{ "counts": { "adjacent": 10, "core": 3, "errors": 0, "negative": 77, "total": 90 }, "date": "2026-09-07", "errors": [], "fresh_content_days": 21, "generated_at": "2026-09-07T19:21:03Z", "items": [ { "age_days": 3, "arxiv_id": "2609.05157", "authors": [ "Weichen Winston Yin", "Jacob M. Taylor", "Dirk R. Englund", "Frank H. L. Koppens" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.05157", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "lean_formal_proving_agents", "mathlib_retrieval" ], "published": "2026-09-04", "score": 9.5, "source": "arxiv-ai4math-core", "summary": "Formalizing mathematics in a proof assistant, where a machine checks every definition, statement and proof, has set a new standard of rigor. Large language models are now capable of formalizing autonomously, even at the scale of whole textbooks. We bring this standard of rigor to physics, where theoretical arguments carry idealizations that are rarely stated fully, and any logical gaps could have a cascading effect on interdependent results. Recognizing the need to evaluate autoformalization systems for physics, we release AxQM, 1,019 kernel-checkable proof-synthesis tasks over 479 items drawn from the textbook Quantum Computation and Quantum Information by Nielsen and Chuang. The tasks are stated in a custom Lean library of finite-dimensional quantum mechanics. By task count, it is the largest proof-synthesis benchmark in physics by a factor of four. AxQM is derived from a near-complete formalization of the formal portions of the textbook, so every task is guaranteed a solution, which we keep private. Grading of the benchmark is done deterministically by the Lean kernel, which checks that the proof compiles, that no sorry appears in it or in any declaration it depends on, and that it introduces no new axioms.", "title": "AxQM: A Textbook-Scale Benchmark for Formal Proof Synthesis in a Library of Finite-Dimensional Quantum Mechanics", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.05157" }, { "age_days": 7, "arxiv_id": "2608.30238", "authors": [ "Gregory Morse" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "arxiv:2608.30238", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-31", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Classical lower bounds show that multiplying two degree-three polynomials over $\\mathbb F_2$ requires nine scalar products in bilinear or quadratic models. They do not settle unrestricted Boolean multiplicative complexity: an XOR--AND circuit may reuse nonlinear intermediate wires, and Boolean equality is taken modulo $x_i^2=x_i$, so a multiplication can lower algebraic degree. Let $\\operatorname{Mul}_4:\\mathbb F_2^8\\to\\mathbb F_2^7$ output the seven coefficients of the product of two four-term binary polynomials. We prove that its unrestricted XOR--AND multiplicative complexity is exactly nine. This resolves, for a natural vector-valued quadratic function, the Boyar--Find question of whether a quadratic-circuit lower bound can persist against unrestricted nonlinear reuse. The proof is structural rather than exhaustive. A useful purely quadratic prefix is forced onto the three rational places of $\\mathbb P^1(\\mathbb F_2)$. In a hypothetical eight-AND circuit, the unique non-useful gate must carry a cubic high part. Any useful continuation then forces a rational tangent and exposes a first Hasse jet, while exterior jet separation together with Boolean idempotence prevents the same defect from exposing the second Hasse jet. The required useful suffix therefore cannot exist. A complete Lean 4 formalization verifies the Boolean-ANF semantics, the unrestricted circuit model, and the exact theorem; it uses no project-specific axiom or native decision procedure. The same zero-defect flag argument gives multiplicative complexity six for three-term multiplication, and the method isolates the multi-defect obstruction for five terms.", "title": "Unrestricted Boolean Multiplicative Complexity of Four-Term Binary Polynomial Multiplication: Rational Places, Hasse Jets, and the Failure of Nonlinear Feedback", "updated": "2026-08-31", "url": "https://arxiv.org/abs/2608.30238" }, { "age_days": 9, "arxiv_id": "2608.29270", "authors": [ "Hojae Han", "Jongyoon Kim", "Sanghyeok Park", "Dongwook Cheon", "Yeachan Park", "Myung Jae Jeon", "Sunjong Choe", "Soonho Kong", "Wonseok Hur", "Seung-won Hwang", "Donghoon Hyeon" ], "content_date": "2026-08-29", "freshness": "fresh", "id": "arxiv:2608.29270", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "lean_formal_proving_agents" ], "published": "2026-08-29", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Autoformalization translates informal mathematical theorems into code for proof assistants such as Lean. A central challenge is that current evaluation metrics can accept type-correct but misaligned statements or reject correct statements written in a different formulation. Inspired by Pass@$k$, we propose SA-Pass (*Semantic Alignment Pass*), which tests formal statements using auxiliary statements called *shadows* that characterize the intended statement. A generated statement receives full credit only when it compiles, implies each shadow (forward check), and is implied by their conjunction (backward check). We instantiate SA-Pass in ShadowBench, a Lean 4 full autoformalization benchmark of 178 postgraduate- to research-level problems spanning eight mathematical areas. Claude Code (Opus 4.8) with Numina-Lean-Agent reaches $61.8\\%$ compile rate and $11.2\\%$ SA-Pass. Across outputs generated by six agentic configurations, SA-Pass achieves $98.8\\%$ binary agreement with expert judgments. An early version of ShadowBench served as the benchmark for Track 4 of the ICML 2026 AI4Math Challenge.", "title": "SHADOWBENCH: Toward Reliable Automatic Evaluation of Semantic Alignment in Autoformalization", "updated": "2026-09-02", "url": "https://arxiv.org/abs/2608.29270" }, { "age_days": 4, "arxiv_id": "2609.03478", "authors": [ "Ján Pastorek" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "arxiv:2609.03478", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-09-03", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We report on our ongoing project to develop a computational pipeline, AutoGraphForge, for an automated graph-theoretic conjecturing-refuting-formalizing-proving system. Conjecture generation is counterexample-guided and runs in rounds: a Graffiti3 generator proposes conjectures over a small, evolving snapshot table $T$ (initially a few hundred graphs with their computed invariants) that grows only by counterexamples to its own conjectures. A novelty filter of $559$ classical and folklore relations, closed under transitive composition and linear identity substitution, decides via a linear program whether a candidate is already implied by known results. Surviving candidates are tested against a dataset of about $348,000$ graphs, unioning the complete House of Graphs invariant export, the exhaustive census of all connected graphs on at most nine vertices, several extremal families (strongly regular, minimal Ramsey, Cayley, cages, barbells, lollipops, spiders), and random models. Counterexample-search algorithms then attack the remainder. Run for several rounds on an HPC cluster, the loop yields $6,522$ conjectures that survived the refutation dataset, the novelty filter and every active-search run -- among them nontrivial relations between the annihilation number and the edge-cover number for bipartite and regular graphs, which we prove by hand. A subsequent formalization and proving stage deterministically translates each surviving conjecture into a Lean 4 statement skeleton; every candidate proof is kernel-verified against a pinned mathlib4 and our custom invariant preamble. This stage integrates two neural provers -- DeepSeek-Prover-V2-671B (served with vLLM) and the Lean-specialised OProver-32B -- behind the independent kernel check. It is implemented end-to-end and passes initial sanity checks, with the full pipeline currently running on the cluster.", "title": "AutoGraphForge: Towards Automated Graph Theory Discovery", "updated": "2026-09-03", "url": "https://arxiv.org/abs/2609.03478" }, { "age_days": 8, "arxiv_id": "2608.29750", "authors": [ "Yinjie Li" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "arxiv:2608.29750", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-30", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Harwit and Sloane conjectured that every nonsingular entrywise-nonnegative matrix $A\\in\\mathbb R^{n\\times n}$ satisfies $\\|A^{-1}\\|_F\\ge 2n(n+1)^{-1}\\|A\\|_{\\max}^{-1}$, with equality precisely for positive multiples of $S$-matrices. Cheng proved the conjecture in odd dimensions, while Frankel and Urschel proved the even-dimensional case for $n\\ge1000$. We complete the remaining even-dimensional cases. Starting from the structural identities in Frankel--Urschel Lemma 2.1, we derive an exact global defect budget and combine binary rounding with Gram projection. A refined ten-row obstruction handles every even $n\\ge66$; a finite exact calculation handles $4\\le n\\le64$, $n\\ne6$; and a separate multi-column energy argument treats $n=6$. The order-two case follows from a direct calculation. The new even-dimensional proof has been formalized in Lean 4, with Frankel--Urschel Lemma 2.1 as its sole external mathematical input. Together with Cheng's odd-dimensional theorem, this proves the S-matrix conjecture in every dimension.", "title": "The S-matrix conjecture", "updated": "2026-08-30", "url": "https://arxiv.org/abs/2608.29750" }, { "age_days": 8, "arxiv_id": "2608.29592", "authors": [ "Jungyeom Kim", "Jihyeok Park" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "arxiv:2608.29592", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-30", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "We resolve three open problems concerning parsing expression grammars (PEGs). We construct a single language $C$ satisfying $C\\in\\mathsf{LIN}\\cap\\mathsf{PEG}$ and $C^R\\in\\mathsf{LIN}\\setminus\\mathsf{PEG}$. This proves that some linear context-free language is not a PEG language and that PEG languages are not closed under reversal, confirming a conjecture of Loff, Moreira, and Reis. Factoring the same witness resolves the concatenation-closure problem of Rubtsov and Chudinov negatively, in the strong form $\\mathsf{PEG}\\cdot\\mathsf{REG}\\not\\subseteq\\mathsf{PEG}$ despite $\\mathsf{REG}\\cdot\\mathsf{PEG}\\subseteq\\mathsf{PEG}$. It also refutes closure under Kleene star, homomorphisms, and substitutions. Our main technique converts scaffolding automata (SCAs), which characterize reversals of PEG languages, into dynamic data structures in the cell-probe model. For any suitably local serialization of a problem with preprocessing, updates, and a final Boolean query, an SCA recognizer yields an exact deterministic cell-probe data structure whose operation costs are proportional to the corresponding encoding lengths. Cell-probe lower bounds can therefore prove SCA non-membership and, by reversal, PEG non-membership. We apply this transfer to Multiphase Inner Product using one-symbol update blocks and a query suffix of length $O(\\log n)$, while keeping both the language and its reversal linear context-free. Ko's cell-probe lower bound then yields the witness above. The arguments are additionally formalized in Lean 4.", "title": "Separating Parsing Expression Grammars using Cell-Probe Lower Bounds", "updated": "2026-08-30", "url": "https://arxiv.org/abs/2608.29592" }, { "age_days": 9, "arxiv_id": "2608.28997", "authors": [ "Maher Kallel", "Mohamed El Louadi" ], "content_date": "2026-08-29", "freshness": "fresh", "id": "arxiv:2608.28997", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-29", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "In May 2026 an OpenAI model produced a counterexample to the Erdős unit distance conjecture. Five mathematicians published a human-verified version the same day, and the result entered the literature within weeks. In August 2026 the same laboratory published ten mathematical and theoretical computer science results, each accompanied by a machine-checkable Lean 4 certificate with no unproved steps. Four weeks later, one remained the subject of an unresolved dispute over whether its formalization meant what it claimed. We argue that this difference is structural. We distinguish three layers of verification: derivational validity, which a kernel checks; representational fidelity, whether the formal statement means the intended question; and epistemic significance. Only the first is mechanizable. Making it effectively free therefore does not eliminate verification work but shifts the burden to layers dependent on scarce expert attention. Measurements of the August corpus illustrate the shift. The kernel-checked proofs total 20.6 MB, while the statements requiring human audit total 55.6 KB, a ratio of 379 to 1. Yet those statements contain 218 bespoke definitions rather than relying on community-vetted ones. The audit surface is therefore small in volume but irreducibly expert. We argue that machine checking produces verification abundance while leaving adjudication scarce. We propose a six-category taxonomy of representational mismatch, a disclosure schema for machine-generated mathematical claims, and implications for software, cryptography, and regulated decision systems.", "title": "Verification abundance, adjudication scarcity: what happens to mathematical knowledge when proof checking becomes free", "updated": "2026-08-29", "url": "https://arxiv.org/abs/2608.28997" }, { "age_days": 4, "arxiv_id": "2609.04279", "authors": [ "Yuankai Guo", "Xiaozhe Hu" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "arxiv:2609.04279", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-03", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Let $Σ$ denote the class of functions $f(z) = z + b_0 + b_1 z^{-1} + \\cdots$ that are analytic and univalent in the exterior unit disk $Δ^* = \\{z \\in \\mathbb{C} : |z| > 1\\}$. In 1962, Ch. Pommerenke proved that if $F$ and $G$ are convex functions in $Σ$, then every convex linear combination $H = λF + (1-λ)G$ ($0 < λ< 1$) remains univalent and belongs to $Σ$. In Hayman's problem collection (Research Problems in Function Theory, Problem 6.10), Pommerenke raised the question of whether $H$ is necessarily also a convex function. We resolve this question in the negative by constructing an explicit counterexample in $Σ$ with parameters in $\\mathbb{Q}(i)$. The argument is self-contained and has been formally certified in the Lean 4 proof assistant.", "title": "A Counterexample to a Problem of Pommerenke on Convex Functions in the Class $Σ$", "updated": "2026-09-03", "url": "https://arxiv.org/abs/2609.04279" }, { "age_days": 5, "arxiv_id": "2609.02978", "authors": [ "Diar Heidary" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "arxiv:2609.02978", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-09-02", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The fully independent SparseStack sketch is a vertical stack of $s$ independent CountSketch matrices, scaled by $s^{-1/2}$, so that every column has exactly $s$ nonzero entries. We prove that it is an oblivious subspace embedding for $d$-dimensional subspaces with distortion $ε$ and failure probability $δ$ when $m = O((d+\\log(1/δ))/ε^2)$ and $s = O(\\log(d/δ)/ε)$, with explicit constants. These are the parameters conjectured by Nelson and Nguyen (FOCS 2013) for this construction; the row count is optimal by their lower bound. The proof bounds the even moments of the Gram error. A conditional-expectation coupling replaces each signed one-hot column selector by a vector with independent three-point entries, at the cost of a constant factor per moment order. The three-point law has a three-dimensional $L_2$ space, so multiplication by an entry is a $3 \\times 3$ Jacobi matrix, and the $2q$-th moment becomes a vacuum matrix element of a deterministic operator on a finite tensor product, graded by total occupation. The operator has three grade bands, and we bound each band on the grade-$ν$ sector by $C(\\sqrt{(d+ν+1)/m} + (d+ν+1)/m + (ν+1)/s)$ with $C = 3+\\sqrt{2}$. The key step is a shared-factor inequality: each row block of the positive operator attached to one tensor slot is rank one with trace $d$, and the sum over $\\ell$ slots sharing the same external factor has norm at most $d+\\ell-1$. A $2q$-step expansion and Markov's inequality complete the argument, which is finite-dimensional and does not use Gaussian comparison. The theorem has been formally verified in Lean 4. The proof was developed with AI systems under the author's direction, as disclosed in the paper.", "title": "SparseStack Is an Optimal Oblivious Subspace Embedding", "updated": "2026-09-02", "url": "https://arxiv.org/abs/2609.02978" }, { "age_days": 7, "arxiv_id": "2609.00101", "authors": [ "Qianli Ma" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "arxiv:2609.00101", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-31", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We completely solve Colombo's 1928 determinant problem. For distinct real $x_1,\\ldots,x_N$, $N\\geq 2$, and an integer $D\\geq 1$, we prove that $\\det[(x_j-x_i)^D]\\neq 0$ if and only if $D\\geq N-1$ and either $N$ is even or $D$ is even. The even-exponent case follows from Dyn--Goodman--Micchelli (1986); the remaining odd case is proved by a strict Pfaffian sign theorem. The new odd-exponent theorem and its complete proof chain have also been formalized in Lean 4.", "title": "Colombo's Determinant Problem", "updated": "2026-08-31", "url": "https://arxiv.org/abs/2609.00101" }, { "age_days": 3, "arxiv_id": "2609.05358", "authors": [ "Hikaru Manabe" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.05358", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-09-04", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "A subtraction game is played on a heap of tokens. The players take turns removing s tokens for some s in a fixed set S of positive integers, and the player who cannot move loses. The sequence of Sprague-Grundy values of such a game is eventually periodic. We ask when it is purely periodic, meaning periodic from the very start, for the three-move sets S={a,b,c} with 0=2, we give an explicit sufficient criterion for pure periodicity. For every non-additive set that satisfies it we determine the least period, all P-positions in closed form, and all nim-values, and the additive case c=a+b is treated separately. We conjecture that the criterion is also necessary, and we prove this for the period a+b whenever c>=2(a+b). The criterion is a finite test on the angle rho = c mod (a+b), built from the P-position pattern of the two-move game {a,b}, and the admissible angles form explicit unions of arcs in Z/(a+b)Z.", "title": "Purely Periodic Three-move Subtraction Games", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.05358" }, { "age_days": 6, "arxiv_id": "2609.00706", "authors": [ "Haobo Ma", "Wenlin Zhang", "Manuel Israel Cázares" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "arxiv:2609.00706", "kind": "paper", "label": "adjacent", "matched_signals": [ "reasoning_rl_distillation" ], "published": "2026-09-01", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "The SAIR Mathematics Distillation Challenge on Equational Theories asks a solver to classify whether one magma identity implies another and, for either verdict, to return a certificate accepted by a deterministic Lean judge. We present a single-file solver organized as a cheapest-first cascade. Its false branch combines coefficient tests over structured algebra families, bounded finite-model search, an explicit central-groupoid witness, and several infinite-carrier witnesses. Its true branch is a proof-producing ordered unit superposition procedure with Knuth-Bendix ordering, bidirectional demodulation, indexing, memoised substitution, and anytime size deepening. Search results remain outside the trusted base: successful derivations are replayed as small Lean terms, and countermodels are rechecked by the competition judge. The frozen solver is a 189,504-byte Python file with SHA-256 f2392533c9f4c03b.... In local runs through official judge revision 2848228, it produced accepted certificates for all 1,889 rows of the six public sets with no language-model calls. Separate measurements recorded full agreement on the 800 published Stage 1 evaluation-distribution problems, 100 accepted rows in the canonical Marathon manifest without tokens, and 200 accepted rows in the hosted playground. These are regression and playground measurements, not a leaderboard result and not evidence about a hidden set. All quantitative claims are tied to immutable result ledgers; the paper makes no completeness or comparative-superiority claim.", "title": "A Certificate-Producing Cascade for Equational Implication: The SAIR EQT2 Stage 2 Solver", "updated": "2026-09-01", "url": "https://arxiv.org/abs/2609.00706" }, { "age_days": 7, "arxiv_id": "2608.30221", "authors": [ "Zijun Gao", "Weihan Zhang" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "arxiv:2608.30221", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-31", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "For Gaussian approximation over high-dimensional rectangles under unrestricted covariance, Chernozhukov et al. (2023b) conjectured that the $n^{-1/4}$ rate, up to logarithmic factors, is near-optimal. We show that, under the coordinatewise subexponential condition with scale $B_n$ and the marginal variance lower bound condition with constant $b$ in Chernozhukov et al. (2023b), the approximation error in dimension $d$ is bounded by \\begin{align*} C_b\\min\\left\\{ 1,\\, \\left(\\frac{B_n^2}{n}\\right)^{1/3}\\{\\log(2dn)\\}^{7/3} + \\frac{B_n}{\\sqrt n}\\{\\log(2dn)\\}^{5/2} \\right\\}. \\end{align*} In particular, for bounded $B_n$ and polynomial dimension, the new bound is $n^{-1/3}$ and therefore falsifies the polynomial-dimensional $n^{-1/4}$ near-optimality conjecture. The proof uses a two-stage interpolation and a rank-free matrix-weighted Gaussian surface bound, which may be of independent interest. The initial proof attempt was generated by ChatGPT 5.6 Pro (OpenAI) and subsequently corrected and rewritten by the authors. The machine-checked Lean formalization of the proof can be found at the GitHub repository (https://github.com/WeihanZhang2001/cubic-root-gaussian-approximation-under-unrestricted-covariance).", "title": "Cubic-Root Gaussian Approximation under Unrestricted Covariance", "updated": "2026-08-31", "url": "https://arxiv.org/abs/2608.30221" }, { "age_days": 0, "authors": [ "Henrik Böving" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover/lean4:c40679c304a1", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: enable checking lean4export via leanchecker (#15050)", "updated": "2026-09-07", "url": "https://github.com/leanprover/lean4/commit/c40679c304a1f8324981783c12275e109b051349" }, { "age_days": 0, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover/lean4:64906da38cdd", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `lake check` to check a project against external checkers (#14990)", "updated": "2026-09-07", "url": "https://github.com/leanprover/lean4/commit/64906da38cdd68f83829f45f6fafe35468f06f7b" }, { "age_days": 0, "authors": [ "Yi.Yuan" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9ba2df1bca85", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(RingTheory/Localization): restore IsLocalization.surj' (#42967)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/9ba2df1bca855b78ba697fd2e7189b452706113d" }, { "age_days": 0, "authors": [ "Laurance" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3869467432b0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(Geometry): remove unnecessary hypothesis (#43444)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/3869467432b00af32e79e99304b399f3bb7305e8" }, { "age_days": 0, "authors": [ "Anne Baanen" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:21118bea64cf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: perf(Tactic/Linter/InternalConstructor): try `foldInfo` instead of `foldInfoM` (#43431)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/21118bea64cfdd323d5cfc23c75244afb8c6c3d2" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f86d48590e31", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Topology/Separation/Hausdorff): add `tendsto_nhds_unique_of_forall` (#42986)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/f86d48590e31eef586e6c45443c5b361ac562526" }, { "age_days": 0, "authors": [ "Bhavik Mehta" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:1630b9783430", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/PowerSeries): coeff of a power series times a numeral (#42252)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/1630b9783430ca92ac56008bb24885b3618462c4" }, { "age_days": 0, "authors": [ "Xavier Roblot" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bf0ef6d9e897", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory/Ideal): generalize span_singleton_dvd_span_singleton_iff_dvd and emultiplicity_eq_emultiplicity_span (#40557)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/bf0ef6d9e8976e7a6d2feaf607906bfe87150c06" }, { "age_days": 0, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d3debb31025b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory): krull dimension of a polynomial ring in an infinite number of variables (#41098)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/d3debb31025b1a1bf90ea8260bfa29e495bc7d65" }, { "age_days": 0, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ced9ce50c607", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(RingTheory): `Ideal.span` corollaries of Krull's height theorem (#41401)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/ced9ce50c60731de14ef28727c1440f8e6ce8f02" }, { "age_days": 0, "authors": [ "Michael Stoll" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:751af11de020", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory/Height/EllipticCurve): naïve height and approximate parallelogram law (#43463)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/751af11de0208780dda5326b40c54b3859607d03" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:bc176b987120", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(NumberTheory): a carmichael number has at least 3 prime factors (#43417)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/bc176b98712028d938efa4bb036847d56ccc11dd" }, { "age_days": 0, "authors": [ "Attila Gáspár" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d2005a20451c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/AffineSpace/Homogenization): generalize `hom_ext` to `LinearMapClass` (#43350)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/d2005a20451c42d01a3eb8a6b0b8260f8be791f8" }, { "age_days": 0, "authors": [ "Attila Gáspár" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3abe635ff592", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(LinearAlgebra/AffineSpace/Homogenization): add `SMulCommClass` instance (#43416)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/3abe635ff5923b6784af0b1b241dcdd072dc18c2" }, { "age_days": 0, "authors": [ "Bhavik Mehta" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:5a548ade0ff9", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data/Nat/Factorization/Basic): add mul_factorization_le (#43477)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/5a548ade0ff9df0651e91073f2411139928a835b" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:156b4fb35005", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Data): two appended lists are sorted iff (#43457)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/156b4fb3500549c5983e06348faca9d6ee499841" }, { "age_days": 0, "authors": [ "Evgenia Karunus" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d33de8948e73", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Analysis/Normed/Module/Basic): add enorm_algebraMap', enorm_algebraMap (#43365)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/d33de8948e7368495fb46a90c01c4fe87535c2b5" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a5ac9c97ee93", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(AlgebraicTopology/SimplicialSet): `MulStruct.nonempty` (#42474)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/a5ac9c97ee93a2e78226b2e3c3c28901024a5630" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:32c66916aa0b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Polynomial/Splits): specialization of `Split.of_splits_map_of_injective` to `algebraMap` (#43353)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/32c66916aa0b25d2686b4d481d1e1da6074b0bc6" }, { "age_days": 0, "authors": [ "Joël Riou" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c0972e259fb8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Homology): better sign for the connecting homomorphism for the contravariant long exact sequence of Ext-groups (#43492)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/c0972e259fb87ccc7e5b904e0e29de491b00ab23" }, { "age_days": 0, "authors": [ "Yaël Dillies" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:059a625dc060", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/Group/Pointwise): `sdiv` lemmas (#43541)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/059a625dc060f300817caf908fa4ed021a218aa7" }, { "age_days": 0, "authors": [ "Michael Rothgang" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a120a09d6fba", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: standardise names for coercions from morphism classes to morphisms (#43367)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/a120a09d6fbab8b455ec7ef85ec007562f1268da" }, { "age_days": 0, "authors": [ "Salvatore Mercuri" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9939342d317f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: make the `coe` for `Valuation.Completion` simp normal (#43428)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/9939342d317fa8c1adac30aa416859d7d900ddc5" }, { "age_days": 0, "authors": [ "Felix Pernegger" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:a5e8aa18995c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: fix minor spacing issues (#42918)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/a5e8aa18995c6ce0f7ae4ca74a07b38e4b05b4ee" }, { "age_days": 0, "authors": [ "Thomas Browning" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:795fd4166115", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/Ideal/GoingUp): use `Ideal.under` (#43414)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/795fd41661154639228c2bbcd0e1a83b73763a97" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9122aca6a04d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/Irreducible): use `to_dual` (#43336)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/9122aca6a04d5c30806c970381ebbd5c58a00c65" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8f8ecef6d22b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/CompleteSublattice): correct the argument type of `subtype_apply` (#43527)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/8f8ecef6d22b4d65a563627b10a82294857c03f1" }, { "age_days": 0, "authors": [ "Jovan Gerbscheid" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4d65fcffb092", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order): use `to_dual` in various places (#43323)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/4d65fcffb0920ad96c87ecf96edd39da7be3210c" }, { "age_days": 0, "authors": [ "Wenrong Zou" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:3c2928f1647f", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(MvPowerSeries/Derivative): make coeff ring implicit (#43334)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/3c2928f1647fe59cb105026ec98ee0f99369d3e5" }, { "age_days": 0, "authors": [ "Luigi Massacci" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:26508b677d4c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Matrix/Block): update forgotten lemma/doc with \"new\" IsUpperTriangular (#43263)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/26508b677d4c04116ae62fdc5a238bac01f37434" }, { "age_days": 0, "authors": [ "Jeremy Tan Jie Rui" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:43dec076e3f2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(GroupTheory): remove some more `set_option`s (#43439)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/43dec076e3f271960eae3c968776c8b954e99a52" }, { "age_days": 0, "authors": [ "Harald Husum" ], "content_date": "2026-09-07", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:cbe65a92231a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-07", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Data): fix typos (#43181)", "updated": "2026-09-07", "url": "https://github.com/leanprover-community/mathlib4/commit/cbe65a92231a23c45c323ca8c23db6b677e43ceb" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-09-05", "freshness": "fresh", "id": "github:leanprover/lean4:5549307b4a93", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: apply `moreServerOptions` to package modules (#15042)", "updated": "2026-09-05", "url": "https://github.com/leanprover/lean4/commit/5549307b4a93889ed1cb48d7436a2d02df8bf62a" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-09-05", "freshness": "fresh", "id": "github:leanprover/lean4:c155094f54ea", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-05", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: `precompileLibrary` & `precompileImports` (#15015)", "updated": "2026-09-05", "url": "https://github.com/leanprover/lean4/commit/c155094f54eab345cca3da867dbd888a34fbf0d2" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:caeb31af36e8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: move more rarely-updated `Core.Context` field into the cold subobject (#15017)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/caeb31af36e85816478690002640bb99803c7d14" }, { "age_days": 3, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:d54b02f2c0f4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: remove withPosition in `macro` and `elab` (#15019)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/d54b02f2c0f475431ed0a94b5412dc57fc39ace6" }, { "age_days": 3, "authors": [ "Marc Huisinga" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:9de86005af50", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: register missing builtin node kinds (#15030)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/9de86005af5061b5ccf438d01134ee6d3ecea6b3" }, { "age_days": 3, "authors": [ "Wojciech Różowski" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:67526ae54d73", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: introduce `findMatchingDecl?` for code quality checks in `Lean.Linter` (#14880)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/67526ae54d733251644d5cebb9fa5a77318fecc4" }, { "age_days": 3, "authors": [ "Marcus Rossel" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:3dfca7a8d139", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add a `Decidable` instance for `bif` (`cond`) (#15018)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/3dfca7a8d1392b0d0f38261f78be0db28a1d9c23" }, { "age_days": 3, "authors": [ "Garmelon" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:dc3f80b6d501", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: set up downstream-force label (#15021)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/dc3f80b6d5014f20d4419b3561436d8206666e46" }, { "age_days": 3, "authors": [ "Garmelon" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:1f2b22be1d94", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: measure instructions:u and cycles:u (#15007)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/1f2b22be1d9437b1a35d1fd6a550961e18dbc17f" }, { "age_days": 3, "authors": [ "Garmelon" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "github:leanprover/lean4:a7a70895d565", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-04", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: fix downstream-force label (#15028)", "updated": "2026-09-04", "url": "https://github.com/leanprover/lean4/commit/a7a70895d56519603980c39c23ed808fbc06e1cc" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "github:leanprover/lean4:ed9ac0991b23", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: heartbeat and theap in one thread-local (#14982)", "updated": "2026-09-03", "url": "https://github.com/leanprover/lean4/commit/ed9ac0991b23a6acc530aa3592a6c4f7c905a9a5" }, { "age_days": 4, "authors": [ "Robert Joseph" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "github:leanprover/lean4:37cf1eab12d4", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add intersection emptiness symmetry lemmas (#14794)", "updated": "2026-09-03", "url": "https://github.com/leanprover/lean4/commit/37cf1eab12d49238a8e004112e5e44365eb874db" }, { "age_days": 4, "authors": [ "Garmelon" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "github:leanprover/lean4:587744298655", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: tweak adaptation PR \"waiting for CI\" message (#14999)", "updated": "2026-09-03", "url": "https://github.com/leanprover/lean4/commit/58774429865502f05c63239266aac30ef1e91ef7" }, { "age_days": 4, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "github:leanprover/lean4:137a88d9d363", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-03", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: remove `LEAN_LAZY_RC` (#15006)", "updated": "2026-09-03", "url": "https://github.com/leanprover/lean4/commit/137a88d9d363d6f0c60de75d4cef02a26f38962e" }, { "age_days": 5, "authors": [ "Robin Arnez" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "github:leanprover/lean4:19c79593c47b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: allow disabling termination warnings when using `addPreDefinitions` (#14912)", "updated": "2026-09-02", "url": "https://github.com/leanprover/lean4/commit/19c79593c47bb8dd3371327c08fc80775d8488af" }, { "age_days": 5, "authors": [ "Kim Morrison" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "github:leanprover/lean4:6778cc834279", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add List.mergeSort_append and List.mergeSort_pair (#14995)", "updated": "2026-09-02", "url": "https://github.com/leanprover/lean4/commit/6778cc8342791e48cc5b8aa6243ce16e2bed582b" }, { "age_days": 5, "authors": [ "Julien Cretin" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "github:leanprover/lean4:c632a0a0e434", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: doc: fix typo in the doc example of List.lex (#14987)", "updated": "2026-09-02", "url": "https://github.com/leanprover/lean4/commit/c632a0a0e434a951cdcf61bb4da3344abadd5587" }, { "age_days": 5, "authors": [ "Kim Morrison" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "github:leanprover/lean4:3facd362febf", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-02", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: forbid process narrative in PR descriptions in CLAUDE.md (#14997)", "updated": "2026-09-02", "url": "https://github.com/leanprover/lean4/commit/3facd362febfedef5d1711297f541806a51abe1a" }, { "age_days": 6, "authors": [ "Aaron Liu" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "github:leanprover/lean4:552755077915", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: swap names of `Dyadic.not_lt` and `Dyadic.not_le` (#14890)", "updated": "2026-09-01", "url": "https://github.com/leanprover/lean4/commit/552755077915ae65e0740ecd1aee3ac9a0de0757" }, { "age_days": 6, "authors": [ "Yoshiya Hinosawa" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "github:leanprover/lean4:0f523461d7a0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-09-01", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update actions/checkout in lake new template (#14984)", "updated": "2026-09-01", "url": "https://github.com/leanprover/lean4/commit/0f523461d7a0b12e7ab76e86d8cab60c362af9ef" }, { "age_days": 7, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "github:leanprover/lean4:1e67d51928ad", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: perf: avoid `setTransparency` when the transparency is already in effect (#14967)", "updated": "2026-08-31", "url": "https://github.com/leanprover/lean4/commit/1e67d51928ad6394f643c32fb36b222e03fcee48" }, { "age_days": 7, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "github:leanprover/lean4:c8e19cca2547", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: use the correct calling convention when over-applying a closure in `lean_apply_m` (#14969)", "updated": "2026-08-31", "url": "https://github.com/leanprover/lean4/commit/c8e19cca2547a89c3aba401afaab9a8808f490a2" }, { "age_days": 7, "authors": [ "Siddharth" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "github:leanprover/lean4:138ca9f20763", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: characterize when T-division equals zero (#8204)", "updated": "2026-08-31", "url": "https://github.com/leanprover/lean4/commit/138ca9f20763523c4093baa092cf371e89535098" }, { "age_days": 7, "authors": [ "Kitamado" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "github:leanprover/lean4:f0b9e56cd455", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `Repr` instance for `Vector` (#14545)", "updated": "2026-08-31", "url": "https://github.com/leanprover/lean4/commit/f0b9e56cd4556b014e13f8b121eda8d9c922c73d" }, { "age_days": 7, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "github:leanprover/lean4:0e6944a82599", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-31", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-08-31", "url": "https://github.com/leanprover/lean4/commit/0e6944a825993b20d0834f2f825a3439bad58515" }, { "age_days": 8, "authors": [ "Henrik Böving" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "github:leanprover/lean4:2a5b1a2f7ec5", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: more primitives for challenge (#14972)", "updated": "2026-08-30", "url": "https://github.com/leanprover/lean4/commit/2a5b1a2f7ec519ab9f6196acd8c8e735c7e5a2b2" }, { "age_days": 8, "authors": [ "Kyle Miller" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "github:leanprover/lean4:ac0f56e6f6c8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-30", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: app elaborator infotrees should have context when there is ambiguity (#13815)", "updated": "2026-08-30", "url": "https://github.com/leanprover/lean4/commit/ac0f56e6f6c8022a0b8df4ffd0738bc20723e1ef" }, { "age_days": 9, "authors": [ "Kyle Miller" ], "content_date": "2026-08-29", "freshness": "fresh", "id": "github:leanprover/lean4:e5b02e920133", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-29", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: completions for `@[delab app.foo]` attribute (#14971)", "updated": "2026-08-29", "url": "https://github.com/leanprover/lean4/commit/e5b02e92013389c07722c7f86c4069387a343741" }, { "age_days": 3, "arxiv_id": "2609.05386", "authors": [ "Jan Snellman" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.05386", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "For $2 \\times 2$ matrices $A_1,\\dots,A_k$, write $[A_1,\\dots,A_k]$ for the left-normed iterated commutator $[\\dots[[A_1,A_2],A_3],\\dots,A_k]$, and $I_k$ for the ideal, in the $3k$-variable reduced-coordinate polynomial ring $R_k$, cutting out its vanishing locus. We prove, for every $k \\geq 2$ over any field of characteristic $\\neq 2$, and as four independently-established results rather than one bundled claim: $I_k$ has codimension 2; $I_k$ has exactly 3 minimal generators; $R_k / I_k$ is Cohen-Macaulay; and $I_k$ is radical. The last of these, together with an explicit component count resting on a non-containment argument, assembles into the Primary Decomposition Theorem: $I_k = P_2 \\cap \\cdots \\cap P_k$ is an irredundant primary decomposition into exactly $k-1$ primes, following an explicit recursive block-involvement pattern. The proof identifies $I_k$ as the ideal of $2 \\times 2$ minors of an explicit $2 \\times 3$ matrix (a determinantal ideal, not merely one that looks determinantal), and invokes classical determinantal-ideal theory (Bruns-Vetter) and an explicit rank-2 Jacobian witness on every component (Serre's criterion) for the algebraic and radicality halves respectively.", "title": "The coordinate ring of the k-fold iterated commutator locus for 2x2 matrices", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.05386" }, { "age_days": 3, "arxiv_id": "2609.04898", "authors": [ "Aziz Ben Amor", "Drish Mali", "Mann Acharya", "Vijayasri Iyer", "Sébastien Bratières" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.04898", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Repository-scale refactoring requires coding agents to propagate a single change across many interdependent files without altering program behavior, yet to our knowledge no existing harness isolates the design choices that determine agent success on this task. We present RefactorPlatform, an open-source evaluation harness that holds the environment fixed and varies each design axis explicitly: model backbone (via OpenRouter and GitHub Copilot CLI), execution regime (baseline, retrieval-augmented, and multi-agent), and prompt specificity. Each run executes in an isolated workspace with live terminal streaming, per-task logging of tokens, diffs, and transcripts, AST-based verification, and exportable telemetry for audit and reproduction. Demonstrating the platform on 100 multi-file RefactorBench tasks across four model families, we illustrate the analyses it supports: AST-aware chunking outperforms naive token-window chunking by 25-30% across prompt modes, whereas naive retrieval falls below the retrieval-free baseline; a lean retrieval-augmented single agent (86%) beats the sub-agent configuration we evaluated (66%) on matched tasks with no task passing under delegation that fails under retrieval; and retrieval's accuracy gains absorb its token overhead, leaving cost per successful refactoring unchanged. RefactorPlatform is open-sourced to make refactoring-agent evaluation reproducible and auditable.", "title": "RefactorPlatform: An Open-Source Harness for Controlled Evaluation of Repository-Scale Refactoring Agents", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.04898" }, { "age_days": 3, "arxiv_id": "2609.04591", "authors": [ "Zhipeng Deng" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.04591", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle \\[ T=\\text{conv}\\{(-c,0),(c,0),(0,s)\\},\\qquad s=\\frac{766}{\\sqrt{625565}},\\qquad c=\\frac{197}{\\sqrt{625565}}. \\] The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected $Λ$-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy $\\|R\\|<27131/25000$. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally \\[ E(T)\\ge D:=\\frac{82074390584}{84861020075} =0.9671624323094728\\ldots \\] Hence, the convex universal cover of Moser's worm \\[ \\frac{\\text{area}(T)}{D^2} =\\frac{11511821678274125}{44639604443512928} =0.257883595112076188\\ldots. \\]", "title": "Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.04591" }, { "age_days": 3, "arxiv_id": "2609.05005", "authors": [ "Jineon Baek", "Byung-Hak Hwang", "Joonhyun La", "Hongseok Yang" ], "content_date": "2026-09-04", "freshness": "fresh", "id": "arxiv:2609.05005", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-04", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Algebraic combinatorics often seeks bijections that explain identities between distributions object by object. Encoding combinatorial objects as words lets automata theory study such a bijection as a word-to-word computation and measure its memory, input access, and control of output order. This refines existence questions by asking which computational mechanisms a bijection requires. We develop this viewpoint for Dyck paths. Our motivating example is the $q,t$-Catalan polynomial. Let $D_n$ be the set of Dyck paths of semilength $n$, let $D=\\bigcup_{n\\ge 0}D_n$, and let $area, dinv, bounce \\colon D\\to\\mathbb{N}$ be the standard statistics. Then, \\[ C_n(q,t)=\\sum_{P\\in D_n}q^{area(P)}t^{bounce(P)} =\\sum_{P\\in D_n}q^{dinv(P)}t^{area(P)}. \\] Haglund's zeta map $ζ\\colon D\\to D$ gives a bijective proof: it preserves semilength and sends $(dinv,area)$ to $(area,bounce)$. By contrast, the full symmetry $C_n(q,t)=C_n(t,q)$ still lacks a direct explanation: no explicit, uniform, semilength-preserving bijection is known that swaps area and dinv on every Dyck path. Polyregular maps from automata theory provide a natural computational starting point, but we prove that neither $ζ$ nor the classical height-sweep bijection witnessing Narayana symmetry is polyregular. The missing mechanism is global ordering by numerical levels whose range grows with the input. We call this a \\emph{rank sort} and introduce \\emph{weighted-rank polyregular maps} (WRP), extending polyregular maps by one such sort and containing both bijections. Nevertheless, WRP is a proper subclass of deterministic logspace. We prove that $ζ^{-1}$ lies outside WRP and that no WRP map can realise a semilength-preserving area-dinv swap. Thus the rank-sorting strategy behind $ζ$ cannot be extended within WRP to exchange the two statistics.", "title": "A Computational Obstruction to Swapping Area and Dinv: An Automata-Theoretic View of the $q,t$-Catalan Symmetry", "updated": "2026-09-04", "url": "https://arxiv.org/abs/2609.05005" }, { "age_days": 4, "arxiv_id": "2609.04481", "authors": [ "Pietro Coretto" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "arxiv:2609.04481", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-03", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "The computational revolution is advancing at an unprecedented pace. The combination of proof-assistant technologies and generative AI tools has recently enabled the solution of complex problems in pure mathematics at a scale that seemed unattainable only a few years ago. However, these technologies have not yet become standard tools in the development of statistical theory. In this paper, we do not present new theoretical results. Instead, we discuss five case studies involving classical problems in statistics and describe how they can be analyzed using a machine proof-checking. Our goal is not to propose a definitive workflow, but to stimulate reflection on how these technologies may transform theoretical research and advanced statistical education. We focus on two main aspects. First, statistical theory often compresses substantial mathematical content into expressions such as \"under the usual regularity conditions\". Formalization in a machine-verifiable language forces each assumption to be explicit, reveal hidden dependencies, and provide a deeper understanding of the formalized objects. Second, we argue that the statistical community could benefit from a collaborative effort to build repositories of formalized axioms, definitions, and theorems, supporting more precise and reliable theoretical developments. Finally, we discuss the role of these tools in graduate education. Just as high-level programming languages revolutionized empirical research by enabling rapid experimentation and prototyping, machine-assisted formalization may introduce a new paradigm for the development, verification, and communication of statistical theory.", "title": "Statistical Theory in the Age of Machine-Assisted Mathematics: Rethinking How Theory Is Made and Taught", "updated": "2026-09-03", "url": "https://arxiv.org/abs/2609.04481" }, { "age_days": 4, "arxiv_id": "2609.04076", "authors": [ "Wladimir Silva" ], "content_date": "2026-09-03", "freshness": "fresh", "id": "arxiv:2609.04076", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-03", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We present an operator-decomposition architecture that mathematically maps a global operator into independently executable local operators, reducing the maximum quantum circuit depth at the cost of classical reconstruction and sampling overhead. By framing complex Quantum Circuits around an operator in a vector space that can be algebraically pre-decomposed, AOD complements quantum error correction and error-mitigation approaches by performing algebraic decomposition before quantum execution. Our approach leans in the computer science definition of a Monoid: a design pattern and mathematical concept consisting of a data type, a combining function that is associative, and a safe identity (neutral) element that does not change other values when combined. Simulation wise we define a MapReduce programming model where the addition (+) is the reducer, thus leveraging a naturally stable commutative monoid which carries zero \"negative-probability tax\" or phase conflicts. Furthermore, we define a Vector Space of Linear Operators over Additive Abelian Groups that benefit from this paradigm, including: Inner Products, Series expansions, Traces and Convolutions. Finally, we present the mathematical foundations and simulation results for this paradigm.", "title": "Algebraic Operator Decomposition: A Partitioned Architecture for Noise-Resilient Quantum Computing", "updated": "2026-09-03", "url": "https://arxiv.org/abs/2609.04076" }, { "age_days": 5, "arxiv_id": "2609.02156", "authors": [ "Yechi Zhou" ], "content_date": "2026-09-02", "freshness": "fresh", "id": "arxiv:2609.02156", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-02", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We solve the Euclidean-ball case of the higher-dimensional Shepp covering problem. More precisely, we give an exact criterion for full limsup coverage of the $d$-dimensional torus, $d\\ge 2$, by independently centered Euclidean balls with an arbitrary decreasing sequence of radii. Let $X_1,X_2,\\ldots$ be independent Haar-uniform points, let $r_1\\ge r_2\\ge\\cdots\\downarrow 0$, and put $u_n(z)=m(B(0,r_n)\\cap B(z,r_n))$ and $H(z)=\\sum_{n\\ge 1}u_n(z)$. Then every point belongs to infinitely many of the balls $B(X_n,r_n)$ almost surely if and only if $\\int_{\\mathbb{T}^d}\\exp(H) dm=\\infty$. In dimension one this condition is equivalent to Shepp's criterion. No regular-variation or comparable-scale assumption is imposed on the radii. The main difficulty is shared noise: after spatial decomposition, the same Poisson input acts on many uncovered cells, so their descendants are not conditionally independent. We overcome this by establishing an extinction bound for monotone population recursions driven by positively associated innovations. Together with Poissonization and spatial localization this proves sufficiency, while a second-moment estimate and the zero-one law prove necessity.", "title": "The higher-dimensional Shepp problem: an exact criterion for random ball coverings of tori", "updated": "2026-09-02", "url": "https://arxiv.org/abs/2609.02156" }, { "age_days": 6, "arxiv_id": "2609.00579", "authors": [ "Lara Marinov", "Aditya Thimmaiah", "Jayanth Srinivasa", "Junyi Jessy Li", "Milos Gligoric" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "arxiv:2609.00579", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-01", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) have shown proficiency in various software engineering tasks, such as code generation and translation. However, a key limitation in their performance may be their (lack of) understanding of programming-language semantics. Even when explicit semantics are given, it remains unclear whether LLMs apply those rules or lean on priors learned during pre-training instead. We study if LLMs lean on priors or given semantics with a novel task--Program Executability Prediction (PrEx)--that asks models to predict whether a program is semantically valid or invalid (and, if invalid, which formal rule it violates) given the program's syntax and operational semantics. Because PrEx requires both valid and invalid programs, we build a dataset with systematically generated invalid transformations derived from valid programs. We evaluate open-source coding LLMs under two semantic formalisms and two semantic shifts across Human-Written, LLM-Translated, and Fuzzer-Generated program splits. Our findings show that LLMs lean on pre-training priors rather than systematically applying the given rules, performing especially poorly on modified semantics and degrading further as program complexity increases. PrEx is available at https://github.com/EngineeringSoftware/prex.", "title": "Predicting Program Exit Code with LLMs and Programming Language Semantics", "updated": "2026-09-01", "url": "https://arxiv.org/abs/2609.00579" }, { "age_days": 6, "arxiv_id": "2609.00614", "authors": [ "Peter J. Waddell" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "arxiv:2609.00614", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-01", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Like pairwise distances, quartets can be highly redundant and correlated on a phylogenetic tree, and their number grows on the order of n^4 rather than n^2. I explore BME-like weights for reweighting quartet scores before summing them to score a full tree. Three weights are considered on an unrooted binary tree: w_ext(q)=2^(-I_ext(q)), w_int(q)=2^(-I_int(q)), and w_tot(q)=2^(-I_tot(q))=w_ext(q)w_int(q), where the exponents count specified internal nodes in the minimal connecting subtree of a quartet. Exact tree-shape counts, total quartet-weight sums, and internal-edge crossing sums are calculated for all unlabeled unrooted binary tree shapes on 6-10 taxa. For w_ext, the total quartet weight is tree-shape-invariant and the edge-crossing sum depends only on split size. For any n-leaf tree, we prove sum_q w_ext(q)=(n-2)(n-3)/8, and the sum over quartets crossing an internal edge with split a|b equals (a-1)(b-1)/4. Exact tree-shape-specific normalizers are also derived for w_int and w_tot. A degree-corrected hard-polytomy extension is given for multifurcating trees, and a conditional consistency result shows that these positive weights preserve consistency when the underlying quartet estimates are themselves consistent for the true induced quartet states. These results provide a mathematical foundation for evaluating and applying BME-like quartet weights to reduce redundancy with the particular aim of improving statistical efficiency with finite data.", "title": "BME-like Quartet Weights for Phylogenetic Trees", "updated": "2026-09-01", "url": "https://arxiv.org/abs/2609.00614" }, { "age_days": 6, "arxiv_id": "2609.01766", "authors": [ "Stijn Cambie", "Erik Kalviainen" ], "content_date": "2026-09-01", "freshness": "fresh", "id": "arxiv:2609.01766", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-09-01", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We construct an infinite walk in $\\mathbb{Z}^3$ whose steps come from a fixed set of sixteen vectors and no three of whose vertices are collinear, answering a problem of Gerver and Ramsey popularized as Erdős Problem 193.", "title": "An infinite small-step $\\mathbb Z^3$-walk with no collinear triple", "updated": "2026-09-01", "url": "https://arxiv.org/abs/2609.01766" }, { "age_days": 7, "arxiv_id": "2609.00313", "authors": [ "Rohan Pandey", "Sunjae Kwon", "Hong Yu" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "arxiv:2609.00313", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-31", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Scientific discovery depends on finding prior literature that shapes what comes next. Existing retrieval systems optimize for relevance and popularity, often favoring central papers over less familiar works that later prove generative. We introduce \\textbf{MUSES}, a million-instance benchmark for prospective intellectual-roots retrieval over a fixed 2.33M-paper corpus, with roughly 140K test instances per familiarity tier. To our knowledge, it is the first prospective benchmark at this scale with a shared retrieval task and author-confirmed paper-level root labels. Alongside it, \\textbf{CiteRoots} pairs a scalable rhetorical layer over local citation text (LLM judge $κ= 0.896$ versus human gold) with a paper-level author-endorsed layer ($n = 1{,}518$ generative-inspiration pairs from 753 focal papers). MUSES organizes difficulty along two axes: a \\emph{familiarity} axis spanning CiteNext, CiteNew, and CiteNew-Isolated, and a \\emph{functional} axis spanning broad citations, rhetorical roots, and author-endorsed roots. Across 9 method classes, a lean multi-centroid retriever built on SPECTER2 is strongest. Hit@100 falls from 0.534 on CiteNext to 0.424 on CiteNew, 0.205 on rhetorical CiteNew, and 0.171 on author-endorsed CiteNew, a $3.1\\times$ decline. In a registered eight-lens full-test audit, roughly half of broad-tier test instances remain unsolved at K=1{,}000. Rhetorical role and author endorsement are distinct: the same judge agrees with endorsement at $κ= 0.037$. We release MUSES, both CiteRoots layers, and a distilled open companion judge for future work on prospective retrieval and intellectual roots.", "title": "MUSES: A Benchmark for Prospective Intellectual-Roots Retrieval", "updated": "2026-08-31", "url": "https://arxiv.org/abs/2609.00313" }, { "age_days": 7, "arxiv_id": "2608.30604", "authors": [ "Samuil Petkov" ], "content_date": "2026-08-31", "freshness": "fresh", "id": "arxiv:2608.30604", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-31", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Let $ζ(G)$ denote the minimum number of parts in a partition of $V(G)$ in which every part induces either a clique or an independent set. Erdős and Gimbel asked whether, for $G_n\\sim G(n,1/2)$, the difference $χ(G_n)-ζ(G_n)$ tends to infinity with high probability. We resolve this problem along the full sequence $n\\to\\infty$ and prove that $\\mathbb P(χ(G_n)-ζ(G_n)\\ge ((\\log 2)^2/4)\\log(200/153)\\,n/(\\log n)^3)\\to1$. This gives a lower bound at the conjectured scale $n/(\\log n)^3$. We also obtain a phase-resolved refinement: if $δ_n$ is the fractional part of the standard independence-number center, then the coefficient may be replaced by $(\\log 2)^2A_4(δ_n)/4-o(1)$, where $A_4$ is explicit, continuous, nonconstant, and satisfies $A_4(δ)>\\log(200/153)$ for every $δ\\in[0,1]$. The proof uses signed cocoloring profiles supported on four consecutive class sizes and remains uniform across jumps of the natural class-size cutoff. An exact signed-overlap identity separates local cell rewards from a binary cycle-space factor. A canonical decomposition into high cells and a capped residual matching, together with an endpoint-table comparison and an injective restriction of residual even edge sets, yields the required second-moment bound. A bounded-differences argument then amplifies the resulting rare signed witness to a high-probability cocoloring.", "title": "A Full-Sequence Quantitative Gap Between the Chromatic and Cochromatic Numbers of a Random Graph", "updated": "2026-08-31", "url": "https://arxiv.org/abs/2608.30604" }, { "age_days": 8, "arxiv_id": "2608.29734", "authors": [ "Jef Pauwels" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "arxiv:2608.29734", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "In 2010, Pál and Vértesi found a family of finite-dimensional strategies for the $I_{3322}$ Bell inequality whose optimized values appeared to converge as the local Hilbert-space dimension grew. They conjectured that this limit is the supremum over all finite-dimensional quantum strategies, but that no finite-dimensional strategy attains it. We prove both claims. The proof uses the symmetry of the Bell functional to associate every strategy with a finite matrix of probabilities, one for each pair of spectral subspaces of Alice and Bob. This matrix gives an upper bound on the Bell value, and finite-dimensional strategies built from the repeating structure found by Pál and Vértesi approach it as the dimension grows. If the bound were attained exactly in finite dimension, the optimality conditions would then require a state that cannot be normalized. Consequently, the set of finite-dimensional quantum correlations is not closed in the $(3,3,2,2)$ scenario, the smallest Bell scenario where this can happen. Moreover, approaching the supremum requires unbounded local dimension. The core of the proof was formalized in Lean~4.", "title": "The quantum supremum of the $I_{3322}$ Bell inequality is not attained in finite dimension", "updated": "2026-08-30", "url": "https://arxiv.org/abs/2608.29734" }, { "age_days": 8, "arxiv_id": "2608.29496", "authors": [ "Nadejda Drenska", "Matthew Lemoine", "Gowri Priya Sunkara", "Yu Wang", "Sri Lakshmi Sravani Devarakonda", "Steven B. Heymsfield" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "arxiv:2608.29496", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Accurate estimation of body-composition outcomes, including body fat percentage (BFP), bone mineral density (BMD), and appendicular lean mass (ALM), is important for evaluating metabolic, skeletal, and muscular health. Direct assessment using dual-energy X-ray absorptiometry (DXA), however, requires specialized equipment and involves ionizing radiation. We propose a target-aware, state-adaptive $p$-Dirichlet energy-flow graph neural regression ($p$SADE-GNR) framework for estimating these outcomes from non-invasive anthropometric measurements. A neural encoder maps participant representations to hidden states that are propagated over an outcome-specific participant-similarity graph by a state-adaptive forward-Euler discretization of the graph $p$-Dirichlet energy flow. Graph distances weight each original or latent coordinate by its normalized absolute training-fold correlation with the outcome. Using clinical data from the Pennington Biomedical Research Center and five-fold cross-validation, the correlation-weighted model using the original standardized measurements achieved the lowest root mean squared error in all nine primary outcome-cohort combinations and outperformed previously reported support vector regression or least-squares support vector regression reference values in eight of nine comparisons. Autoencoder, variational-autoencoder, and Gaussian-mixture variational-autoencoder representations generally did not improve primary-outcome prediction or reduce computational cost. In an exploratory age-prediction analysis including ALM, BMD, and BFP as predictors, the correlation-weighted GMVAE model achieved the lowest mean error in all three cohorts. These results support target-aware, state-adaptive $p$-Dirichlet graph neural regression for non-invasive body-composition estimation.", "title": "Target-Aware State-Adaptive $p$-Dirichlet Graph Neural Regression for Non-Invasive Body-Composition Estimation", "updated": "2026-08-30", "url": "https://arxiv.org/abs/2608.29496" }, { "age_days": 8, "arxiv_id": "2609.00062", "authors": [ "Xiyuan Zhou", "Zhuoqi Li", "Xinlei Wang", "Yirui He", "Yuhao Wu", "Yuheng Cheng", "Yan Xu", "Junhua Zhao", "Jinjin Gu" ], "content_date": "2026-08-30", "freshness": "fresh", "id": "arxiv:2609.00062", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-30", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Data contamination undermines the reliable evaluation of large language models (LLMs) on mathematical problem solving. While rewriting-based evaluation mitigates memorization, existing methods lack guarantees of problem validity and answer correctness. We propose Proof-Verified Benchmark Rewriting (RePro), the first framework to integrate Lean-oriented neural automated theorem provers (ATPs) into benchmark rewriting, which rewrites problems and regenerates answers with correctness ensured by Lean-verified proofs. Experiments on GSM8K and MATH show that RePro's retained rewritten instances achieve 100% well-definedness, feasibility, and answer correctness, while existing methods still produce invalid or incorrect instances. Moreover, several models exhibit accuracy drops on proof-verified rewritten benchmarks, suggesting that their performance is sensitive to surface-level and structural variations and may partly reflect memorization effects. Our source code and data are available at https://github.com/AI4Engi/RePro.", "title": "RePro: Proof-Verified Benchmark Rewriting for Reliable Evaluation of LLM Mathematical Problem Solving", "updated": "2026-08-30", "url": "https://arxiv.org/abs/2609.00062" }, { "age_days": 9, "arxiv_id": "2608.29391", "authors": [ "George Xi Wang", "Henghao Li", "Shan Lin", "Yunge Wen", "Jiaqian Hu", "Yuhua Jin" ], "content_date": "2026-08-29", "freshness": "fresh", "id": "arxiv:2608.29391", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-29", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Floating things invite touch. We present Feelium, a blimp-based telepresence platform that enables visual embodiment and touch interaction through its inflatable skin. Through a VR headset, a remote person inhabits the blimp, looking out of it first-person, appearing on its skin as a face or avatar, and steering it through the room. Partners in the room pat it, press a palm against it, draw on it, or lean into it; the skin senses each contact, renders it into the wearer's view in VR spaces. Touch thus provides a physical interaction channel for remote presence, turning the skin into a shared surface between remote and co-located partners.", "title": "Feelium: A Touchable Blimp Body for Aerial Telepresence", "updated": "2026-08-29", "url": "https://arxiv.org/abs/2608.29391" }, { "age_days": 10, "arxiv_id": "2608.28541", "authors": [ "Javier Aguilar Martín" ], "content_date": "2026-08-28", "freshness": "fresh", "id": "arxiv:2608.28541", "kind": "paper", "label": "negative", "matched_signals": [ "negative:vision_world_models", "tool_use_agents" ], "published": "2026-08-28", "score": -1.1, "source": "arxiv-ai4math-core", "summary": "A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. We characterize what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. The gate quotient makes the question precise: acceptance-with-certainty determines the model exactly on the reachable query set; beyond reach is gauge. On a minimal ring instrument we prove the extreme case (a wrong-topology filled-disc artifact unfalsifiable by any sampling gate and bitwise harmless at play) and measure, with LLM synthesis across three model families, how one knob (a channel of width gamma) walks the same artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified. Three principles organize the empirics. First, danger is topology relative to reach: a channel the planner can use collapses the blind model's exploitation (play cost 1.09 to ~0 over a knee at gamma ~ 0.1), while a hidden channel with the same first Betti number keeps it at full strength (1.12). Second, repair is parameter-bound and sensor-bound: no family recovers the region from outside evidence; from inside, models pose the right topology but cannot pin its parameters, and the posed topology tracks the guiding persistent-homology summary's wrong beta_1 (a sensor with a measured geometric resolution limit), not the truth. Third, mitigation must match the error's dimension and direction: point fences fail against the one-dimensional boundary, a dimension-matched persisted fence collapses exploitation to a two-lesson transient (0.999 to 0.058), and the dual freedom certificate collapses the invented-mode failure symmetrically (1.769 to 0.029). In n dimensions the shell makes misidentification near-certain while the danger stays fully exploitable: the two axes are independent.", "title": "An Enclosed Mode Is a Gauge Choice: Topology Relative to Reach in Certified Code World Models", "updated": "2026-08-28", "url": "https://arxiv.org/abs/2608.28541" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }