{ "counts": { "adjacent": 15, "core": 5, "errors": 0, "negative": 68, "total": 88 }, "date": "2026-09-14", "errors": [], "fresh_content_days": 21, "generated_at": "2026-09-14T19:54:44Z", "items": [ { "age_days": 4, "arxiv_id": "2609.11319", "authors": [ "Joshua Ong Jun Leang", "Haonan Li", "Zheng Zhao", "Xinyi Shang", "Wenda Li", "Zhengzhong Liu", "Erix Xing", "Shay Cohen", "Eleonora Giunchiglia" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.11319", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents", "seed_author:Wenda Li", "verifier_guided_reasoning" ], "published": "2026-09-10", "score": 14.9, "source": "arxiv-ai4math-core", "summary": "Most of mathematical knowledge has been communicated through so-called informal use of mathematics and natural language. With large language models (LLMs) being highly adept in using natural language, they achieve strong performance, yet not perfect, in informal mathematical reasoning. Restraining LLMs to informal reasoning misses out on the opportunity to use the discrete verification abilities that machines offer through machine-checkable proofs. In this paper, we bridge the gap between informal and formal reasoning by integrating Lean signals into the informal reasoning process. We introduce Magenta, a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof. A statement judge verifies whether the formalisation preserves the original problem, while an error-attribution judge routes failed attempts either to mathematical re-derivation or local Lean repair. Magenta achieves 100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026. When paired with the open-weight K2-Horizon-7B reasoner, it solves all six IMO 2026 problems. Our analysis shows that statement adjudication is essential for preventing false certificates and that feedback-guided correction outperforms independent resampling on difficult problems.", "title": "Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.11319" }, { "age_days": 6, "arxiv_id": "2609.09264", "authors": [ "Idan Davidovich", "Debargha Ganguly", "Vikash Singh", "Vipin Chaudhary" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.09264", "kind": "paper", "label": "core", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 7.9, "source": "arxiv-ai4math-core", "summary": "Leading benchmarks for formal theorem proving with large language models are small collections drawn from competition math, such as the IMO and Putnam, that poorly represent field-specific applications. We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. Addressing a field underrepresented in Mathlib, it covers finite and countable Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers.", "title": "StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.09264" }, { "age_days": 4, "arxiv_id": "2609.12039", "authors": [ "Alexander Krentsel", "Shubham Agarwal", "Mert Cemri", "Shu Liu", "Sidharth Sankhe", "Ziming Mao", "Matei Zaharia", "Ion Stoica" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.12039", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-09-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Software development follows an implementation-verification loop in which developers or agents iteratively revise an implementation until an evaluator, such as a test suite, accepts it. The evaluator checks the implementation against a set of requirements under a model of the deployment environment. Yet even a formal proof that the implementation satisfies the requirements under the model cannot guarantee acceptable behavior after deployment. Requirements only approximate stakeholder intent, and the model only approximates the real deployment environment. We call these together - requirement gap and model gap - the two-gap framework, which unifies the main failure modes of agentic software engineer-ing: reward hacking exploits omissions in the requirements or model, while hallucination widens the gaps by fabricating requirements or environment assumptions. Because neither gap can generally be certified closed in an open, changing world, the goal shifts from closing them to continuously narrowing them. We therefore propose an assurance-revision loop that uses deployment evidence to revise the requirements, model, or evaluator when stakeholders reject the resulting behavior. We then cast assured agentic development as a resource-allocation problem over human judgment, agent capability, and compute. The two principal bottlenecks mirror the two gaps: human judgment for the requirement gap and faithful, costly evaluation for the model gap. Reality remains the final verifier: acceptable behavior under actual deployment conditions is the ultimate test, while predeployment evaluations remain proxies for it.", "title": "Reality Is the Final Verifier: On Two Key Gaps in Agentic Software Engineering", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.12039" }, { "age_days": 4, "arxiv_id": "2609.11085", "authors": [ "Vikash Singh", "Debargha Ganguly", "Aman Goel", "Ali Torkamani", "Xiaoxue Han", "Joseph Lilien", "Ferhat Erata", "Vipin Chaudhary" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.11085", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "verifier_guided_reasoning" ], "published": "2026-09-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Neurosymbolic systems rely on mathematical solvers to guarantee reasoning correctness, yet solvers are fundamentally blind to whether a formal translation maintains strict reference-equivalence to a designated formalization. We formalize this vulnerability as Verdict-Preserving-Unfaithfulness (VPU): a failure mode where an incorrect encoding executes successfully and matches the expected verdict. We theoretically prove that structural, verdict-only verification heuristics are mathematically bounded to chance-level detection on these deceptively valid traces. To resolve this, we introduce Generative Verification (GenV), which distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score by repurposing the language model's native vocabulary space. Mechanistic analysis via decision-projected logit lenses and sparse autoencoders shows this generative readout natively extracts precise spatial error coordinates without explicit localization training. Empirically, our oracle-mined verifier (GenV+HN) achieves 0.961 AUROC in reference-equivalence verification, generalizes zero-shot across unseen translators and divergent formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation.", "title": "Beyond Solver Verdicts: Generative Reward Models for Autoformalization", "updated": "2026-09-11", "url": "https://arxiv.org/abs/2609.11085" }, { "age_days": 4, "arxiv_id": "2609.11174", "authors": [ "Yukiko Kato" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.11174", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-09-10", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "This note consolidates the core of the Quasi-Closed World Graph Model for Conflict Resolution (QCW-GMCR), which extends the standard Graph Model for Conflict Resolution with Belnap's four-valued logic to represent option-level epistemic ambiguity, and pairs the framework with a machine-checked Lean 4 formalization. QCW-GMCR combines: (1) FOUR-valued option assignments with compositional propagation to state-level feasibility; (2) graded reachability (definite, credible, possible) based on an FDE-inspired transition-warrant semantics, with definite reachability related to FDE consequence in the Boolean fragment; (3) axiomatized deterministic reductions from four-valued assessments to binary decisions, including four canonical operators reflecting distinct risk attitudes; and (4) catastrophe-avoiding equilibrium concepts with a quasi-closed-world safety invariant. A four-valued hypergame extension captures heterogeneous subjective assessments across decision makers. We state the core definitions and results and report the parts verified in Lean 4 with mathlib, including the classical GMCR stability hierarchy, algebraic and compositional properties of FOUR-valued conjunction, properties of the canonical reductions, and the graded reachability hierarchy. The formalization also helped identify and correct earlier claims, including a knowledge-monotonicity axiom replaced by truth monotonicity. This preprint provides a stable, citable record of the framework and its current formal verification status.", "title": "A Four-Valued Graph Model for Conflict Resolution: Core Framework and a Machine-Checked Formalization in Lean 4", "updated": "2026-09-11", "url": "https://arxiv.org/abs/2609.11174" }, { "age_days": 6, "arxiv_id": "2609.08921", "authors": [ "Antonio Acuaviva" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.08921", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We give a negative solution to the complemented subspace problem for Banach spaces with unconditional bases over both the real and complex fields. For every $ρ>0$, we construct a projection $P_ρ$ of norm less than $1+ρ$ on a separable superreflexive space \\begin{equation*} X_ρ=\\left(\\bigoplus_{j=1}^{\\infty}\\ell_{p_j}^{N_j}\\right)_2, \\qquad p_j\\downarrow2, \\end{equation*} such that $Z_ρ=P_ρ(X_ρ)$ and its dual $Z_ρ^*$ have Schauder bases but admit no unconditional bases. Over the real field, both spaces have Gordon--Lewis local unconditional structure (GL-lust) but fail Dubinsky--Pełczyński--Rosenthal local unconditional structure (DPR-lust), disproving a conjecture of Figiel, Johnson and Tzafriri. In particular, neither is isomorphic to a Banach lattice, giving a negative solution to the separable Banach-lattice complemented subspace problem. A modification of the construction also shows that the class of separable real Banach lattices is not primary. A Lean 4 formalisation of the main results accompanies the paper.", "title": "A negative solution to the complemented subspace problem for Banach spaces with unconditional bases", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.08921" }, { "age_days": 4, "arxiv_id": "2609.12266", "authors": [ "Behnam Hashemi", "Yuji Nakatsukasa" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.12266", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "It is known that the Sherman--Morrison (SM) formula is not numerically stable. In recent work, we introduced SMIR, an algorithm that incorporates iterative refinement to enhance the SM backward error. In this paper we take a different route: adapting an algorithm of Govaerts, originally designed for general bordered linear systems, we develop a modified Sherman--Morrison (MSM) method whose built-in self-correction makes it surprisingly resilient. Whereas standard SM requires the solution of two $n\\times n$ linear systems, MSM requires three; by contrast, SMIR requires $2+k$ solves, where $k$ is the number of IR steps and can be substantially larger than three, when IR converges slowly. We then derive backward and forward error bounds for both SM and MSM. The SM backward error bound established here is stronger than the one proved in [Hashemi \\& Nakatsukasa 2026]: it accounts for every rounding error and holds with no conditions on the size of the capacitance. From these bounds we extract growth factors that are cheap to compute a posteriori and can be used to certify the backward and forward stability of SM and MSM on a given problem. In our experiments, MSM consistently produces backward stable solutions, and is therefore observed to be forward stable as well. A formal proof of the stability --- or instability --- of MSM remains an open problem.", "title": "Error bounds for the Sherman-Morrison formula and its modification with improved stability", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.12266" }, { "age_days": 4, "arxiv_id": "2609.12106", "authors": [ "Danny Hucke" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.12106", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-10", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove a lower bound of Ω(log n/ log log n) on the approximation ratio of the global grammar-based compression algorithm Greedy. To our knowledge, the previously best lower bound was a constant, and the existence of a nonconstant lower bound had remained open for more than twenty years. Our bound holds on an infinite family of words of length n, over alphabets of growing size, for every execution using left-to-right occurrence replacement and arbitrary tie-breaking. The lower bound is also formally verified in Lean 4.", "title": "A Non-constant Lower Bound for Grammar-Based Compression with Greedy", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.12106" }, { "age_days": 5, "arxiv_id": "2609.10520", "authors": [ "Chengkai Zhu", "Xin Wang" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.10520", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.", "title": "Private communication via zero-private-capacity quantum channels", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.10520" }, { "age_days": 5, "arxiv_id": "2609.10793", "authors": [ "Yuri N. Berdinsky" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.10793", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We develop a machine-checked construction of non-Gaussian functional integrals using the Henstock--Kurzweil gauge integral and Chernoff product approximations. The central object is a finite family of bosonic modes with action S(phi) = (1/2) phi^T A phi + lambda * sum_i phi_i^4, where A is positive definite. We prove that the one-mode integral I(omega, j, lambda) is finite, strictly positive, monotone and infinitely differentiable in the coupling lambda on [0, infinity). Its derivatives are given by convergent integrals of phi^{4k} with the same weight, not by the divergent perturbative series. The M-mode influence functional factorises into one-mode integrals and is bounded by its Gaussian value. A Chernoff / Lie--Trotter splitting handles the non-commutativity of the free and non-Gaussian generators. All statements are formalised in Lean 4 with Mathlib; the accompanying file HkNonGaussian.lean is free of sorry and uses only the standard axioms propext, Classical.choice, Quot.sound. Four illustrative applications are worked out at the level of explicit formulas: the Duffing oscillator, local volatility (CEV) in finance, Wilson--Cowan neural fields, and non-Gaussian quantum reservoirs. The construction is completely direct and does not use Wick rotation, Wiener measure, zeta-regularisation or analytic continuation back from imaginary time.", "title": "Henstock--Kurzweil Gauge Integral in the Non--Gaussian Regime: A Machine--Verified Construction", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.10793" }, { "age_days": 5, "arxiv_id": "2609.10281", "authors": [ "Achyuth Jayadevan" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.10281", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For an ordinary finite presentation $P=\\langle x_1,\\ldots,x_n\\mid R\\rangle$, put $G(P)=F_n/\\langle\\langle R\\rangle\\rangle$. We construct a primitive-recursive predicate $V$ with $G(P)''=1 \\Longleftrightarrow \\exists c\\in\\mathbb{N}: V(P,c)=1$. Thus finite presentations of metabelian groups are recursively enumerable, answering Kourovka Problem 17.124. An effective form of the Bieri-Strebel covering construction, using signed Laurent relations and rational separation, gives a family of finitely presented metabelian groups cofinal under epimorphisms. Products of conjugates of defining relators witness these epimorphisms. The construction and enumeration theorem are formalized in Lean 4.", "title": "Finite presentations of metabelian groups: effective enumeration via Laurent relations", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.10281" }, { "age_days": 5, "arxiv_id": "2609.09938", "authors": [ "Hao Shen", "Jiaqi Wang", "Lihong Zhi" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.09938", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-09", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that every trace-zero matrix $A\\in M_n(\\mathbb{C})$ admits a representation $A=BC-CB$ with $B,C\\in M_n(\\mathbb{C})$ and $\\lVert B\\rVert\\lVert C\\rVert\\le K\\lVert A\\rVert$, where $K$ is an absolute constant independent of $n$, and $\\lVert\\cdot\\rVert$ denotes the operator norm. For a fixed $t>0$, the proof splits according to whether $\\lVert\\operatorname{Re}(e^{\\mathrm{i}θ}A)\\rVert_1\\ge tn\\lVert A\\rVert$ holds for all $θ\\in\\mathbb{R}$, where $\\lVert\\cdot\\rVert_1$ denotes the trace norm. When this lower bound holds, we construct a commutator representation directly. Otherwise, the vector-selection theorem of Marcus, Spielman, and Srivastava yields smaller trace-zero compressions whose norms are small enough for the induction to close. We also construct an explicit family of zero-diagonal Hermitian unitaries that forces a lower bound of order $\\sqrt{\\log n}$ for $\\lVert B\\rVert\\lVert C\\rVert$ when either factor is required to be diagonal in the prescribed basis. The same family admits $\\varepsilon$-pavings with fewer than $2\\varepsilon^{-2}$ blocks and representations by two normal factors with optimal norm product $1/2$. This establishes a distinction between unrestricted commutator bounds and bounds under a prescribed diagonal restriction. The main results and their essential inputs are formalized in Lean 4 using Mathlib. The development also includes a formal derivation of the Kadison-Singer state-extension theorem from the same vector-selection theorem.", "title": "A Dimension-Independent Commutator Bound", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.09938" }, { "age_days": 6, "arxiv_id": "2609.08431", "authors": [ "Barinder S. Banwait" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.08431", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For an elliptic curve $E/\\mathbb{Q}$ of rank two with complex multiplication, Coates, Liang and Sujatha gave a criterion for the vanishing of $Sha(E/\\mathbb{Q})[p^\\infty]$ at a good ordinary prime $p$ and applied it to five such curves for $p < 30{,}000$. We prove a cyclotomic criterion of the same kind: outside an explicit set of primes, the normalised second Taylor coefficient of the Mazur-Tate-Teitelbaum $p$-adic $L$-function at the central point is a $p$-adic unit if and only if the cyclotomic $p$-adic regulator is a unit and $Sha(E/\\mathbb{Q})[p^\\infty] = 0$, and, by the theory of Bannai and Kobayashi, if and only if an explicit combination of three critical Hecke $L$-values of weight $2p - 1$ has valuation exactly two. Following the algorithm of Stein and Wuthrich, we compute the regulator for the same five curves at every good ordinary prime below $30{,}000$: it is a unit at all but three of the $8{,}050$ primes outside the excluded set. The one case that the criterion of Coates, Liang and Sujatha left open, $p = 577$ for $y^2 = x^3 + 34x$, is settled by the new criterion. A Lean 4 formalisation of the first equivalence, assuming stated results from the literature, is provided.", "title": "Second derivatives of $p$-adic $L$-functions and the Shafarevich--Tate group of rank-two CM elliptic curves", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.08431" }, { "age_days": 6, "arxiv_id": "2609.08319", "authors": [ "Kay Akiyama" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.08319", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that no strongly regular graph with parameters $(266, 45, 0, 9)$ exists. The proof is formalized in Lean 4 and Mathlib without external infeasibility certificates or assumed classification theorems. A hypothetical graph gives a rank-$12$ integral Gram lattice with an integral centroid. A Lorentzian change of form, a marked $D_7$ gluing, and an explicit rank-six complement produce a positive-definite even unimodular lattice of rank $24$, together with the original indexed family of $220$ vectors. Harmonic theta identities and a root-isolation inequality force the root system $A_{11} \\perp D_7 \\perp E_6$. First and second moments then exclude the possible complements: the final case reduces to an impossible binary projection identity $4x + 4y - 2z = 50$. A type-$A$ subcase is closed by a separate classification-free proof of the known nonexistence of a quasi-symmetric $2$-$(56, 12, 9)$ design with intersections $0, 3$. That argument constructs a Krein graph and forces a Steiner $3$-$(12, 4, 1)$ design, contradicting its replication equation. The formal theorem depends only on the three standard Lean axioms and has also been checked independently with nanoda. The archived formalization is release v2.0.0.", "title": "Nonexistence of a Strongly Regular Graph with Parameters (266,45,0,9): A Certificate-Free Lean Proof", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.08319" }, { "age_days": 6, "arxiv_id": "2609.08160", "authors": [ "Andreas Andreakis" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.08160", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Change-data capture (CDC) feeds downstream systems like caches, search indexes, and data warehouses from a database's log of committed row changes. When bootstrapping, adding a table, or repairing downstream data, a pipeline must also copy existing rows. Merging this copy with the active log introduces the copy-to-log handoff problem. Changes must not fall through a gap, and older copied state must not overwrite a newer logged update or resurrect a deleted row. DBLog, developed at Netflix, addressed this problem by reading tables in chunks and interleaving those reads with the live log. Watermarks identify the changes that overlap each read, and the log wins when a copied row is stale. Debezium and Flink CDC have since adapted this design. Earlier work proved that applying the original algorithm's copied rows and logged changes in their emitted order reconstructs the source's rows, including the effect of every logged insert, update, and delete processed. Generalized DBLog asks when the same result holds for variants of that design. We state the conditions the source and capture implementation must satisfy. Once copying and reconciliation are complete, we prove that the result holds across all selected tables and key ranges even when their rows were read at different times. A single database snapshot is not required for the copy. Further logged changes advance the reconstructed state one event at a time. We establish these guarantees for classic watermarking, Debezium's signal-table and read-only modes, Flink CDC's parallel chunks, reads and dumps tied to exact log positions, and engine-consistent backups whose log position lies within known bounds. The complete theory is machine-checked in Isabelle/HOL, its core independently verified in Lean 4, and the protocols are also examined by bounded model checking in TLA+.", "title": "Generalized DBLog: A Verified Contract for Interleaving Database Rows with a Change Log", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.08160" }, { "age_days": 6, "arxiv_id": "2609.08528", "authors": [ "Mario Raso", "Daniele Venturi" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.08528", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-08", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For each integer $n\\geq 1$, let $N(n)$ denote the number of distinct subsets of $\\{2,\\ldots,n+1\\}$ obtained by choosing one forbidden residue class modulo each integer from $2$ to $n$; this is OEIS sequence A396595 (https://oeis.org/A396595). Equivalently, $N(n)$ is the initial-restriction complexity of the family of global residue-profile survivor sequences. We derive a closed formula, depending on the parity of $n$, for the number of locally distinct residue profiles, and an exact inclusion--exclusion formula for profiles realizing a prescribed survivor set. We prove that $\\log N(n)$ has order $n/\\log n$, with any possible leading constant between $\\log 2$ and $2\\log 2$. For prime traces, the logarithm of their number is asymptotic to $(\\log 2)n/\\log n$. Our main comparison theorem shows that $N(n)$ is exponentially equivalent to the block complexity of prime-admissible subsets of an interval of length $n$. The combinatorial component of the private composite coordinates argument used in the comparison theorem is formalized in Lean 4/Mathlib. We also establish an exact structural recurrence, characterize extendibility by a residue-class covering criterion, and give a dynamic enumeration algorithm. As further illustrations of the model, we exhibit purely periodic global profiles generating prime-valued survivor sequences for which we have not identified corresponding OEIS entries.", "title": "Counting Survivor Sets: Exponential Equivalence with Prime-Admissible Sets", "updated": "2026-09-08", "url": "https://arxiv.org/abs/2609.08528" }, { "age_days": 7, "arxiv_id": "2609.08007", "authors": [ "Jeffrey S. Baggett" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "arxiv:2609.08007", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We prove that the realization graph of every graphical degree sequence is maximally Hamiltonian: it is Hamilton-laceable when bipartite on more than one vertex, and Hamilton-connected otherwise. This answers Problem P59 of Mütze's survey of combinatorial Gray codes, and the Hamiltonicity question recorded as open by Barrus, in the strongest form either admits. The argument is an induction on the number of ground vertices, cutting the realization graph at a single ground vertex into fibers and the quotient they lie over. The proof is formalized in Lean 4 and checked by its kernel, with seven results cited from the literature and nothing else assumed. Its engine is a classification. The realizable neighborhoods of a ground vertex form a shifted family -- one closed under replacing an element by a smaller one -- and the quotient is the Johnson graph of that family. Such a Johnson graph can fail to be Hamilton-connected, and we determine exactly when: the failures are one explicit family of examples, the Y-families, and each of them fails between a single pair of its members. A shifted family with a greatest member never fails, and those families are exactly the shifted matroids, where the conclusion already follows from the theorem of Naddef and Pulleyblank on the graphs of 0/1-polytopes. The obstruction lives entirely outside the matroid case, which is why it has not been met before.", "title": "Maximal Hamiltonicity of realization graphs of degree sequences", "updated": "2026-09-07", "url": "https://arxiv.org/abs/2609.08007" }, { "age_days": 7, "arxiv_id": "2609.07750", "authors": [ "Yury N. Berdinsky" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "arxiv:2609.07750", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We classify all natural, conformally covariant, symmetric (0,2)-tensors of conformal weight -2 and differential order less than or equal to 4 in dimension 4, built from the metric, the Schouten tensor, covariant derivatives, and the Kulkarni-Nomizu product. We prove that the space of such tensors is exactly 2-dimensional, spanned by the Bach tensor (order 2) and the Eastwood-Singer tensor (order 4). The algebraic core is formally verified using Lean 4 with Mathlib. The 8x11 constraint matrix and divergence-free condition are verified computationally with exact rational arithmetic. Both English and Russian versions provided; Russian version available as ancillary.", "title": "Classification of Conformally Covariant 2-Tensors from the Kulkarni--Nomizu Product in Dimension 4", "updated": "2026-09-07", "url": "https://arxiv.org/abs/2609.07750" }, { "age_days": 7, "arxiv_id": "2609.07745", "authors": [ "James Alexander Schreib" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "arxiv:2609.07745", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-07", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "For a fixed graph F, the F-degree of a vertex v in a host graph H is the number of subgraphs of H isomorphic to F that contain v, and H is F-irregular if its F-degrees are pairwise distinct. We show that every finite connected graph F on at least three vertices admits a finite connected F-irregular host. For noncomplete F, the proof builds the host from a threshold graph with one deleted edge; when the minimum degree is at least two, a small incidence gadget with distinct weighted column sums separates the remaining exceptional vertices. The construction also yields infinitely many pairwise non-isomorphic finite connected F-irregular hosts for every noncomplete F. The complete-pattern case follows from a theorem of Chartrand, Holbert, Oellermann and Swart. A Lean 4 formalization of Theorem 1.1 is described, taking the published complete-pattern theorem as its sole custom axiom.", "title": "A construction of F-irregular graphs", "updated": "2026-09-07", "url": "https://arxiv.org/abs/2609.07745" }, { "age_days": 7, "arxiv_id": "2609.07238", "authors": [ "Ahaan Kallat" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "arxiv:2609.07238", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-09-07", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "Let $a(n)$ be the sequence A158690 in the On-Line Encyclopedia of Integer Sequences (OEIS), defined by the exponential generating function $\\sum_{n\\ge0} a(n)t^n/n! = 1+\\sum_{m\\ge1}\\prod_{j=1}^m(1-e^{-(2j-1)t})$. We prove two congruence conjectures of Peter Bala. The first states that, for every integer $k\\ge1$, the sequence $a(n)$ modulo $k$ is eventually periodic with period dividing $\\varphi(k)$. We prove the stronger statement that the Carmichael function $λ(k)$ is an eventual period. The second conjecture asserts the shifted Gauss congruences $a(np^r+i)\\equiv a(np^{r-1}+i)\\pmod{p^r}$ for every $i\\ge0$, every prime $p$, and all $n,r\\ge1$. Both results follow from a general theorem for exponential generating functions of the form $G(e^t-1)$ with $G\\in\\mathbb Z[[y]]$, together with the standard power-sum formula for Stirling numbers of the second kind.", "title": "A Proof of Bala's Congruence Conjectures for A158690", "updated": "2026-09-07", "url": "https://arxiv.org/abs/2609.07238" }, { "age_days": 0, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:5e7db968cc3e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: move infotree and snapshottree utils (#15133)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/5e7db968cc3e288662c34d148fe934d7c2929882" }, { "age_days": 0, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:088be5f36f2e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: remove lossy syntax separator array coercions (#15020)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/088be5f36f2ec96da3279f0e56f164dc6a2e7ce9" }, { "age_days": 0, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:9632ea4c76f8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep the space before a `hygieneInfo` antiquotation (#15025)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/9632ea4c76f83a21119f89a14871b3236d4d51d9" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:dc34e5f5cf9c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: support loading lake check and lake comparator input directly from export files (#15157)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/dc34e5f5cf9c42dd783471b525abbe66c0194270" }, { "age_days": 0, "authors": [ "Gaëtan Serré" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:d3a0781b9001", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `Float.fma` and `Float32.fma` with logical model (#15024)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/d3a0781b9001b66763f1e61c400cbc5f49abb5f5" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:669e6b41806c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `--paranoid` to `lake check` and `lake comparator` (#15145)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/669e6b41806c0fade055f6fe05cd8abba200982f" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:a2233a321503", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add --inadvisably-no-sandbox to comparator (#15156)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/a2233a3215034a623e36ffda47bf7ed2458cca29" }, { "age_days": 0, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:2f417f704211", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/2f417f704211f4413b857f4afae3cc46fd5b7cd3" }, { "age_days": 0, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:db1b21a57c5d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove redundant `sepBy1` in `subst` parser (#15029)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/db1b21a57c5dbeae231bbf78fa3e88d43b714558" }, { "age_days": 0, "authors": [ "Garmelon" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover/lean4:e20f62782c5e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: add downstream labels via comment (#15155)", "updated": "2026-09-14", "url": "https://github.com/leanprover/lean4/commit/e20f62782c5e3293519c1db2c4b1e0a2e27b21a3" }, { "age_days": 0, "authors": [ "Moritz Firsching" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9cb3970b1fb6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Data/Nat/Choose/Central): move and rename `four_pow_le_two_mul_add_one_mul_central_binom` (#42606)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/9cb3970b1fb61911f7e8892dffcde5aa4a0661cc" }, { "age_days": 0, "authors": [ "Kim Morrison" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:147cccedb040", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix: use the PR number in the deprecation reminder message (#43786)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/147cccedb04098422b4baaf4cd1760785f344a42" }, { "age_days": 0, "authors": [ "Jireh Loreaux" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d0a6fafa3cdb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: add `Filter.HasBasis.iInf_of_finite` (#43760)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/d0a6fafa3cdb0a09944ec57001c21e1ef4d0bc5e" }, { "age_days": 0, "authors": [ "Bingyu Xia" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a812e2ff7699", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Radical): radical of principal ideals in a UFD (#40857)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/a812e2ff769925671a79bdb9329588a9a4eefcce" }, { "age_days": 0, "authors": [ "Nicola Falciola" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:e4fe5149c780", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/Matrix/GeneralLinearGroup/Defs): add the proof of the range of toGL to be the ker of the determinant and the induced equivalence (#41786)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/e4fe5149c780ed4c97793131a29d351c31f4ec50" }, { "age_days": 0, "authors": [ "Laurance" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cf6bde11431e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Euclidean): affine span of orthocenter and vertex is altitude (#43480)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/cf6bde11431e913de1d8804126d8006a7fb187c4" }, { "age_days": 0, "authors": [ "Julian-Kuelshammer" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:268cf14b35c2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Fintype/Defs): add DecidableLE (∀ a, β a) (#43425)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/268cf14b35c2f790fe21d1818efc40e8d1f9fe8b" }, { "age_days": 0, "authors": [ "Jun Kwon" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:67248ba34806", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics/Graph): edge cut of `Graph` (#37865)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/67248ba34806c60bf24b5e99f0f09946ffc465c9" }, { "age_days": 0, "authors": [ "KG" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4c448402f0cb", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Combinatorics): link `Nat.Partition` to `YoungDiagram` (#39722)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/4c448402f0cb5aaf89016d2c38943ea9b87a6c6e" }, { "age_days": 0, "authors": [ "Xavier Roblot" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1e691b019aed", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/QuadraticAlgebra): classify quadratic algebras by their discriminant (#42708)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/1e691b019aed663664d2bd19fbbe7116c874f646" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bff860aee43b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Homology): the functor `F.rightDerivedFunctorPlus` is triangulated (#43267)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/bff860aee43bb5674c8db2947aaa341406aec372" }, { "age_days": 0, "authors": [ "Sankalp Thakur" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ecd2edf95073", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: doc(Data/Rel): clarify the SetRel representation (#42354)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/ecd2edf95073c8344529cfb2225390972c0bc945" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3a33b9d42956", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-09-14 (#43789)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/3a33b9d429567334f36d10d5143d63baed20ae3e" }, { "age_days": 0, "authors": [ "mathlib-update-dependencies[bot]" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fe17e590176e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-09-13 (#43772)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/fe17e590176eea00b6912e09ed52280cc0d60128" }, { "age_days": 0, "authors": [ "mathlib-nolints[bot]" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:fc0226e6ff30", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "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 (#43787)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/fc0226e6ff30332e06526a3b56feb635696ad605" }, { "age_days": 0, "authors": [ "Zhao Yuyang 赵雨扬" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:609b2d37236b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: redefine `Finsupp.indicator` using `Finsupp.onFinset` (#33434)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/609b2d37236ba0f4fce719315d0ccab5e31b6ccf" }, { "age_days": 0, "authors": [ "Gabe" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:435b9d6493fc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Tactic/Simproc/ExistsAndEq): fix two typos (#43797)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/435b9d6493fce6b243c9d5d113d936eac0f30051" }, { "age_days": 0, "authors": [ "Robert Hawkins" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f4a240391885", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/HopfAlgebra): remove left-over `noncomputable`s (#43638)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/f4a240391885f7de0ab4b0ab821485924a8cbd62" }, { "age_days": 0, "authors": [ "Alex Meiburg" ], "content_date": "2026-09-14", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b3fdd89b576a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-14", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Num/Lemmas): golf `transfer` tactic (#41167)", "updated": "2026-09-14", "url": "https://github.com/leanprover-community/mathlib4/commit/b3fdd89b576ab58db98f3fd0cbc86752740643c0" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover/lean4:68867f360f1e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: rename lake challenge to lake comparator (#15146)", "updated": "2026-09-13", "url": "https://github.com/leanprover/lean4/commit/68867f360f1ef0aa486f71d06e4d65884f36a29f" }, { "age_days": 1, "authors": [ "Wojciech Nawrocki" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover/lean4:d48866da828a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: trigger PR body check on label removal (#15149)", "updated": "2026-09-13", "url": "https://github.com/leanprover/lean4/commit/d48866da828ada369bae5ec95dd0aee5ef0f29c7" }, { "age_days": 1, "authors": [ "Mac Malone" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover/lean4:d01ad55af54a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: uploadable dependency outputs (#15141)", "updated": "2026-09-13", "url": "https://github.com/leanprover/lean4/commit/d01ad55af54a91cdc7bbd118ba654404613d2cbd" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover/lean4:a774e4050e13", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: default location for comparator config (#15147)", "updated": "2026-09-13", "url": "https://github.com/leanprover/lean4/commit/a774e4050e13bc8e7b9074f18094197484573685" }, { "age_days": 1, "authors": [ "Henrik Böving" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover/lean4:3824dbfae621", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: allow satisfied RUP clauses in the LRAT checker (#15144)", "updated": "2026-09-13", "url": "https://github.com/leanprover/lean4/commit/3824dbfae621555ca41ba0aa66d9b8cd26ddd2ea" }, { "age_days": 1, "authors": [ "Robin Arnez" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7d22123e148c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf: remove `simp` from three lemmas that were tried on every `<=` (#43778)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/7d22123e148c78424d2bd4a7bc78f790e6ba45cf" }, { "age_days": 1, "authors": [ "Alex Loitzl" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:37355d3aab85", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: fix: typo in TextBasedLinter (#43769)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/37355d3aab855ea95f69a5dfacce1d877d9e5354" }, { "age_days": 1, "authors": [ "Kim Morrison" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2ff8073df352", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: `Std.Total` instance for InvImage (#43326)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/2ff8073df352b7cb74638403c464ed5cd3f97ce2" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7f22e856c19e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Order/SuccPred/Limit): small theorems and generalizations (#42480)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/7f22e856c19eeabc38d75733b71d7e44167307f3" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3fc1f443cb40", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(ClickSuggestions): support assigning metavariables in the goal (#43597)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/3fc1f443cb40de60c1581d4111da6097fc6dfb3d" }, { "age_days": 1, "authors": [ "Justus Springer" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8d52ea9a145a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AlgebraicGeometry/AffineSpace): affine space is smooth (#39710)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/8d52ea9a145a9255c4d301c0d1a1b8bf6e59305a" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f508fa49b941", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Tactic/GCongr): deprecate `Tactic/GCongr/CoreAttrs` (#43594)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/f508fa49b941037007135bdea650664f7aeb38cf" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:182c4c30cdc5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data/Real/Basic): `no_expose` the private operations (#38198)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/182c4c30cdc58b70f2ba77d56f31b1c4048e9522" }, { "age_days": 1, "authors": [ "Harald Husum" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c0bf07f38300", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data): tidy markdown headers (#42671)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/c0bf07f3830014f66d85f8fa417b1f7d9696555c" }, { "age_days": 1, "authors": [ "Robin Carlier" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:64401b008cde", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Monoidal): scope `□` and `⋔` notations (#43199)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/64401b008cded3daa998c178fe966fd4b0f89c3d" }, { "age_days": 1, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-13", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2cf4ee5352a8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-13", "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/Zero): use `to_dual` (#43554)", "updated": "2026-09-13", "url": "https://github.com/leanprover-community/mathlib4/commit/2cf4ee5352a8e00b29f718c08d2e28c9ccf53f37" }, { "age_days": 2, "authors": [ "Sofia Rodrigues" ], "content_date": "2026-09-12", "freshness": "fresh", "id": "github:leanprover/lean4:c6ef814f2db9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-12", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: refcounting and error reporting in the libuv bindings (#14796)", "updated": "2026-09-12", "url": "https://github.com/leanprover/lean4/commit/c6ef814f2db974248c4408691a87a6ed92c1ca0c" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:53d83477fb54", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: avoid non-linearity in pushproj (#15136)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/53d83477fb548cde0bc848538b03ce6bc6cc7aaf" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:be73c1638d08", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: avoid non-linearity in match elaborator toposort (#15126)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/be73c1638d0861502071926f8a230898585d1770" }, { "age_days": 3, "authors": [ "Henrik Böving" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:fdb88c3cfce3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: avoid non-linearity in LRAT trimming (#15124)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/fdb88c3cfce3dccf2cab61d715c24212336a1de1" }, { "age_days": 3, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:624fffaa54c6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: keep `Info` of elaborations that pass a hole through (#15068)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/624fffaa54c6fd58390e352483e920956b9102e4" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:5023e7e8985d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: do not hoist `Decidable` values in `pullInstances` (#15128)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/5023e7e8985d17047e61ed11b342cc886901815b" }, { "age_days": 3, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:f93dd43980cf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: separator-preserving `Syntax.identComponents?` (#15057)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/f93dd43980cfb6fbfc6a19c4a3f87daf50e908b1" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:de6d209315a6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: bundle the `con-leche` external checker with release toolchains (#15130)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/de6d209315a66e527041a89d85381e029dbd8f74" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:a714e8333f9d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `erased` declarations in `do` notation (#15090)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/a714e8333f9d53bc26ba7568f23c59b1c1772946" }, { "age_days": 3, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:25dd64ed1669", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: missing order instances for `UIntX` and `IntX` (#15122)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/25dd64ed166962afc32d89bcf3b717e8ad3571d3" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:c3f46bf42229", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: keep configure's jj fallback from snapshotting the working copy (#15129)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/c3f46bf42229fca5edb662444404715552d04796" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:9095e9a09e6d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: ci: move `macOS aarch64` from merge queue to master check (#15123)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/9095e9a09e6dd2e9731c158e6304745a6d9d27d5" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-11", "freshness": "fresh", "id": "github:leanprover/lean4:79cf0e44e8aa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-11", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: CI: have restart-on-label wait for the cancelled run before restarting it (#15121)", "updated": "2026-09-11", "url": "https://github.com/leanprover/lean4/commit/79cf0e44e8aac9aceb09d68a8d2c8078bb10986d" }, { "age_days": 4, "arxiv_id": "2609.10916", "authors": [ "Taylor Gordon" ], "content_date": "2026-09-10", "freshness": "fresh", "id": "arxiv:2609.10916", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-10", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "A point set is universal for planar graphs on $n$ vertices if every such graph has a straight-line drawing without crossings whose vertices belong to the set. We construct universal point sets of size $n^{1+o(1)}$, improving the previous quadratic upper bound. Our construction uses the reduction of Bannister, Cheng, Devanny, and Eppstein from universal point sets to superpatterns for $213$-avoiding permutations. We represent these permutations by ordered rooted forests and construct a small family of intervals containing every such forest. The result follows from a straightforward bound on the size of the family of intervals. GPT-6 Astra assisted in developing the construction and proof.", "title": "Almost Linear Universal Point Sets for Planar Graphs", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.10916" }, { "age_days": 5, "arxiv_id": "2609.10461", "authors": [ "Marc Kegel", "Shana Yunsheng Li", "Qiuyu Ren" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.10461", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We construct a $3$-generator $9$-relator group with unsolvable word problem. We use the group to construct two fixed-size Adian--Rabin families of group presentations, one with $4$ generators and $11$ relators, and another with $2$ generators and $10$ relators. As a consequence, $\\#_7(S^2\\times S^2)$ is topologically unrecognizable and $\\#_9(S^2\\times S^2)$ is smoothly unrecognizable. These algebraic and topological results improve the previous best known bounds by Borisov, Tancer, and Gordon. The construction of the group builds upon an example of Borisov and uses additional HNN extensions and Tietze eliminations to reduce the size of the presentation. We also provide a machine-checked Lean~4 formalization of the algebraic results.", "title": "Small undecidable groups and unrecognizable 4-manifolds", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.10461" }, { "age_days": 5, "arxiv_id": "2609.10525", "authors": [ "Xiaoyu Li", "Andi Han", "Jiaojiao Jiang", "Junbin Gao" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.10525", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Language generation in the limit asks for valid unseen elements from every exhaustive positive presentation of an unknown infinite language. We characterize this task for arbitrary families over a countable universe. Generation is possible exactly when each target can be assigned a finite positive witness so that the targets activated by any finite sample have an infinite common intersection. The necessary direction follows from a universal normalization: a search through unconfirmed histories converts any successful generator into one depending only on the observed set. We then ask how large compatible witnesses must be. Positive separation width records the smallest uniform size bound, with two further levels for unbounded finite witnesses and the absence of any compatible finite-witness assignment. Every level occurs. Countable families admit singleton witnesses, explicit families realize every finite width, and a union of two families with infinite common cores requires unbounded finite witnesses. Finally, countable-support and finite-profile obstructions explain why local combinatorial data cannot determine generation in the limit. The characterization and full width hierarchy are checked in Lean, including the simplified normalization and a direct diagonal capture lemma. The accompanying Lean development is maintained at https://github.com/xiaoyulics/language-generation-characterization", "title": "Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarchy", "updated": "2026-09-10", "url": "https://arxiv.org/abs/2609.10525" }, { "age_days": 5, "arxiv_id": "2609.09687", "authors": [ "Hazem Ibrahim", "Yasir Zaki" ], "content_date": "2026-09-09", "freshness": "fresh", "id": "arxiv:2609.09687", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-09", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Studies of careers in science, film, music, and books report a common pattern. When a person's most successful work arrives is close to a random draw over the works they produce. How large their successes tend to be, in contrast, follows a stable, person-specific factor. We test whether this pattern holds for open-source software careers and whether it changed when generative AI coding tools arrived. From the complete public record of GitHub push events (2015-2025), we reconstruct 102.2M career works by 6.15M contributors, and for the 908k contributors whose repositories publish packages, we measure each work's impact by how many downstream packages come to depend on it. First, we find that the timing of a career's biggest hit is close to a lottery over their works, as in science and the arts, with a small, replicable lean toward early career that grows as careers get longer. Second, some coders reliably produce higher-impact work than others, but this lasting personal factor accounts for only part of why impact persists (about a fifth in our primary specification); the rest behaves like momentum, success feeding on itself for a period of time. Third, within the same contributors, this structure did not change after ChatGPT's release. The stable factor's weight grew by about as much as it grew for an earlier cohort that simply aged, and subtracting the effect of aging from the effect of generative AI puts the shift at +0.03 (95% CI [-0.22, +0.23]), indistinguishable from zero. The success pattern documented in science and the arts therefore describes open-source careers too, and it shows no detectable break across the arrival of generative AI. These results have implications for how track records on open platforms should be read and on what to expect from generative AI for the careers built on them.", "title": "Chance, Persistent Advantage, and the Generative-AI Era in Open-Source Package Careers", "updated": "2026-09-09", "url": "https://arxiv.org/abs/2609.09687" }, { "age_days": 6, "arxiv_id": "2609.09033", "authors": [ "Sevag Gharibian", "Carsten Hecht", "Dorian Rudolph" ], "content_date": "2026-09-08", "freshness": "fresh", "id": "arxiv:2609.09033", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-08", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We prove quantitative lower bounds on the semidefinite extension complexity of the set of separable quantum states on $\\mathbb{C}^d\\otimes\\mathbb{C}^d$. We consider semidefinite programs (SDPs) that approximate the maximum acceptance probability of a measurement over separable states, the optimization problem underlying QMA(2). In the extended-formulation model of Harrow, Natarajan, and Wu (HNW), all measurements share a common feasible region and an objective-independent embedding of product states that exactly reproduces their acceptance probabilities. For every $0<θ<2/7$, there are constants $c_θ,a_θ>0$ such that, for sufficiently large $d$, any such SDP with uniform additive error $0