit/913e6df6e5a54fc3bfc03c49a382f7dace967fc7" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:6d9787cda00f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: keep `Init` out of the `lake check` test projects (#15326)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/6d9787cda00f5ae1c0aeca349d3072716fa7524a" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:a23e3ce89704", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: test: enable the subtraction-with-borrow `grind` example (#15349)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/a23e3ce897045c8a86914dc0088692314be2df30" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:2830e0d9675e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: make USize folding more aggressive (#15277)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/2830e0d9675ea420b5ab9cb55a1e0a0eae3e39cc" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:aee6d42280de", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: normalize `-0 : Int` to `0` (#15363)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/aee6d42280defdf84888844e1ac16f3fc804ee7c" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:059fb8ae4da6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make `grind` understand the `Bool`-valued signed comparisons `BitVec.slt` and `BitVec.sle` (#15370)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/059fb8ae4da638fa0ecd806e9cbbdf1676c702ef" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:48bfd58f952d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: invalidate type class resolution cache entries when instances or unification hints change (#15354)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/48bfd58f952d46dbb554be55261e34f67596d48f" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:d0c575dc701e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: drop type class resolution cache entries recorded in rolled-back environment changes (#15355)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/d0c575dc701ef33a51d337b8166c336ef06656b6" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:e39e715e5018", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: `Sym.DSimp.zetaDelta` should unfold let-bound variables in head position (#15362)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/e39e715e5018b4b923ea9bf59271cdb45fc745bd" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:1e92f02237ce", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support the unsigned value of `sshiftRight` in `grind`'s bit-vector homomorphism rules (#15365)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/1e92f02237ce2f4910cfe5ed9c6b6f8dbf15575e" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:02c16a9da34a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support signed `~~~` in `grind`'s homomorphism rules (#15369)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/02c16a9da34a44ac6371c7e7d28d3799197bb103" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:47f4cf80fe10", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support signed `<<<` by a variable amount in `grind`'s bit-vector homomorphism rules (#15367)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/47f4cf80fe1088c42b53fd7b647d040a721321e2" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:32ac62681efe", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support `rotateLeft` and `rotateRight` in `grind`'s bit-vector homomorphism rules (#15364)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/32ac62681efed8ec10fd1eabea3f11c5a94762ee" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:0518648ae888", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support `BitVec.pow` in `grind`'s homomorphism rules (#15350)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/0518648ae8883a689da564b7bb0c9db7e4e706c7" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:1f38be1b144b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support `++` in `grind`'s bit-vector homomorphism rules (#15348)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/1f38be1b144b8f6e2a450d526c9c5617d81d425a" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:368dc838819f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: make `simp [f]` and `dsimp [f]` in `sym =>` mode behave like the default simplifier (#15366)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/368dc838819f6a8e6537e5c854312493dde9de62" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:b12696a4958f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: generation-tracked scoped environment extensions (#15353)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/b12696a4958f94c05429e36b3d8e4f53de350d42" }, { "age_days": 1, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:7cf0f85ef700", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: generation-tracked environment extensions (#15352)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/7cf0f85ef7002e62d3f5e652ab8fc9219e81575a" }, { "age_days": 1, "authors": [ "Leonardo de Moura" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover/lean4:ddbe8182954b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `grind_norm` for comparing the `simp`- and `Sym.simp`-based `grind` normalizers (#15375)", "updated": "2026-09-27", "url": "https://github.com/leanprover/lean4/commit/ddbe8182954ba0b92011f28c28e5b89f25404790" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c3f56bbeb998", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(undergrad-yaml): `Holder` -> `Hölder` (#44233)", "updated": "2026-09-27", "url": "https://github.com/leanprover-community/mathlib4/commit/c3f56bbeb99803b7af1ede060190ba65c7cc5e8f" }, { "age_days": 1, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3cb72cfd416d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(scripts): update nolints.json (#44238)", "updated": "2026-09-27", "url": "https://github.com/leanprover-community/mathlib4/commit/3cb72cfd416d1b5ec4b930d67648ef036a5df24f" }, { "age_days": 1, "authors": [ "TJHeeringa" ], "content_date": "2026-09-27", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b63f6e8a68d2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-27", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Analysis/Calculus): rename ApproximatesLinearOn.(anti)lipschitz (#44231)", "updated": "2026-09-27", "url": "https://github.com/leanprover-community/mathlib4/commit/b63f6e8a68d220e3b3bc4f3792bb53650d375f24" }, { "age_days": 2, "authors": [ "Xavier Roblot" ], "content_date": "2026-09-26", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8accc04827c3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-26", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal): the `⊥` and `⊤` cases of the pointwise action on ideals (#44070)", "updated": "2026-09-26", "url": "https://github.com/leanprover-community/mathlib4/commit/8accc04827c389e678c3ef83e623b402e7480394" }, { "age_days": 2, "authors": [ "David Kurniadi Angdinata" ], "content_date": "2026-09-26", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:516d31250e96", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-26", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: fix misspellings in declaration names (#44049)", "updated": "2026-09-26", "url": "https://github.com/leanprover-community/mathlib4/commit/516d31250e96c4e8e76888c3d8e2e43a9642b9ee" }, { "age_days": 3, "arxiv_id": "2609.30817", "authors": [ "Rahul Chandelkar", "Samrath Chadha" ], "content_date": "2026-09-25", "freshness": "fresh", "id": "arxiv:2609.30817", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Every finite nonempty incomplete uniquely decipherable code with maximum word length $k$ has an uncompletable word of length at most $4k^2-3k$. The bound is independent of the number of codewords and their total length. Deleting a complete codeword cycle gives a finite path-counting identity; Kraft equality then supplies a short word of deficient compressed mass. Cyclic averaging and padding turn it into an uncompletable word. Conditional expectation makes the construction polynomial-time and also decides completeness. First-return words extend the bound to mortal families of nonnegative integer $n\\times n$ matrices with joint spectral radius at most one, provided every strongly connected component has a vertex meeting every cycle. Such a family has a zero product of length at most $4n^2-3n$. A binary partial deterministic family with $2k-1$ states has shortest zero product of length $k^2+k-1$, establishing the optimal quadratic order. The bounds and the explicit-code algorithm, including its polynomial work bound, are proved in Lean.", "title": "Quadratic bounds for uncompletable words and matrix mortality", "updated": "2026-09-25", "url": "https://arxiv.org/abs/2609.30817" }, { "age_days": 3, "arxiv_id": "2609.31246", "authors": [ "Aryak Sen", "Pratik Karmakar", "Silviu Maniu", "Angelo Saadeh", "Pierre Senellart" ], "content_date": "2026-09-25", "freshness": "fresh", "id": "arxiv:2609.31246", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The semiring framework and its extensions form the basis of a rich collection of theoretical results and implementations for provenance tracking of database queries. Many real-world queries use aggregation and conditions on the aggregate values. Support for such queries has been proposed by introducing semimodule elements as aggregate values and formal comparisons between aggregate values as tuple annotations, which takes the approach outside the standard semiring framework. In this work, we show how to introduce a semantics for the provenance of such queries in arbitrary commutative semirings with monus (or m-semirings), without the need for additional operators. This semantics is shown to agree with the standard provenance of the aggregation-free self-join rewriting of HAVING COUNT(*) queries in semirings that are absorptive and where times distributes over monus. We derive algorithms for this semantics and implement them within the ProvSQL system, with viable performance on a real-world dataset for probabilistic query evaluation.", "title": "Provenance of HAVING Queries in Semirings with Monus", "updated": "2026-09-25", "url": "https://arxiv.org/abs/2609.31246" }, { "age_days": 3, "arxiv_id": "2609.31334", "authors": [ "Lars Becker", "María Inés de Frutos-Fernández", "Leo Diedering", "Floris van Doorn", "Sébastien Gouëzel", "Evgenia Karunus", "Edward van de Meent", "Pietro Monticone", "Jasper Mulder-Sohn", "Jim Portegies", "Joris Roos", "Michael Rothgang", "James Sundstrom", "Jeremy Tan" ], "content_date": "2026-09-25", "freshness": "fresh", "id": "arxiv:2609.31334", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-25", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We present the formalization of Carleson's theorem in the proof assistant Lean. This paper describes the mathematical content, organization of the project, the blueprint, and the main design decisions behind the formalization. It is the result of a large collaborative effort, written and developed in public.", "title": "Formalizing Carleson's Theorem in Lean", "updated": "2026-09-25", "url": "https://arxiv.org/abs/2609.31334" }, { "age_days": 4, "arxiv_id": "2609.30588", "authors": [ "Shirley Anugrah Hayati", "Moyan Zhou", "Patricia Anugrah Setiani", "Ruizi Wang", "Joseph Chee Chang", "Dongyeop Kang" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.30588", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-24", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "As researchers tackle interdisciplinary problems, they face the need to deepen expertise in primary areas while rapidly acquiring knowledge in secondary domains. Generative AI (GenAI) is increasingly positioned to meet this need, from general-purpose chat assistants to Deep Research tools marketed as autonomous research agents. Prior work has examined how researchers use GenAI to support single-discipline or general research tasks. However, we know little about the goals and GenAI practices in interdisciplinary research. We conducted a longitudinal study and semi-structured interviews with 15 interdisciplinary researchers to examine how interdisciplinary researchers actually orchestrate GenAI. Findings show that researchers leaned on GenAI to fill knowledge gaps while maintaining epistemic agency for novelty discovery. We also uncovered an expertise paradox: GenAI outputs were hardest to verify when most needed. Our empirical insights motivate GenAI designs that calibrate verification to researchers' expertise, nudge toward cross-domain synthesis, and adapt prompting and outputs to disciplinary conventions.", "title": "Orchestrating GenAI for Interdisciplinary Research", "updated": "2026-09-24", "url": "https://arxiv.org/abs/2609.30588" }, { "age_days": 4, "arxiv_id": "2609.29201", "authors": [ "Filippo Fruzza", "Sofiane Al Kassar", "Rachele Lamioni", "Chiara Galletti", "Antonio Attili" ], "content_date": "2026-09-24", "freshness": "fresh", "id": "arxiv:2609.29201", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-24", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Lean premixed hydrogen flames are highly susceptible to thermodiffusive instabilities, which generate complex cellular structures and enhance propagation speed. In practical combustors, incomplete premixing introduces spatial variations in local equivalence ratio upstream of the flame. This work investigates how the length scale of inlet fuel stratification affects the structure and propagation of lean laminar hydrogen flames using direct numerical simulations with detailed chemistry and transport. Controlled sinusoidal perturbations of fuel mass fraction are imposed at moderate amplitude, leading to local equivalence-ratio variations of $φ\\simeq 0.45-0.55$ in the flame region. Seven stratification wavelengths, from $λ= 15.4δ_f$ to $133.3δ_f$, are examined at constant density-weighted global equivalence ratio. Additional unity-Lewis-number simulations separate geometrical effects from differential transport. The results reveal a strongly scale-dependent response. In unity-Lewis-number flames, stratification organises the front at the imposed wavelength and monotonically increases flame surface area and propagation speed with wavelength. With differential diffusion, large wavelengths ($λ\\gtrsim 40δ_f$) produce a similar large-scale organisation, with rich channels forming forward bulges and lean channels recessed cusps, while thermodiffusive cells remain superimposed. This increases flame surface area and global propagation speed. At smaller wavelengths ($λ\\lesssim 29δ_f$), composition gradients interfere with intrinsic thermodiffusive cellular dynamics, reducing flame surface area and propagation speed relative to the perfectly premixed reference. These findings identify stratification length scale as a key parameter controlling the interaction between moderate mixture inhomogeneity and thermodiffusive instability in lean hydrogen flames.", "title": "Effect of fuel stratification length scale on thermodiffusively unstable lean hydrogen flames", "updated": "2026-09-25", "url": "https://arxiv.org/abs/2609.29201" }, { "age_days": 5, "arxiv_id": "2609.28591", "authors": [ "Alexander Gamburd" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.28591", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-23", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "On 8 September 2026 OpenAI announced a proof of finite-time blowup for the three-dimensional Navier-Stokes equations with smooth data and forcing: 166 pages produced in 88 hours by ten thousand agents, certified by 616,000 lines of Lean, and read in full, at the moment of this writing (20 September 2026), by no human being. This essay asks what such an artifact -- text, certificate and announcement -- is, and what follows from accepting it as a proof. Mathematics was the Enlightenment's existence proof of autonomous reason: for three centuries every certified theorem could be understood by anyone who followed its demonstration, and the distance between the two was zero by construction. A certified proof no one can follow reopens that distance, and a community that accepts it adopts, without a vote, the constitution Hobbes drafted for the Leviathan, in which authority and not truth makes the law. The essay distinguishes the demonstrated from the revealed (certified); names, in Panofsky's terms, the coming age a Middle Ages in reverse and its authority a subhuman superintelligence; and locates the turning point not in what the machine produces but in what we accept. Since acceptance is the one sovereign sanction the companies cannot manufacture, it proposes a covenant in place of either boycott or capitulation: the community's cooperation given to that producer which strictly observes its practices of legibility, disclosure and responsibility, withheld from any that does not, and the covenant kept plural, with the history of the Indigenous nations among rival empires as its guide. The Sirens of the title promise knowledge, not understanding. Daemmerung is the light at both ends of the day, and whether this Aufklaerungsdaemmerung is a dusk or a dawn depends on what is done at the moment of acceptance, which is not yet past.", "title": "The Siren Call of Silicon Leviathan: Reflections on blowup and Aufklärungsdämmerung", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.28591" }, { "age_days": 5, "arxiv_id": "2609.27647", "authors": [ "Scott Armstrong", "Tuomo Kuusi", "Amélie Loher" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.27647", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-23", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove an upper bound on the homogenization length scale which is a fixed power of the coarse ellipticity ratio for coefficient fields that satisfy a finite range of dependence assumption.", "title": "Homogenization at a polynomial scale in high contrast", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.27647" }, { "age_days": 5, "arxiv_id": "2609.27638", "authors": [ "Hiroyuki Nakahata" ], "content_date": "2026-09-23", "freshness": "fresh", "id": "arxiv:2609.27638", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-23", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "AI-generated software changes make it increasingly important to determine what a change preserves, where local consistency fails to extend globally, and which alternatives remain. We develop the foundations of Algebraic Architecture Theory (AAT) from Atoms, typed primitive facts, and Laws, equations that objects must satisfy. A reading specifies what counts as structure and which operations and laws to preserve. The main reconstruction theorem identifies the category of full geometries and all their structure-preserving morphisms with an independently defined category of local models, up to equivalence. Objects are recovered up to isomorphism and morphisms between fixed endpoints uniquely. The theory addresses gluing, diagnosis, transport, classification of changes, and reconstruction. From finite Atom families we construct cores closed under operations and geometries with sites and coefficients. We give conditions under which a Cech obstruction detects the existence of a global state and, through comparison with repair semantics, a global repair. We compare diagnoses and give a finite criterion for uniform invariance given computable finite data. Transport along exact changes has a universal property and commutes with base change on exact pointed pullback squares. Comparisons of routes generated from the same square, finite comparison diagram, and geometry factor into an invertible comparison and an idempotent normalization. We characterize when observations determine comparison preservation and classify compatible lifts. Encodings of lens and protocol semantics preserve and reflect laws and recover semantics-preserving morphisms. Applications classify and count operation-preserving changes and extend morphisms uniquely from finite tables. Corresponding Lean declarations are listed in the appendix.", "title": "Foundations of Algebraic Architecture Theory: A Rising Sea of Geometry, Transport, Comparison, and Reconstruction", "updated": "2026-09-23", "url": "https://arxiv.org/abs/2609.27638" }, { "age_days": 6, "arxiv_id": "2609.25933", "authors": [ "Yuwei Chuai", "Thomas Renault", "David Rand", "Mohsen Mosleh" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.25933", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Concerns about inauthentic accounts, including foreign actors posing as domestic voices, are central to debates about online discourse. Yet, little is known about accounts with inaccurate location claims and how they behave when discrepancies between their claimed and actual locations become publicly visible. In November 2025, X introduced an \"About this account\" feature that discloses each account's platform-inferred location of operation. We leverage this intervention in a large-scale quasi-experimental study of 8,200 politically engaged accounts claiming a U.S. location, comparing accounts whose disclosed locations matched versus contradicted their claims across 1.3 million posts and 3.6 million replies over 21 weeks. Before disclosure, location-mismatched accounts posted more misleading, scam-related, and cryptocurrency-related content, but showed no distinctive partisan leaning. Difference-in-differences estimates show that disclosure reduced the posting activity of location-mismatched accounts by 13.1% with the largest declines among accounts revealed to be in Africa (29.2%) and Asia (24.4%), and among accounts with VPN flags, username changes, or scam- and crypto-heavy content. Additionally, the decline in their replies was concentrated in interactions with U.S.-based recipients (10.3%), whereas replies to non-U.S.-based recipients showed no statistically significant change. Conversely, there was no significant change in average audience engagement with their posts. Location transparency thus works primarily by inducing restraint among the disclosed accounts rather than by shifting audience behaviour, and the accounts it constrains look at least as much like cross-border fraud as foreign political influence.", "title": "Location transparency reduces activity by accounts misrepresenting their location on X", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.25933" }, { "age_days": 6, "arxiv_id": "2609.26776", "authors": [ "Jaime Enrique Lincovil Curivil", "Alexandre Galvão Patriota" ], "content_date": "2026-09-22", "freshness": "fresh", "id": "arxiv:2609.26776", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-22", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Birnbaum's theorem states that the sufficiency and conditionality principles jointly imply, and are implied by, the likelihood principle. To enable formal certification of the results in Lean, we make the conditionality relation explicit through a finite-sample formulation based on \\cite{Evans2013}. We reformulate the theorem as a statement about classes of statistical procedures that preserve statistical relations, and show that the proof reduces to the propagation of evidential equality along chains of conditionality-related inference bases (experiment--observation pairs). The main results are illustrated by Venn diagrams, and a worked finite example exhibits two pairs of inference bases: one related by conditionality but not by sufficiency, and the other related by sufficiency but not by conditionality. For finite parameter spaces with at least two points, the class of likelihood-invariant procedures with codomain $[0,1]$ is strictly contained in the class of sufficiency-invariant procedures.", "title": "Birnbaum's principles in Venn diagrams: Extended version with Lean verification", "updated": "2026-09-22", "url": "https://arxiv.org/abs/2609.26776" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }