{ "counts": { "adjacent": 15, "core": 3, "errors": 0, "negative": 68, "total": 86 }, "date": "2026-08-23", "errors": [], "fresh_content_days": 21, "generated_at": "2026-08-23T15:49:10Z", "items": [ { "age_days": 8, "arxiv_id": "2608.15432", "authors": [ "Tadd Mao", "Tianjun Zhong", "Dhruva Arekar", "Yuming Feng", "One An", "Jiani Huang", "Xujie Si", "Ziyang Li" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.15432", "kind": "paper", "label": "core", "matched_signals": [ "autoformalization", "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-15", "score": 12.5, "source": "arxiv-ai4math-core", "summary": "In formal verification, both the autoformalization of statements and automated proof search have been studied extensively. While automated proof search can produce a formal proof that compiles, the generated proof does not necessarily reflect how the natural-language argument arrives at its conclusion--a property we refer to as faithfulness. With faithfully formalized proofs, one can check the reasoning behind a human- or AI-written argument, and assist mathematicians in formalizing their proof sketches. However, it is particularly challenging due to misalignment of formal proof tactics and natural language reasoning. In this work, we rigorously describe a set of five necessary conditions a faithful formal proof must satisfy, and introduce Pistis, an agentic, oracle-guided proof search that produces formal Lean proofs that satisfy them. At its core is a novel faithfulness-preserving divide-and-conquer search, which we name OrderDecompose, that tracks citation dependencies and blocks unfaithful shortcuts, paired with a refutation search, that surfaces gaps and errors in the natural language proof source. OrderDecompose completes proofs that baselines cannot close even within a 12-hour budget, and its artifacts compile over 33$\\times$ as fast as prior work's. We apply Pistis on the first three books of Euclid's Elements, producing high-quality artifacts containing faithful formal proofs. Under a blinded human study and an LLM-as-a-judge protocol on rigorous rubrics, Pistis-generated proofs are favored over prior works--2.89$\\times$ and 5.2$\\times$ as often by human reviewers and the LLM judge, respectively. It further uncovers gaps in Euclid's proofs and their translation, and can accept or refute natural language proofs written by humans or AI, demonstrating that faithful formalization is useful as a proof-checking tool.", "title": "Does the Proof Prove It That Way? Faithful Formalization of Elements Proofs", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.15432" }, { "age_days": 4, "arxiv_id": "2608.19009", "authors": [ "Yajie Yin" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.19009", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents", "verifier_guided_reasoning" ], "published": "2026-08-19", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors. Yet the verification literature uses the word \"level\" to mean at least five different things: verification granularity, concept abstraction, risk tier, system-stack layer, and the epistemic source of the ground truth. We propose Verification Autonomy Levels (VAL), a meta-standard that classifies any verification scheme along a single axis: where does the verification spec come from, and what does the verdict guarantee? VAL ranges from L0 (LLM self-declaration; no deterministic anchor) through L2 (objective ground truth; correctness only) to L3/L4 (decidable systems with single-property or domain-level completeness), with L5 impossible in the unrestricted case. Central to VAL is the completeness blind spot: substitution- and sampling-based verifiers can confirm that proposed candidates hold, but cannot prove that no candidate was missed. We further identify a dichotomy the literature has not stated: completeness is reachable only for formally specifiable properties, whereas empirical open-world verification (fact-checking, diagnosis) caps at anchored correctness (L2). We document this gap empirically across four domains (symbolic mathematics, behavior monitoring, medical diagnosis, and code generation, the last a reverse validation with predictions stated before evidence) and in the strongest formal-verification baseline in our survey, whose authors note the verifier focuses on the correctness of each step. We show the levels of granularity, concept hierarchy, risk, and system stack are orthogonal to VAL, resolving a systematic conflation across 17 surveyed papers. Code and full assessment are released as supplementary material.", "title": "Grading the Graders: Verification Autonomy Levels (L0-L5) for LLM Reasoning", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.19009" }, { "age_days": 8, "arxiv_id": "2608.16947", "authors": [ "Ian D'Ambrosio" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.16947", "kind": "paper", "label": "core", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-15", "score": 6.5, "source": "arxiv-ai4math-core", "summary": "Huang, Lou, and Xiao introduced Dynamic Mixture-of-Experts Serving and gave an O(sqrt(log k))-competitive randomized algorithm for its integral primal problem, where k is the number of replica GPUs beyond the mandatory copy of each expert. Their matching lower barrier applies to an auxiliary dual and leaves the primal order open. We prove that the randomized primal competitive ratio is in fact Theta(1) for arbitrary numbers of experts. The upper bound reduces reciprocal-max service costs to chasing positive bodies with covering row sparsity two. A finite tangent envelope approximates each reciprocal epigraph within a constant factor, summable positive resets convert accumulated service into movement, and a nonexpansive balanced projection removes the positive-body algorithm's resource augmentation. Combining the resulting fractional path with Lazy Threshold Rounding gives E[ALG] <= 10 C_PB OPT + (5 C_PB + 2) k + 16, where C_PB is the absolute constant from Chasing Positive Bodies at resource augmentation one and covering sparsity two. The full reduction, rounding composition, and quantified main theorem are machine-checked in Lean 4 relative to exact formal interfaces for the two cited source theorems. Deterministic rational controls and a fresh independent replay accompany the formal proof.", "title": "A Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.16947" }, { "age_days": 4, "arxiv_id": "2608.19093", "authors": [ "Mengwei Su", "Kaiwen Yang", "Hao Xu", "Chih-Lin I" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.19093", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning", "lean_formal_proving_agents" ], "published": "2026-08-19", "score": 4.9, "source": "arxiv-ai4math-core", "summary": "Among $n+1$ equiprobable equal-energy signals in $\\R^n$ under additive white Gaussian noise with maximum-likelihood decoding, which arrangement maximizes the probability of correct decoding? The question is Shannon's, recorded by Rice in 1950. Mulgund proved in 2026 that the regular-simplex value bounds the correct-decoding probability of every signal set at every signal-to-noise ratio, leaving open whether the simplex is the only maximizer. This paper determines the equality cases in a form stronger than uniqueness. A signal set other than a regular simplex falls strictly below the bound at every positive signal-to-noise ratio. Hence a code meeting the bound at one positive operating point is already a regular simplex, up to vertex relabeling and an orthogonal map. In probabilistic form, among the correlation matrices that signal sets induce, any matrix other than the identity gives a lower-orthant probability strictly above its independent counterpart at every finite threshold, leaving no room for a nontrivial equality. No code of ambient dimension below $n$ attains the bound. Under an energy budget $E$ with unrestricted blocklength the optimal codebook is uniquely the regular simplex of circumradius $\\sqrt{E}$. Every optimal codeword therefore exhausts its allowance. Equality in the Simplex Mean Width Conjecture likewise occurs only at the regular simplex. The proof strengthens the first self-convolution step of Mulgund's argument with Royen's correlation theorem. The single-parameter rigidity is machine-checked in Lean 4.", "title": "The Equality Cases of the Weak Simplex Conjecture", "updated": "2026-08-19", "url": "https://arxiv.org/abs/2608.19093" }, { "age_days": 3, "arxiv_id": "2608.20153", "authors": [ "Dingzirui Wang", "Xuanliang Zhang", "Keyan Xu", "Qingfu Zhu", "Wanxiang Che" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.20153", "kind": "paper", "label": "adjacent", "matched_signals": [ "autoformalization" ], "published": "2026-08-20", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Large language models (LLMs) have shown growing potential for automated theoretical computer science (TCS) research, yet existing benchmarks remain far from realistic research settings. We introduce \\ourbenchmark, an expert-validated benchmark for evaluating LLMs on frontier, end-to-end TCS research. \\ourbenchmark contains $175$ instances drawn from papers accepted to STOC, FOCS, SODA, and COLT in 2025-2026, preserving paper-specific definitions, assumptions, and proof dependencies, with expert-verified Lean formalizations and proofs. Evaluations of leading LLMs reveal that current models remain far from reliably completing the full research pipeline. In particular, autoformalization is the sharpest bottleneck: the best model achieves only $11.5$ on translating natural-language claims into formal theorem statements, compared with $28.6$ Pass@8 when proving human-provided formal statements. Building on \\ourbenchmark, we further develop an automated TCS research framework that generates, formalizes, filters, and proves new claims. Of $64$ generated claims, only $6$ ultimately pass expert evaluation and proof verification, indicating that beyond formalization, limited research taste remains another major barrier to autonomous TCS research.", "title": "FormalTCS: Benchmarking End-to-End Frontier Formal Theoretical Computer Science Research of Large Language Models", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.20153" }, { "age_days": 3, "arxiv_id": "2608.19847", "authors": [ "Benqi Liu", "Kangkang Deng", "Zichen Wang", "Zaiwen Wen" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.19847", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-20", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Augmented Lagrangian methods are effective for nonlinear equality-constrained optimization, but solving their nonlinear primal subproblems can be expensive. For smooth nonconvex problems with deterministic or stochastic objectives, we propose a nonlinear-residual linearized augmented Lagrangian method (NR-LALM) that replaces this subproblem by a regularized Gauss-Newton-type step while retaining the classical multiplier update based on the nonlinear constraint residual. The resulting step is computed from one symmetric positive-definite linear system, but the mismatch between the linearized primal model and the nonlinear-residual update produces a quadratic constraint-linearization error in the multiplier identity. We show that this error can be controlled under local regularity; multiplier boundedness and trajectory localization are derived rather than assumed. With fixed, accuracy-independent parameters, deterministic NR-LALM finds an $\\varepsilon$-approximate Karush-Kuhn-Tucker (KKT) pair in $O(\\varepsilon^{-2})$ iterations and first-order oracle evaluations. For stochastic objectives, a projected stochastic path-integrated differential estimator with safeguarded restarts requires, in expectation, $O(\\varepsilon^{-3})$ stochastic-gradient evaluations and $O(\\varepsilon^{-2})$ constraint and Jacobian evaluations. Compactness and a Kurdyka-Lojasiewicz condition further yield finite-length convergence of the deterministic primal-dual sequence. An optional minimum-norm second-order correction reduces the constraint-linearization error from second to fourth order without changing the complexity orders. All theoretical results are formalized in Lean 4. Numerical experiments confirm the predicted error orders and show favorable performance on high-dimensional deterministic and stochastic problems.", "title": "A Fixed-Penalty Linearized Augmented Lagrangian Method with Classical Multiplier Updates", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.19847" }, { "age_days": 4, "arxiv_id": "2608.19058", "authors": [ "Mahadee Al Mobin", "Md. Shariful Islam" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.19058", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-19", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We state and prove the Theorem: for primes $p < 10^n$ with base-$10$ expansion $p = \\sum_{k=0}^{n(p)-1} d_k(p) 10^k$, the positional digit probabilities $P_n(d \\mid k)$ satisfy \\[ \\lim_{n \\to \\infty} P_n(d \\mid k) = \\begin{cases} 1/10, & k \\ge 1,\\ d \\in \\{0,\\dots,9\\}, \\\\[4pt] 1/9, & k = \\mathrm{lead},\\ d \\in \\{1,\\dots,9\\}. \\end{cases} \\] The limiting behavior splits cleanly into two distinct mechanisms: an arithmetic regime for interior digits and an Archimedean regime for the leading digit. For fixed interior positions ($k \\ge 1$), digit extraction modulo $10^{k+1}$ reduces the problem to prime counts in reduced residue classes, where uniform distribution follows from Siegel--Walfisz (with Bombieri--Vinogradov allowing $k$ to grow with $n$). For the leading digit, the $1/9$ limit is not a Benford-type scale invariance, but arises from the local near-constancy of the prime density $1/\\log t$ within single decades combined with a Toeplitz-type error averaging. Explicit classical and conditional error bounds are recorded for both regimes.", "title": "The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers", "updated": "2026-08-19", "url": "https://arxiv.org/abs/2608.19058" }, { "age_days": 4, "arxiv_id": "2608.18723", "authors": [ "Ghislain Dorian Tchuente Mondjo" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.18723", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-19", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Telecom operators traditionally offer predefined tariff grids, forcing users to choose from a limited set of plans. This paper proposes BFTR (Budget-First Tariff Recommendation), a complete algorithmic framework integrating eight Budget-First strategies, including two original hybrid approaches: Recursive Hybrid (conditional interpolation) and Knapsack-First Hybrid (priority knapsack). Unlike existing approaches that adjust prices upward to guarantee a minimum margin, BFTR guarantees the absence of overcharging by systematically aligning the final price with the catalog reference price. We mathematically formalize each strategy, prove the existence of an offer for any positive budget, and prove that the price deviation (surcharge) is zero for all strategies that do not use interpolation with correction. A detailed comparative analysis confronts BFTR to ten main existing tariff models on ten dimensions. Experiments on a dataset of 974 customers inspired by the Nigerian MTN market show that: (i) Recursive Hybrid is optimal for the customer (100% budget used, 29.9 GB volume, utility 0.946, 0% overcharging), (ii) Piecewise offers the highest volume (39.7 GB) with 0% overcharging, (iii) Power Law provides an excellent compromise (99.9% budget, 38.1 GB, 0% overcharging). All strategies achieve a zero surcharge, confirming the theoretical guarantees. A sensitivity analysis on the weighting parameter alpha (0.2 - volume priority, 0.5 - balance, 0.8 - budget priority) shows that utility rankings evolve logically. Execution times (< 10 ms) and very low failure rates (0% for robust strategies) confirm the operational viability of the system. The formal proof of the absence of overcharging constitutes a major theoretical contribution.", "title": "Budget-First Tariff Recommendation (BFTR): A Complete Algorithmic Framework for Telecom Plan Recommendation without Overcharging", "updated": "2026-08-19", "url": "https://arxiv.org/abs/2608.18723" }, { "age_days": 5, "arxiv_id": "2608.17274", "authors": [ "Hongru Zhao" ], "content_date": "2026-08-18", "freshness": "fresh", "id": "arxiv:2608.17274", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-18", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We study the von Neumann entanglement entropy generated by a Haar distributed passive interferometer acting on $n$ equally squeezed input modes with fixed nonzero squeezing strength $s$. Previous work established proportional weak typicality for integer R'enyi orders $α\\geq 2$ and stated a sublinear von Neumann result, while the proportional von Neumann case remained open. For a subsystem of $k_n$ modes satisfying $k_n/n\\to r\\in(0,1)$, we prove that, for every $\\varepsilon>0$ and all sufficiently large $n$, $\\mathbb{P}\\left(\\left|\\frac{S_{1,n}}{\\mathbb{E}S_{1,n}}-1\\right|\\geq\\varepsilon\\right)\\leq2\\exp\\left[-\\frac{c_{s,r}\\varepsilon^2n^2}{\\log^2(en)}\\right].$ The proof represents the entropy as a singular value statistic of a principal block of $UU^{\\mathsf T}$, where $U$ denotes the unitary interferometer. It regularizes the logarithmic singularity at the endpoint corresponding to a pure Gaussian mode and applies concentration on the unitary group. The result establishes proportional von Neumann weak typicality and further implies almost sure convergence of $S_{1,n}/\\mathbb{E}S_{1,n}$ to $1$, a typical volume law, and the variance bound $\\mathrm{Var}(S_{1,n})=O_s(\\log^2 n)$. An accompanying Lean 4 development verifies the proof chain.", "title": "Weak Typicality of von Neumann Entanglement Entropy in Gaussian Boson Sampling", "updated": "2026-08-18", "url": "https://arxiv.org/abs/2608.17274" }, { "age_days": 5, "arxiv_id": "2608.17741", "authors": [ "Olga Mashkova", "Asaad Mohammedsaleh", "Fernando Zhapa-Camacho", "Robert Hoehndorf" ], "content_date": "2026-08-18", "freshness": "fresh", "id": "arxiv:2608.17741", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-18", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "OWL 2 DL ontologies, grounded in the description logic $\\mathcal{SROIQ}$, express large knowledge bases in biomedicine and the Semantic Web. Neuro-symbolic (NeSy) learners over description logics either embed the ontology in a continuous space, abandoning classical entailment, or restrict to the Horn fragment $\\mathcal{EL}^{++}$, which has a single canonical model. We present Baobab, which compiles a $\\mathcal{SROIQ}$ ontology with a finite ABox into a Sentential Decision Diagram (SDD): it saturates a propositional core under a consequence-based calculus and instantiates the remaining $\\mathcal{SROIQ}$ features (nominals, number restrictions, and the role axioms) over the active domain. The SDD's evidence-conditioned weighted model count then trains a perception network to recognize real images under partial ABox supervision: on an ontology that exercises every distinctive $\\mathcal{SROIQ}$ feature, a CNN learns to read MNIST digits coupled by a successor relation and recovers latent ontology concepts that an independent perception leaves at chance. When the supervision admits several ontology-consistent completions, an independent perception collapses onto one, a reasoning shortcut: we show that a mixture indexed by the query's justifications can represent the calibrated posterior no independent perception can, and that seeding it from the circuit's enumerated completions attains the Bayes-optimal posterior on a real-image MNIST task where single-WMC and learned mixtures (the BEARS-ensemble hypothesis class) do not: to our knowledge the first to characterize and mitigate reasoning shortcuts in a non-Horn description logic. Soundness of the compiler and the representation result are machine-checked in Lean 4. Code is available at https://github.com/bio-ontology-research-group/baobab.", "title": "Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits", "updated": "2026-08-18", "url": "https://arxiv.org/abs/2608.17741" }, { "age_days": 5, "arxiv_id": "2608.17634", "authors": [ "Satpreet Makhija" ], "content_date": "2026-08-18", "freshness": "fresh", "id": "arxiv:2608.17634", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-18", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "The $\\operatorname{do}$-operator is described graphically by deleting arrows into its targets and functionally by replacing their mechanisms with constants. To call these operations equivalent is not yet a mathematical statement: one returns a graph and remembers only the targets, whereas the other returns mechanisms and also remembers the imposed values. We make a dependency-level comparison precise for deterministic acyclic structural causal models with finitely many endogenous variables. If $\\operatorname{Graph}(F)$ extracts the dependencies of a mechanism family $F$, our main theorem is $\\operatorname{Graph}(F^ι)=\\operatorname{Surg}(\\operatorname{Graph}(F),T_ι)$. Thus replacing target mechanisms removes exactly the dependencies removed by graph surgery. For a model $M=(G,F)$ whose graph may contain unused arrows, we characterize when the same equality holds with $G$ in place of $\\operatorname{Graph}(F)$; it holds for every intervention exactly when $G$ records the dependencies of $F$ exactly. We then define the intervened model, characterize its run, show how sequential interventions combine, and prove that an outcome depends only on interventions at its actual dependency ancestors. All principal results are machine-checked in an accompanying Lean 4 development.", "title": "Graph Surgery and the Do-Operator: A Precise Correspondence for Acyclic Structural Causal Models", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.17634" }, { "age_days": 5, "arxiv_id": "2608.17880", "authors": [ "Ibrahim Mian", "Shayaan Siddique" ], "content_date": "2026-08-18", "freshness": "fresh", "id": "arxiv:2608.17880", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-18", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "Erdős problem 647 asks whether any $n > 24$ satisfies $\\max_{m 0.14) -- coverage is bought at a price the account states. We then price the remaining distance from the certified witness to what a user experiences: a machine-checked design law (TV <= tanh(a_q w_thr)) turns the served-TV target into a threshold knob, and a three-layer audit of its instantiation -- an operator-norm query envelope measured 1.5x from tight, a measured-ellipsoid replacement for the Cauchy-Schwarz ball that buys nothing (0.89x, held-out sound), and the gate's operating point (~700x) -- localizes the entire 1064x gap to the operating point, a price the law now states rather than an unknown. A priced bound is worth nothing on a request one has not seen, so the third link is the quantifier: exchangeable extrapolation across 80 serving histories replaces binary conformal prediction's vacuous certificates with order-statistic bounds that discriminate (0.41 against 0.51 calibration risk). All probabilistic kernels are Lean 4-checked (228 exported theorems, no sorry); which object deserves this machinery at all is settled empirically in a companion paper that adjudicates -- and rejects -- the natural alternative of certifying routing. What ships is an account: risk you can spend, a gap you can read off a law, and a bound that survives the request you have not seen.", "title": "Pricing the Risk of Runtime Compression: Anytime-Valid Admission and a Served-Output Law for Compressed Serving State", "updated": "2026-08-16", "url": "https://arxiv.org/abs/2608.15810" }, { "age_days": 7, "arxiv_id": "2608.15914", "authors": [ "Benny Avelin" ], "content_date": "2026-08-16", "freshness": "fresh", "id": "arxiv:2608.15914", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-16", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We study Gaussian random dynamical systems with coordinatewise $\\tanh$ nonlinearity, where finite precision is modeled by nearest-grid rounding after each step. Gaussian symmetry reduces the dynamics to an exact Markov chain for the normalized squared radius. Rounding makes the origin absorbing, and the total variation distance to the absorbing equilibrium equals the survival probability of the absorption time. At fixed width, we identify the critical gain and prove an absorption cutoff with Gaussian profile as the mesh tends to zero. At fixed precision, global contraction yields a large-dimension absorption cutoff, while positive drift produces metastability. In the supercritical regime, we prove a large-dimension cutoff to a nonzero invariant law and show that, at fixed dimension, its mass near the repelling origin has a power-law asymptotic. All six main results are formalized in Lean 4 on top of Mathlib and independently checked against restatements that import only Mathlib.", "title": "Absorption cutoff and stationary singularities for rounded Gaussian random dynamical systems", "updated": "2026-08-16", "url": "https://arxiv.org/abs/2608.15914" }, { "age_days": 8, "arxiv_id": "2608.15337", "authors": [ "Michele Caprio" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.15337", "kind": "paper", "label": "adjacent", "matched_signals": [ "lean_formal_proving_agents" ], "published": "2026-08-15", "score": 3.5, "source": "arxiv-ai4math-core", "summary": "We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows. For the standard cellular flow in dimension two $V_A(x_1,x_2)=A(-\\sin x_1\\cos x_2,\\cos x_1\\sin x_2)$, if $00$ universal. The same conclusions hold for arbitrary continuous periodic perturbations of planar initial data. Under the physical scaling $V_A(x/\\varepsilon)$ and $d_\\varepsilon=\\varepsilon d$, an order one value gap persists between points at distance $O(\\varepsilon)$ at every positive macroscopic time, so the rescaled solutions have no locally uniformly convergent subsequence. The proof uses the Hamiltonian sandwich $H_{\\mathrm{unc}}\\le H_+\\le\\widehat H$. The upper comparator $\\widehat H$ is a rectangular support function, equivalently an upper expectation over a state-dependent credal set, whose reversed control dynamics possess an invariant comparison channel. We also prove that for any $C^2$ incompressible periodic flow, every $\\varepsilon$-outward barrier certificate has covering radius at most $2d\\varepsilon$ for all sufficiently small $\\varepsilon$. We further discuss implications for statistics and machine learning: rectangular, time-consistent local uncertainty need not imply forgetting of the initial state in the long run, so additional global stability or ergodicity conditions are needed in robust sequential decision making. Two Lean 4 appendices record conditional formalizations of a sufficient $p=e_1$ subregime and of the logical assembly of the rigidity theorem for barrier certificates.", "title": "The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.15337" }, { "age_days": 5, "arxiv_id": "2608.18024", "authors": [ "Haruhisa Enomoto" ], "content_date": "2026-08-18", "freshness": "fresh", "id": "arxiv:2608.18024", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-18", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules. We propose the quotient--submodule equidistribution conjecture: over a representation-finite algebra, the number of quotient-closed subcategories of size $i$ is equal to that of submodule-closed subcategories of size $i$ for every $i$, where size is the number of indecomposable modules in the subcategory. We prove the following cases of the conjecture: (1) the five smallest and five largest values of $i$, hence all algebras with at most nine indecomposable modules; (2) Nakayama algebras; (3) algebras with radical square zero; and (4) representation-directed algebras. In the last case, we classify quotient-closed subcategories by a lower Bruhat interval in a Coxeter group constructed from the Auslander--Reiten quiver, extending the classification of Oppermann--Reiten--Thomas for Dynkin quivers. We also prove that quotient closure defines a finitary convex geometry and classify the functorially finite quotient-closed subcategories by Gen-minimal modules.", "title": "An equidistribution conjecture for quotient-closed and submodule-closed subcategories", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.18024" }, { "age_days": 8, "arxiv_id": "2608.15219", "authors": [ "Yifeng Huang", "Kenny Lau", "Ken Ono", "Peter Paule" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.15219", "kind": "paper", "label": "adjacent", "matched_signals": [ "general_ai_math_reasoning" ], "published": "2026-08-15", "score": 1.9, "source": "arxiv-ai4math-core", "summary": "The Rogers--Ramanujan identities equate a $q$-series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~$5$. Identities of this shape are scarce, and a central problem is to identify the structures that produce them in families. Huang, Jiang, and Oblomkov have proposed a source of a new kind: to each pair of coprime integers $a,b>1$ they attach an infinite-rank $q$-series $Z_{a,b}(q)$, assembled from counts of commuting nilpotent matrix pairs $(A,B)$ with $A^a=B^b$ over finite fields, and they conjecture that it equals an explicit product of $(a-1)(b-1)/2$ modular units of level $a+b$. The $a=2$ cases are the Andrews--Gordon identities; no case with $a>2$ was known. We prove the conjecture for $(a,b)=(3,4)$, $(3,5)$, $(3,7)$, and $(3,8)$. Our proofs pass through a finer sum-to-sum identity, which we conjecture for all $b$ coprime to $3$ and establish for all $b$ when $q=1$. Lau and Ono have since proved that identity in general, and with it the full $a=3$ case. These identities have been formalized and verified in Lean by AxiomProver.", "title": "Algebraic geometric framework of Rogers--Ramanujan identities", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.15219" }, { "age_days": 0, "authors": [ "David Loeffler" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f2916a54665a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: refactor(CategoryTheory/Sites): split long file Sieves.lean (#43014)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/f2916a54665af851fc9a4da901cfc242c47a8922" }, { "age_days": 0, "authors": [ "Stefan Kebekus" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:ca0ba44e151c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: derivative of the Cauchy integral (#41817)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/ca0ba44e151cc208307ca089c512d6f58c3f71ec" }, { "age_days": 0, "authors": [ "Anatole Dedecker" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d606315de483", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: a continuous linear map is invertible iff it is an homeomorphism (#42698)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/d606315de4834f3590e375b09f97064f2885d527" }, { "age_days": 0, "authors": [ "Kirill Kondrashov" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c2d7843e04aa", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: a bilinear form on a module induces a bilinear form in its exterior powers (#42889)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/c2d7843e04aa6cc44fa7e2b39422f24f7b725f00" }, { "age_days": 0, "authors": [ "Snir Broshi" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:79f9e7e742d0", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Order/ConditionallyCompleteLattice): use `ciSup₂_le'` (#43049)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/79f9e7e742d0d1da8ade597ce08367f9b4bb18ad" }, { "age_days": 0, "authors": [ "Dennj" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:585bc2af5365", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(CategoryTheory/Presentable): remove a backward.isDefEq set_option (#42984)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/585bc2af5365567d2206ad8c6988d8d922b33c64" }, { "age_days": 0, "authors": [ "mathlib-splicebot[bot]" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:8d56a84a3286", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Analysis/Complex/Circle): nnnorm and enorm lemmas for circle (#43053)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/8d56a84a328687e57bd0df7c8374743448bd3a27" }, { "age_days": 0, "authors": [ "Whysoserioushah" ], "content_date": "2026-08-23", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:863e60949d80", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-23", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/Homology/HomotopyCategory/Shift): clean up most of set_options (#42448)", "updated": "2026-08-23", "url": "https://github.com/leanprover-community/mathlib4/commit/863e60949d807fe7d4fa4d3714c9b1e7583ee0b3" }, { "age_days": 1, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover/lean4:e3b3b04971c2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: apply specs to goals with a registered WP instance in vcgen (#14883)", "updated": "2026-08-22", "url": "https://github.com/leanprover/lean4/commit/e3b3b04971c27058eb917160d9f2e8bb23296e72" }, { "age_days": 1, "authors": [ "Kyle Miller" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover/lean4:47680c2e6283", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: add missing terminfo on structure fields (#14834)", "updated": "2026-08-22", "url": "https://github.com/leanprover/lean4/commit/47680c2e62831da4daa01abe567b3e4fc509fbae" }, { "age_days": 1, "authors": [ "Dennj" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover/lean4:fd0efc4306a7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: lake: add --fail-fast build option (#14797)", "updated": "2026-08-22", "url": "https://github.com/leanprover/lean4/commit/fd0efc4306a7773c2cd4e079ddaa907426d0f5da" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:769b0a5ad45c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: the Levi-Civita connection on a manifold (#36845)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/769b0a5ad45c8d886c754c0be19835b908f98dcb" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:9221f0553b4c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: immersions in the sense of differentials (#35078)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/9221f0553b4c5db908969be8953a8d802a9c8469" }, { "age_days": 1, "authors": [ "Michael Rothgang" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b78b57f2047c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat: an immersion is an immersion in the sense of differentials (#41796)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b78b57f2047c2f441a7ce779a951cd9db0258a6d" }, { "age_days": 1, "authors": [ "Hagb (Junyu Guo 郭俊余)" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:2092dfa6336b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Order/RelIso/Basic): `swap`s and `compl`s are `Equiv`s (#39549)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/2092dfa6336b2d6bc1c59f04bf4ae98168473907" }, { "age_days": 1, "authors": [ "Seewoo Lee" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:22db545ee906", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(ModularForm): ramanujan-serre derivative maps modular form (#40764)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/22db545ee9063b6472568ce67d4aa679b5d6aa80" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:169f50d4fb7c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Mathlib/Order/SuccPred/Limit): more `WithTop` lemmas about `IsMin`/`CovBy`/`IsSuccLimit` (#38841)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/169f50d4fb7ca23e1c486157044cd42fdf839361" }, { "age_days": 1, "authors": [ "Joseph Myers" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:53c82c1c23ec", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Euclidean/Angle/Incenter): unoriented angle bisection (#32282)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/53c82c1c23ec418ebf7290390bc8108957bef853" }, { "age_days": 1, "authors": [ "Li Jiale" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:4ea8fee3daf7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Euclidean/Angle): the unoriented angle at the center in terms of the angle at the circumference (#41123)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/4ea8fee3daf76c77af65fe338648fc8a66d73d63" }, { "age_days": 1, "authors": [ "Vlad Tsyrklevich" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:f9ad8e48659d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(FreeGroup): `toWord` of multiplication by generators (#42104)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/f9ad8e48659dd31f7ec9c0edd9fccaa0ea2f7fbd" }, { "age_days": 1, "authors": [ "Lua Viana Reis" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c548b86df700", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(ConditionallyCompleteLattice/Indexed): add binary versions of lemmas (#38906)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/c548b86df700001fd02db0e3220bfdbbaa29a346" }, { "age_days": 1, "authors": [ "Simex" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b4a18d645383", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(CategoryTheory/Filtration): add basic filtration API (#42642)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b4a18d6453839533b10534a138338cd821769d8f" }, { "age_days": 1, "authors": [ "Bingyu Xia" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:7fb3681af224", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/GroupWithZero/Associated): transfer `IsRelPrime` between associated elements (#41065)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/7fb3681af224dfd324c196105de0104c9540480c" }, { "age_days": 1, "authors": [ "Violeta Hernández Palacios" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:6dcdb48d50b3", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: make `IsStronglyAtomic.of_wellFounded_lt` into an instance (#42360)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/6dcdb48d50b3625e97312bd8b2a712c98b60db8d" }, { "age_days": 1, "authors": [ "Snir Broshi" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:c38284bc2a05", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: deprecate `Mathlib.Data.Finite.Vector` (#43033)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/c38284bc2a056066b80a5bae0415835c1ecac327" }, { "age_days": 1, "authors": [ "Whysoserioushah" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:22176fbb39fc", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(RingTheory/Valuation): remove all `set_option`s in RingTheory/Valuation (#43011)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/22176fbb39fc91ca9ba8a3e20e5ed8ae442433c9" }, { "age_days": 1, "authors": [ "Aaron Liu" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:b63493a4746b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(FieldTheory/KummerExtension): rename theorems (#42886)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/b63493a4746b4651fceb3bcf3a4651cc36a4b8de" }, { "age_days": 1, "authors": [ "Xavier Roblot" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:72f7f9225f69", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/QuadraticAlgebra): rename Discr to Discriminant (#42975)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/72f7f9225f69d73a0b810f01efa966090775813f" }, { "age_days": 1, "authors": [ "Xavier Roblot" ], "content_date": "2026-08-22", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:67f608e6163a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-22", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Algebra/QuadraticAlgebra): deprecate the old Discr module (#42976)", "updated": "2026-08-22", "url": "https://github.com/leanprover-community/mathlib4/commit/67f608e6163ac30cf48c9c4b8f3e060a5588117e" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:11a83c909715", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: remove the binder form of the Hoare triple notation (#14872)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/11a83c909715868bb14068cadfc35f0dd57ff83b" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:f6c7d68c7fc2", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: move `PredTrans` combinators into the `PredTrans` namespace (#14882)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/f6c7d68c7fc27e3b60585f30740c7d141d3c5b36" }, { "age_days": 2, "authors": [ "Mac Malone" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:88b5922ce13e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: lake: trace bootstrap `lean.h` (#14853)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/88b5922ce13e1ac42afe1366e4f30666fdd23330" }, { "age_days": 2, "authors": [ "Robert J. Simmons" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:5c0c5995e1d6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: collapse empty DiscrTree tries (#14844)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/5c0c5995e1d69c7ff0eb6860ee109b91ccc2caac" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:5adc41ebee85", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: deprecate the `mvcgen` tactic (#14874)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/5adc41ebee85e17f75c528168058be83e525d989" }, { "age_days": 2, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:03d7a4efd5f7", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: add `experimental.vcgen` option and a `vcgen invariants?` removal notice (#14870)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/03d7a4efd5f74dc886ba33eab424611146d49e03" }, { "age_days": 2, "authors": [ "Lean stage0 autoupdater" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:f8facdb33030", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update stage0", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/f8facdb3303012c0d6806661867fc86e68234641" }, { "age_days": 2, "authors": [ "Kim Morrison" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:5600c6ed6412", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: generate a usable Zulip announcement for patch releases (#14878)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/5600c6ed6412df4aa6dbdc34532f82011968eaad" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:e5eabe597c43", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: fix test name (#14873)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/e5eabe597c43b4a848c0bac78f4205505eac936c" }, { "age_days": 2, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:dd7716da5b36", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: enforce the requested libuv version (#14871)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/dd7716da5b36bc54601dc3f4257fe74123fa2b8a" }, { "age_days": 2, "authors": [ "Kim Morrison" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:5377fdd2a337", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: credit the running user in generated release notes (#14879)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/5377fdd2a337d8faee05500d126070c1f9aceddb" }, { "age_days": 2, "authors": [ "Eric Wieser" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover/lean4:c129c5fda2e6", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: all register_options should be builtin (#14868)", "updated": "2026-08-21", "url": "https://github.com/leanprover/lean4/commit/c129c5fda2e6da773e3fc23afbec64d6dd7efa4b" }, { "age_days": 2, "authors": [ "Pepa Montero Jimena" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:d7f2dbea7d06", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Geometry/Manifold): chart conjugates of self-diffeomorphisms are compatible (#42502)", "updated": "2026-08-21", "url": "https://github.com/leanprover-community/mathlib4/commit/d7f2dbea7d06120b9aabb7c76b2a55256a05437e" }, { "age_days": 2, "authors": [ "Aaron Liu" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:23a3216f0e5b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: feat(Algebra/MonoidAlgebra): add instances for `Infinite` and `Countable` and `Small` (#42239)", "updated": "2026-08-21", "url": "https://github.com/leanprover-community/mathlib4/commit/23a3216f0e5b7f9f5d437409db9f10b34844e6d0" }, { "age_days": 2, "authors": [ "Marcelo Lynch" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:25a7b5ea417a", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore: use `open scoped` where only scoped declarations are used (#42672)", "updated": "2026-08-21", "url": "https://github.com/leanprover-community/mathlib4/commit/25a7b5ea417a23e00b38dc251ef75d366f8cf7fe" }, { "age_days": 2, "authors": [ "Thomas Browning" ], "content_date": "2026-08-21", "freshness": "fresh", "id": "github:leanprover-community/mathlib4:0cd048027c8b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-21", "repo": "leanprover-community/mathlib4", "score": 0.8, "source": "mathlib4-github", "summary": "Recent commit on leanprover-community/mathlib4.", "title": "leanprover-community/mathlib4: chore(Analysis/Normed/Unbundled/SeminormFromConst): remove unnecessary hypothesis (#43022)", "updated": "2026-08-21", "url": "https://github.com/leanprover-community/mathlib4/commit/0cd048027c8b0239cdfe206691bbf2c0a0970078" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:4cf8a3b5e4b8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: rework the vcgen frame procedure API around a commit callback (#14706)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/4cf8a3b5e4b824de413a9a76eb7c33bd9e3f43c3" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:ae12a7964dd8", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: replace the bespoke exception postcondition types with tuples (#14836)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/ae12a7964dd803c03dbb8c119e2931842e0e1fbb" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:298de3bdbfab", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: refactor: a contract clause binds like a `fun` (#14858)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/298de3bdbfab38f3a01be3d0e2ed5a5dcf67f155" }, { "age_days": 3, "authors": [ "Fawad Haider" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:cd5cd282ff7b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: return unboxed uint8 from llvm_is_declaration (#14864)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/cd5cd282ff7b4166e935a2bdf5fa3c5255046337" }, { "age_days": 3, "authors": [ "Leonardo de Moura" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:95b54b70ae19", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: require GMP 6.3.0 (#14833)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/95b54b70ae194e317d3cdc66cd7f163f9bb90418" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:56674f81103e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: make `vcgen` succeed when the goal is closed during initialization (#14857)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/56674f81103e6db956670d4ef13055b7e4293c98" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:8df768b7318d", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: freeze objects when their reference count overflows (#14838)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/8df768b7318df75dbda926f5cb57c6ba18ed4f00" }, { "age_days": 3, "authors": [ "Sebastian Graf" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:de315cfb508e", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: fix: elaborate loop annotations without `open Std.WP` (#14860)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/de315cfb508e9e7bc5e744546fbc329331a64567" }, { "age_days": 3, "authors": [ "Julia Markus Himmel" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:5fe999404d5c", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `constructor` warns when multiple constructors match (#14854)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/5fe999404d5ceb876d5a586608c08e334e162e93" }, { "age_days": 3, "authors": [ "Robin Arnez" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:bd73cfb3857b", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: feat: `Decidable` as subtype of `Bool` (#8309)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/bd73cfb3857bc1cbcbe58eef18ee6bcf7e82eace" }, { "age_days": 3, "authors": [ "Sebastian Ullrich" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "github:leanprover/lean4:875b6b5bcf29", "kind": "github_update", "label": "negative", "matched_signals": [], "published": "2026-08-20", "repo": "leanprover/lean4", "score": 0.8, "source": "lean4-github", "summary": "Recent commit on leanprover/lean4.", "title": "leanprover/lean4: chore: update to mimalloc 3.4.4 (#14477)", "updated": "2026-08-20", "url": "https://github.com/leanprover/lean4/commit/875b6b5bcf293b6ce17ea6a1a977363f1b51d66b" }, { "age_days": 3, "arxiv_id": "2608.19844", "authors": [ "Liyan Wang" ], "content_date": "2026-08-20", "freshness": "fresh", "id": "arxiv:2608.19844", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-20", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "For $n\\geq 4$, let $c(n)$ be the minimum number of distinct circles containing at least three points of an $n$-point set in the Euclidean plane, where the set is neither collinear nor concyclic. Put[F(n)=1+\\binom{n-1}{2}-\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor.]We determine $c(n)$ for every $n\\geq 4$: it equals $F(n)$ apart from three exceptional orders. We also solve the variant in which no three points are collinear; that variant has a single exceptional order. The proofs and exact finite verifications were developed through a collaboration between human researchers and artificial-intelligence systems.", "title": "Circles determined by planar point sets", "updated": "2026-08-20", "url": "https://arxiv.org/abs/2608.19844" }, { "age_days": 4, "arxiv_id": "2608.18999", "authors": [ "Danila Litvinov" ], "content_date": "2026-08-19", "freshness": "fresh", "id": "arxiv:2608.18999", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-19", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Radial clipping does two things at once: it removes the part of a vector outside a ball and retains a bounded vector inside the ball. The removed part produces bias, while the squared norm of the retained part produces energy. We determine the exact joint price of these effects when only a $p$-moment, $10$, then $F{k,n}\\to e^{1/c}I_0(1/c)$, where $I_0$ is the modified Bessel function of the first kind of order zero, and consequently $R_{k,n}\\sqrt{πn}\\to[e^{1/c}I_0(1/c)]^{-1}$. Thus $k\\asymp n^2$ is a smooth Bessel crossover, whereas the scaling order boundary for inverse polynomial weak anticoncentration is $k\\asymp n^2/\\log n$. These conclusions concern the Gaussian surrogate moment criterion; finite dimensional Haar moment transfer and high probability small ball anticoncentration remain separate problems.", "title": "Exact Moments of Gaussian Gram Hafnians Reveal an $n^2/\\log n$ Threshold for Weak Anticoncentration", "updated": "2026-08-17", "url": "https://arxiv.org/abs/2608.17065" }, { "age_days": 7, "arxiv_id": "2608.15900", "authors": [ "Dinh-Khiet Le", "Minh-Quyet Ha", "Hong-Phuc Vu-Dinh", "Takashi Miyake", "Hiori Kino", "Hieu-Chi Dam" ], "content_date": "2026-08-16", "freshness": "fresh", "id": "arxiv:2608.15900", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-16", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Data-driven materials discovery interpolates more reliably than it extrapolates and seldom reaches new structure types. We present MatEvolve, an agentic-AI framework designing crystals, proposing each candidate with a stated rationale and testing it. The agent reasons in an interpretable \\emph{language of motifs}, writing each crystal as a \\emph{motif profile} that describes the recurring geometric patterns---the \\emph{motifs}---composing it. The motif profile serves not merely as a description of a material but as the medium for material design: the agent edits the profile and constructs a crystal from the modified one, and the most promising candidates are validated by first-principles calculation. Applied to the design of rare-earth-lean permanent magnets, MatEvolve---built on the state-of-the-art language model Claude Fable~5 without fine-tuning---reaches new structural prototypes more than three times as often as generative models under an equal validation budget, at a comparable on-target-magnet rate. Beyond design, analysing the discovered crystals' human-readable profiles reveals structure--property relationships.", "title": "Crystal-structure design by agentic AI in a language of motifs", "updated": "2026-08-16", "url": "https://arxiv.org/abs/2608.15900" }, { "age_days": 8, "arxiv_id": "2608.15182", "authors": [ "Vignon Oussa" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.15182", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-15", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "We establish an abstract storage theorem for projectively $C_0$ unitary representations admitting a pair of one-parameter subgroups with conjugation escape. It produces, for every $0<\\varepsilon<1$, a single orbit whose sampling set is relatively separated modulo the projective kernel and whose frame bounds are $(1-\\varepsilon)^2$ and $(1+\\varepsilon)^2$. Two applications are obtained from the same mechanism. First, every nonabelian exponential Lie group admits a near-Parseval frame of left translates for its left regular representation. Consequently, a positive-dimensional exponential Lie group is an FT group if and only if it is nonabelian; in particular, the three-dimensional Heisenberg group admits such a frame. Second, every infinite-dimensional irreducible unitary representation of an exponential Lie group admits a near-Parseval discrete orbit frame. When the effective projective quotient is abelian, the orbit may be chosen to be an orthonormal basis arising from a transported Weyl lattice.", "title": "Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.15182" }, { "age_days": 8, "arxiv_id": "2608.15318", "authors": [ "Sanjit Singh Mehat" ], "content_date": "2026-08-15", "freshness": "fresh", "id": "arxiv:2608.15318", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-15", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "An Euler magic matrix is an integer matrix M with MM^t = gamma I for some gamma != 0, whose squared entries sum to gamma along both main diagonals; it is proper if its squared entries are pairwise distinct. Euler gave a proper example of order 4; Müller settled orders 3 (none exists) and 8; and Kominers settled order 5. We give an order-6 construction, a case not addressed by Müller or Kominers, exhibiting a proper Euler magic matrix of order 6 with gamma = 18500 together with a second, independent one with gamma = 43290. The proof is the explicit matrix and a finite exact verification. We also record an elementary counting bound gamma >= 2485 for proper order-6 examples.", "title": "A proper Euler magic matrix of order 6", "updated": "2026-08-15", "url": "https://arxiv.org/abs/2608.15318" }, { "age_days": 9, "arxiv_id": "2608.14896", "authors": [ "Florian Braun" ], "content_date": "2026-08-14", "freshness": "fresh", "id": "arxiv:2608.14896", "kind": "paper", "label": "negative", "matched_signals": [], "published": "2026-08-14", "score": 0.5, "source": "arxiv-ai4math-core", "summary": "Large language models work well on English and behave in poorly understood ways on languages typologically far from it. Japanese is a clean example, where evaluation still leans on translation quality and JGLUE-style benchmarks, which roll lexical, syntactic and pragmatic competence into a single score. The phenomena on which general-purpose models fail Japanese users are pragmatic: honorifics, in-group and out-group reference, context-sensitive politeness, zero anaphora. I introduce J-PragEval-v0, a minimal-pair benchmark isolating four such phenomena from surface fluency, and combine it with linear probes and teacher-forced log-probability evaluation to ask where inside TinySwallow-1.5B (28 layers, hidden size 1536) the corresponding contrasts live. The four features split three ways. Honorific register sits cleanly in the residual stream: 0.96 balanced accuracy at layer 15, and the model flips its preferred continuation with the scenario on 93 percent of items. Implicit subject and in-group reference are not linearly decodable at the final prompt token (0.48 and 0.38), yet flip rates are 0.77 and 0.79, so the contrast is worked out during generation rather than stored at the prompt. Indirect refusal is the negative case: 0.95 probe accuracy collapsing to a 0.43 flip rate under length-normalised teacher forcing, because the current minimal pairs conflate politeness with continuation length. I also specify Pragmatic Representation Steering, a parameter-free inference-time method that edits residual-stream activations along the class-mean-difference directions probing identifies. Feasibility is argued indirectly rather than demonstrated: the contrastive activation addition baseline, the same geometry the method would inject, recovers probe accuracy within one to two points of logistic regression wherever a linear signal exists. Scaling to Llama-3.1-Swallow-8B is the next step.", "title": "Interpretable Cross-Lingual Alignment in Small Language Models: Probing Cultural and Pragmatic Reasoning in Japanese-English Bilingual LLMs", "updated": "2026-08-14", "url": "https://arxiv.org/abs/2608.14896" } ], "lookback_days": 21, "schema": "ai4math-radar-run-v1", "timezone": "America/Los_Angeles" }