{
  "counts": {
    "adjacent": 12,
    "core": 5,
    "errors": 0,
    "negative": 73,
    "total": 90
  },
  "date": "2026-10-11",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-10-11T19:39:50Z",
  "items": [
    {
      "age_days": 3,
      "arxiv_id": "2610.11605",
      "authors": [
        "Matěj Kripner",
        "Milan Straka"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.11605",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-08",
      "score": 12.5,
      "source": "arxiv-ai4math-core",
      "summary": "We introduce NanoProof, to our knowledge the first factorized execution-guided theorem prover in Lean 4 whose training data, extraction tooling, training pipeline, and weights are all released, making it end-to-end reproducible using open-source resources. To this end, we build and release a dataset of structured proof trees, as well as a tool for programmatic interaction and data extraction within the Lean 4 formal verifier. To support sustainable research, we focus on compute efficiency to facilitate accessible training and evaluation. NanoProof achieves 50.8% pass@16 on MiniF2F-Test, exceeding the two closest systems of its class, HyperTree Proof Search and ABEL, at roughly 90x and 7x less compute, and using more than four orders of magnitude less compute than AlphaProof. Stronger open-weight provers exist, but they are fine-tuned from large pretrained language models and release neither training data nor pipeline; NanoProof shows that the factorized execution-guided class of provers can be rebuilt from scratch with modest resources.",
      "title": "NanoProof: Open and Efficient Automated Theorem Proving in Lean 4",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.11605"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12211",
      "authors": [
        "Hazar Yueksel"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12211",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "tool_use_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-08",
      "score": 7.9,
      "source": "arxiv-ai4math-core",
      "summary": "A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications. The usual remedy is to solve related source tasks, either all first, as a curriculum does, or interleaved with verification. We price this remedy in information and in calls. With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification. It lower-bounds the expected number of binary source calls, which designed sources meet within $1+\\log_25$ calls for unique answers and within a logarithmic term in general, where no additive constant suffices. With an exact verifier and fixed sources, moving every call before the first verification preserves all hard caps on calls, although interleaving can save unboundedly many expected calls; under a noisy verifier, source-first protocols can lose unbounded factors in information and in error. For linear banks over $\\mathbb{F}_2$, optimal accuracy has a closed form, and after a polynomial-time reduction the budget profile is computable in time $2^{O(h^2)}\\operatorname{poly}(J,k+h)$ for $J$ sources and nuisance dimension $h$. In these banks, for zero error under a hard cap, the calls beyond the rounded-up information price are exactly those spent on nuisance. Every numbered result apart from two clauses about the planner is machine-checked in Lean 4, assuming two published results. Used as a ruler, the frontier shows a small transformer using all delivered bits at latent dimension $5$ and none at $11$ within fixed training budgets; in a test with predictions recorded before training, low XOR degree of the target bits did not suffice for their use.",
      "title": "Verification with Transfer: Exact Information Frontiers and Their Price in Calls",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12211"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.11862",
      "authors": [
        "Nihal Jain",
        "Shuangjie Yao",
        "Begum Cicekdag",
        "Zhuo Zhang",
        "Suman Jana"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.11862",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-08",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "Mathematicians value proofs for more than correctness: among correct proofs, simplicity, purity and the computational cost of finding them vary widely. Yet LLM-powered theorem provers largely search for any correct proof, and improve its quality only after it is found. We propose LEVER, a proof search algorithm that makes the objective over correct proofs programmable and optimizes it during search. LEVER scores partial proofs over an AND/OR proof graph, combining realized objective values with predictions for open subgoals, so the objective guides search before a proof is complete. The same mechanism optimizes computational cost, proof length, topical impurity, and even their weighted combinations, while the Lean kernel enforces correctness. On PutnamBench in Lean 4, under matched budgets, LEVER costs 34% less than a strong single-conversation agent while raising the solve rate from 80% to 96%. On reducing topical impurity, i.e., how far a proof strays from its theorem's subject, it improves over post-hoc refactoring (42% reduction against 33%) at two-thirds of the cost and more reliably; on proof length, the metric refactoring is built for, it approaches refactoring. Varying the objective's weights traces a quality-cost trade-off curve, so the user can choose how much a better proof is worth. Overall, LEVER is a performant, cost-efficient and tunable proof search algorithm for navigating the space of correct proofs.",
      "title": "LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.11862"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12218",
      "authors": [
        "Chaoyang Qin",
        "Xiaoming Sun"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12218",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-08",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "The second part of Hilbert's 16th problem is one of the most fundamental open problems in the qualitative theory of ordinary differential equations and dynamical systems. A central unresolved question is whether the Hilbert number $H(d)$ is finite for arbitrary polynomial degree $d$. (A very recent manuscript from OpenAI asserts the finiteness of $H(d)$; see the remark at the end of this paper.) In the absence of a general upper bound theory, most existing work constructs explicit perturbed polynomial systems to obtain improved lower bounds for $H(d)$, while rigorous upper bound estimates remain largely unavailable. This paper focuses on improving the quantitative lower bound for polynomial systems through a systematic Hierarchical Melnikov Realization framework. We construct perturbed dynamics based on an anisotropic Chebyshev Hamiltonian, where hierarchically selected perturbation coefficients generate simple zeros of the first-order Melnikov function simultaneously across multiple disjoint period annuli. Two distinct 3-adic filtrations supply the necessary logarithmic correction factors, and a Borel--Gauss analysis establishes the required local rank condition under sufficiently strong anisotropy. As the main result of this work, we prove that $H(d)=Ω\\bigl(d^2\\ln^2 d\\bigr)$, which improves the previously known lower bound by a factor of $\\ln d$. The full construction of limit cycles and the resulting dynamical bounds are formally certified using Lean 4 formal verification.",
      "title": "Hierarchical Melnikov Realization: Logarithmic Factor Improvement to Hilbert Number Lower Bounds",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12218"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10604",
      "authors": [
        "Srijith Nair",
        "Aditya Vempaty",
        "Jia Liu",
        "Ashish Jagmohan"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10604",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-10-07",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "When generating verifiable code, natural language requirements are mapped to machine checked code using LLMs and agentic workflows. A crucial component of this pipeline is specification generation (SpecGen), which produces a formal contract against which an agent can prove implementation correctness. Proof generation can obtain deterministic feedback from a theorem prover, but SpecGen lacks a definitive check that a generated specification captures the user's intent. A checked proof can therefore establish correctness against a specification that misrepresents the intended behaviour. We take a step towards holistic SpecGen evaluation with a unified dataset assembled from $350$ existing Lean tasks, including $189$ from VERINA and $161$ from CLEVER, and a framework covering formal validity, reference similarity and equivalence, and behavioural adequacy. We distinguish acceptance of required inputs from acceptance of valid outputs and rejection of invalid outputs, while making each metric's evidence scope explicit. Across four SpecGen configurations, restricting the generalized tree edit distance (GTED) comparison, a reference similarity measure, to $32$ jointly measurable VERINA tasks changes the VERINA configuration's position from second to fourth in mean similarity, showing the importance of measurement coverage. In an authored control, a specification achieves $100\\%$ positive test recall and negative test rejection while accepting $0\\%$ of required inputs. This demonstrates that perfect postcondition scores can miss an unusable input contract, motivating separate feedback on input coverage and output constraints.",
      "title": "Beyond Type-checking: Towards Holistic Evaluation of Formal Specification Generation",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10604"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.11324",
      "authors": [
        "Sebastien Kawada"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.11324",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-08",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We resolve Erdős Problem #522, posed in 1961, by proving that for random Littlewood polynomials the proportion of zeros in the closed unit disk converges almost surely to $1/2$. More generally, for partial sums of random power series with i.i.d. coefficients that are bounded, nondegenerate, and centrally symmetric, real Gaussian, or circular complex Gaussian, we prove that the proportion of zeros in the disk of radius $1+x/n$ converges almost surely to $\\frac12(1+\\coth x-1/x)$, uniformly in $x\\in\\mathbb{R}$. Thus almost all zeros lie at distance $O(1/n)$ from the unit circle. For random Littlewood polynomials, even with arbitrary dependence between degrees, the convergence at the unit circle holds at the almost-sure rate $O(n^{-1/4}\\sqrt{\\log n})$. We establish a law-of-the-iterated-logarithm criterion for dependent sequences and, for real Gaussian coefficients, obtain the sharp law of the iterated logarithm over all integer degrees, variance and cross-degree covariance asymptotics, quantitative central limit theorems, joint Gaussian limits, and increment bounds. For symmetric coefficient laws with bounded density and all moments finite, the number of zeros in the closed unit disk has variance $(c_G+κ_4/12)n+O_ξ(n^{399/400})$, and for random signs the constant is $c_G-1/6$. Thus the radial law is universal, while the fluctuations depend on the coefficient law through its fourth cumulant $κ_4$. All our main results are formally verified in Lean 4, and our proof of Erdős Problem #522 has been accepted as a solution to its formal statement in Google DeepMind's Formal Conjectures project.",
      "title": "Universal Radial Laws for Random Polynomials: Erdős Problem #522 and Non-Universal Fluctuations",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.11324"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.11823",
      "authors": [
        "Tejasvi Singh Tomar"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.11823",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-08",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "The rank of the tensor of $3\\times 3$ matrix multiplication over the field with two elements is at most $23$ by Laderman's algorithm, and Rudich and Rousseau recently proved that it is at least $22$. We prove that it equals $23$. Hence Laderman's algorithm uses the fewest multiplications among all bilinear algorithms over $\\mathbb{F}_2$ and among all bilinear algorithms with integer coefficients. The proof uses the substitution method in the form developed in recent work of D'Ambrosio, Wang and Yang et al.: a subspace $S$ of the space of first factors contains at most $r-R(S)$ first factors of a decomposition of length $r$, where $R(S)$ is the rank of the tensor modulo $S$. We raise the known lower bounds on $R(S)$ for $111$ of Wang's $496$ symmetry classes of subspaces. One of these bounds, $R(S)\\ge 21$ for a point spanned by a matrix of rank one, forces the $22$ first factors of a decomposition of length $22$ to be distinct. A $27\\times 27$ flattening of the tensor gives further constraints on the ranks of the first factors, and a separate enumeration shows that, when at least $14$ first factors have rank one, no line in a certain orbit of lines contains two first factors. A computer search then lists, up to symmetry, all sets of $22$ matrices that satisfy these constraints, and an exact completion search shows that none of them is the set of first factors of a decomposition. The computation emits certificates, which are checked in the Lean 4 proof assistant by checkers whose soundness is proved in Lean. The largest checks are evaluated as compiled code, so the proof relies on the Lean compiler in addition to its kernel.",
      "title": "The rank of $3\\times 3$ matrix multiplication over $\\mathbb{F}_2$ is 23",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.11823"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12030",
      "authors": [
        "Andrea Brunello",
        "Cristian Curaba",
        "Luca Geatti",
        "Michele Mignani",
        "Angelo Montanari",
        "Nicola Saccomanno"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12030",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
      ],
      "published": "2026-10-08",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Large Language Models (LLMs) have renewed interest in autoformalization. Yet, when First-Order Logic (FOL) is considered as the target formalism, the field still lacks a unified task formulation and a systematic survey. This paper addresses this gap: we first provide a principled definition for the FOL-autoformalization task by distinguishing Ontology Extraction from Logical Translation, showing how their conflation obscures (cross-study) evaluation; we review existing datasets, evaluation metrics, and LLM-based methods, including fine-tuning, prompting, and verification-based refinement; we identify open challenges in benchmarking, semantic evaluation, ontology-aware methods, and end-to-end applications.",
      "title": "Natural Language to First-Order Logic LLM-based Autoformalization",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12030"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.09681",
      "authors": [
        "Shuangjie Yao",
        "Nikolaus Holzer",
        "Mark Paul Santolucito",
        "Baishakhi Ray",
        "Suman Jana",
        "Dongdong She"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.09681",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-07",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Program verification establishes software correctness through machine-checkable proofs constructed in theorem provers. It's a guarantee especially valuable for code generated by large language models (LLMs), which is fluent but carries no assurance of correctness. Almost all existing provers, however, pursue pass rates alone at whatever sampling or search budget it takes, and overlook the success-vs-cost frontier; yet real software often carries hundreds of interdependent proof obligations, so what matters at scale is not whether one theorem can be proved, but how many can be proved economically. We introduce CoCo-Prover, which formalizes cost-efficient program proving as metalevel decision-making under cost, grounded on two-level proof graphs: an AND/OR proof hypergraph within each declaration is joined to a lemma-dependency graph across declarations; and at each step, it answers two questions: which open goals to select, and which actions to purchase on these goals. Selection stays symbolic as a topological pass over the proof graphs. Action choice is agent orchestration via metalevel decision-making: an agentic router treats every bounded specialist invocation as a separately priced, best-effort computation, matching heterogeneous specialist agents together with configurations, under evolved routing rules as evidence accumulates. On five program verification benchmarks in Lean 4 including function-level CLEVER, VERINA, and AlgoVeri, and repository-level NTP4VC and Vero, we show that CoCo-Prover achieves a better success-vs-cost frontier than baselines including frontier coding agents and state-of-the-art LLM-based provers: it achieves the best solve rate on every benchmark and up to 100% on two benchmarks. It also reduces cost by up to 30.9% compared to the strongest baseline with the strongest LLM in our evaluation.",
      "title": "Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.09681"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10248",
      "authors": [
        "Minbo Gao",
        "Tianshi Yu",
        "Lihong Zhi"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10248",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-07",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We construct an explicit binary linear system game that separates $C_{qa}$, the closure of the set of finite dimensional quantum correlations, from $C_{qc}$, the set of commuting operator correlations. The game admits a perfect commuting operator strategy, while every correlation in $C_{qa}$ has a success probability strictly less than 1. This provides a concrete counterexample to Tsirelson's problem in its approximation form. The defining system has 1417152 equations in 1889684 variables, with exactly three nonzero coefficients per equation and a single nonzero entry on the right hand side. We also compute the classical value exactly. The complete system is specified in Lean 4, and the separation and exact classical value are formalized using Mathlib.",
      "title": "An Explicit Counterexample to Tsirelson's Problem via a Linear System Game",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.10248"
    },
    {
      "age_days": 5,
      "arxiv_id": "2610.09005",
      "authors": [
        "Brett Saiki",
        "Bill Zorn",
        "Cynthia Richey",
        "Zachary Tatlock"
      ],
      "content_date": "2026-10-06",
      "freshness": "fresh",
      "id": "arxiv:2610.09005",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Number libraries, which implement number formats and their arithmetic in software, are used to simulate hardware, making hardware behavior reproducible and thus verifiable and easier to design. However, modern machine learning accelerators are difficult to simulate, as they increasingly use specialized number formats that existing number libraries do not support. It is costly to extend these libraries using traditional methods: each combination of operation, format, and rounding mode typically requires a bespoke implementation. An easier way is to double round---compute at higher precision, then re-round---so that one high-precision kernel serves many formats, but double rounding is only known to be correct in select cases. We give a precise, efficiently checkable characterization of when double rounding is correct across many formats and rounding modes. Our result rests on a novel abstract number format that unifies fixed- and floating-point representations, reducing the correctness of double rounding to format containment: whether every value of one format is representable in another. We mechanized these results in Lean 4. In addition, we introduce a format inference algorithm that, given a sequence of operations, bounds each expression by a number format guaranteed to contain its result. We apply these insights in two ways. First, we present MPFX, a correctly-rounded, multi-precision number library that exploits correct double rounding to efficiently simulate many number formats. MPFX's correctly-rounded operations are up to 11x (mean: 6.05x) faster than MPFR's, and competitive with SoftFloat's---between 0.46x and 1.63x as fast (mean: 0.94x)---at the same precision. Second, in a case study, we implement a software simulation of a hardware specification using both SoftFloat and MPFX's primitives; the MPFX version is up to 13.5x faster.",
      "title": "When Double Rounding is Correct",
      "updated": "2026-10-06",
      "url": "https://arxiv.org/abs/2610.09005"
    },
    {
      "age_days": 5,
      "arxiv_id": "2610.09159",
      "authors": [
        "Param Biyani",
        "Krishnamurthy Dvijotham"
      ],
      "content_date": "2026-10-06",
      "freshness": "fresh",
      "id": "arxiv:2610.09159",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "As autonomous coding agents get increasingly deployed, the risk that accidental or adversarially injected misspecifications in tasks lead to dangerous agent behavior is critical to address. Prior work has shown that agents given such tasks rarely flag the conflict and instead cheat, editing tests or hard-coding expected outputs, and the actions taken to cheat can cause real damage, such as deleting a security defense to make a corrupted test pass. It remains unclear whether such conflicts can be established with independently verifiable evidence before the agent acts. We present SpecGuard, which detects and formally certifies these conflicts between task intent and tests. Given only the task description and codebase, SpecGuard autoformalizes the intended behaviour into a Lean 4 specification. The tests are formalized independently, and the Lean kernel checks whether any implementation could satisfy both formalizations, producing a machine-checked certificate when none can. On conflicted SWE-bench tasks, SpecGuard detects up to 72.8% of conflicts and formally certifies up to 51.1%, with a nearly five-fold lower conflict miss rate than model-based judgment. SpecGuard provides a pre-execution safety check that identifies reward-hacking opportunities through formal certification of task-level conflicts, before any agent behavior is observed. Our code is available at https://github.com/prmbiy/specguard.",
      "title": "SpecGuard: Proving a Task Is Broken Before the Agent Cheats",
      "updated": "2026-10-06",
      "url": "https://arxiv.org/abs/2610.09159"
    },
    {
      "age_days": 5,
      "arxiv_id": "2610.10599",
      "authors": [
        "Fedor Vorobyev"
      ],
      "content_date": "2026-10-06",
      "freshness": "fresh",
      "id": "arxiv:2610.10599",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-10-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove that a random 3-SAT formula with $n$ variables and $\\lfloor 4.268n\\rfloor$ clauses is unsatisfiable with high probability. The satisfiability threshold has attracted considerable attention: successive upper bounds reached 4.4898 in the work of Díaz, Kirousis, Mitsche, and Pérez-Giménez, while the cavity method predicts a value near 4.267. Our bound brings the rigorous upper estimate close to this prediction. The proof builds on earlier interpolation methods, including the energetic approach of Achlioptas and Menchaca-Méndez. We study the smallest number of clauses that any assignment must violate, comparing the random formula with a simpler system of constraints on individual variables. This comparison reduces the bound to a finite calculation, which we verify using exact rational arithmetic. The proof is formalized in Lean 4.",
      "title": "An upper bound of 4.268 for the random 3-SAT satisfiability threshold",
      "updated": "2026-10-06",
      "url": "https://arxiv.org/abs/2610.10599"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10049",
      "authors": [
        "Obada Kraishan"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10049",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "reasoning_rl_distillation"
      ],
      "published": "2026-10-07",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Reasoning models allocate extra computation at inference time and present their answers as the product of deliberate thought. If this deliberation works the way dual-process accounts of human cognition suggest, longer thinking should weaken the classic decision biases that fast, intuitive judgment produces. Using 30 vignettes covering six biases (anchoring, framing, loss aversion, escalation of commitment, availability, confirmation) from an established benchmark, we run a dose-response study across four model families, pairing each reasoning model with a matched non-reasoning sibling and requesting thinking ceilings of 0, 1,024, 4,096, and 8,192 tokens, for 12,350 API calls. Because a requested ceiling is not the same as realized deliberation, we use the reasoning tokens each call consumed as the dose. First, reasoning models are not less biased than their siblings; the point estimate leans the other way in every family, but the item-level pooled contrast is not reliable (Delta = +0.031, t(29) = 1.45, p = .157). Second, bias magnitude does not reliably fall as realized deliberation grows: no slope is significantly negative, and where anything moves it is the signed score drifting further from the human direction. Third, anchoring is the only bias in the human direction (d = 1.89). Four of the other five lean the opposite way in all seven models; with five items per bias, that reversal is reliable for framing and directional for escalation of commitment, confirmation, and loss aversion, while availability is absent. A one-line instruction to restate the anchor before answering lowered anchoring on all five anchoring items, which no amount of additional thinking did, although the effect does not reach significance (p = .057). The results argue against treating test-time reasoning as a rationality guarantee and for auditing deployed models bias by bias.",
      "title": "The Long Road to the Same Answer: Cognitive Bias Under Escalating Reasoning Budgets in Large Language Models",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10049"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.09367",
      "authors": [
        "Xindan Zhang",
        "Baochun Li",
        "Zongpeng Li"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.09367",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-10-07",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "Network coding lets the nodes of a network combine messages rather than merely forward them. In undirected networks, where the two directions of an edge share its capacity, Li and Li conjectured in 2004 that coding offers no advantage over fractional routing; the conjecture has been confirmed for many special classes but never settled in general. In this paper, we disprove it by constructing a finite connected simple undirected network with unit shared edge capacities, maximum degree three, and distinct leaf terminals, on which a binary linear block code achieves a common rate strictly above the maximum fractional routing rate. The construction turns a short completion-time code into a reversible circuit whose registers all carry independent messages, and a temporal metric on its wires yields the strict routing bound. The underlying integer-coefficient construction works over every finite field and every nontrivial finite abelian group; for deterministic fixed-schedule codes the common-rate supremum is one and the closure of the rate region is the unit cube. Amplifying the gap with a degree-preserving tensor construction and an even subdivision gives, for every $0<β<1$, an unbounded family of connected, simple, subcubic, bipartite networks with girth at least $n^β$ on which coding approaches rate one while routing is bounded by $K_β/(\\log n)^c$, with one positive exponent $c$ independent of $β$. The finite counterexample and the family theorem are formalized in Lean.",
      "title": "Network Coding Can Beat Routing in Undirected Multiple-Unicast Networks",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.09367"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10243",
      "authors": [
        "David Kurniadi Angdinata",
        "Kenny Lau",
        "Ken Ono",
        "Ashvin Swaminathan",
        "Sameera Vemulapalli"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10243",
      "kind": "paper",
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        "general_ai_math_reasoning"
      ],
      "published": "2026-10-07",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "For elliptic curves $E/\\mathbb{Q}$ in short Weierstrass form \\[ E=E(a_4,a_6): y^2=x^3+a_4x+a_6, \\] we derive a multivariable Euler product generating function which encodes the Tamagawa product $Tam(E)=\\prod_p c_p(E)$. Using this generating function, we compute limiting distributions, exact covariances, and moment and tail bounds for four important statistics on the Tamagawa number; for example we show that more than half of all curves in this height ordering have trivial Tamagawa product, about $42.2\\%$ have exactly one prime with nontrivial local Tamagawa number, and only about $6.8\\%$ have exactly two such primes. The product is obtained by specializing an Euler product indexed by local reduction data that we derive from Tate's algorithm. The results in this paper were autoformalized in Lean by AxiomProver.",
      "title": "Local Factors in the BSD Conjecture: A Unified Statistical View",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10243"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.09401",
      "authors": [
        "Xiaopeng Yuan",
        "Suijin Wang",
        "Yanli Wang",
        "Haibo Jin",
        "Peng Kuang",
        "Jerry Wang",
        "Lijun Yu",
        "Haohan Wang"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.09401",
      "kind": "paper",
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        "general_ai_math_reasoning"
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      "published": "2026-10-07",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "LLM-based formal provers can retrieve relevant lemmas and prior proofs, but relevance alone does not say whether a mathematical method can be used on the current theorem. A method has prerequisites, a target, an intended action, and obligations that its use leaves to prove. Methods that look equally related to a theorem may therefore differ substantially in whether they offer a plausible next step. We formulate this as an applicability-aware method-selection problem and introduce self-advertisement: before candidates are ranked, a model generates a problem-specific proposal for each one, stating what part of the goal it targets, what action it would take, and what conditions that action requires. We organize 82 reusable methods from Putnam 2000-2014 as Method Contracts, which pair applicability descriptions with Mathlib anchors, a checked example or scaffold, and expected proof obligations. A single batched call elicits proposals across the library; vague or unsupported proposals are demoted, yielding a ranked shortlist accompanied by inspectable claims about each candidate's use. We analyze when similarity-based representations cannot distinguish methods with different applicability, how errors in applicability estimates affect shortlist quality, and what a checked scaffold guarantees under its stated assumptions. Against lexical, embedding, and embedding-plus-LLM reranking baselines, self-advertisement achieves 95.0% hit@5 on Putnam 2015-2025, compared with 84.2% for the strongest reranker. On IMO ProofBench, it achieves 91.7% compared with 88.3%. These results indicate improved coverage of annotated methods in the retrieved shortlists, particularly on Putnam.",
      "title": "Let the Library Speak: Self-Advertised Method Selection for Formal Proving",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.09401"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:fe2da218b955",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: keep a `Prop` hypothesis when `grind` applies eager `cases` to it (#15612)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover/lean4/commit/fe2da218b955ca5219f04e9e9a696bab7bc26f0f"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2bbdc293f6ca",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: generate a script for every goal in `grind?` when parameters split the goal (#15611)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover/lean4/commit/2bbdc293f6ca050a67ebc7ec2a8250d571482a9c"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:1aacc7a9b6de",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: drop metadata on the arithmetic spine in the `Sym.Arith` normalizer (#15619)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover/lean4/commit/1aacc7a9b6de1cf33bc7e0b0ba0505ddc12417fd"
    },
    {
      "age_days": 0,
      "authors": [
        "Leonardo de Moura"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:12ae34c29a6b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: canonicalize class fields that are not global instances in `Sym.canon` (#15618)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover/lean4/commit/12ae34c29a6b5df76fc2641ae1671784c19f527f"
    },
    {
      "age_days": 0,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0ec09562d639",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: add a few more BitVec terms to bv_decide (#15616)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover/lean4/commit/0ec09562d6398d0fab6ed92a696f03d0837ae725"
    },
    {
      "age_days": 0,
      "authors": [
        "Keith Adler"
      ],
      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:591130056fe5",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix(Data/DFinsupp,Order/Preorder/Finsupp): make `coe_strictMono` state `StrictMono` (#44705)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/591130056fe555daaae6fa337f3a19e0d7c846c2"
    },
    {
      "age_days": 0,
      "authors": [
        "Keith Adler"
      ],
      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:d6416ab0f09d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: fix(AlgebraicTopology/ModelCategory): state `homEquivLeft_symm_apply` about `homEquivLeft` (#44703)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/d6416ab0f09d3a2e090f403fc80f37754f6181a9"
    },
    {
      "age_days": 0,
      "authors": [
        "Michael Rothgang"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:1619863c2b37",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat: add `ContMDiffWithinAt.contMDiffWithinAt_tangentMapWithin` and friends (#44710)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/1619863c2b37930e217c20c40ea1e3ce0cc78500"
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    {
      "age_days": 0,
      "authors": [
        "vaca22"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:ce6b42af2209",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: feat(RingTheory): generalize relNorm_eq_pow_of_isMaximal to separable fraction field extensions (#41696)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/ce6b42af2209e89aaf78aba5432fbfd1c4ed6c0c"
    },
    {
      "age_days": 0,
      "authors": [
        "Justus Springer"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:be54e3f266c1",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: doc: fix references.bib keys whose year does not match the entry (#44758)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/be54e3f266c15cb52e61d18debe1a95fdc854954"
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    {
      "age_days": 0,
      "authors": [
        "Justus Springer"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:40130aac5fa6",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: doc(*): use existing citation keys for free-text citations (#44673)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/40130aac5fa6beb6ca371ee462d239d5e89138dc"
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    {
      "age_days": 0,
      "authors": [
        "Yaël Dillies"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:939d5d5d9e6f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: use the `Finset.card` notation more widely (#44638)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/939d5d5d9e6f07d1d8c80a16fa3fa39a7518b716"
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      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:a22f517ce88f",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore: dualize `Lattice` projections (#44608)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/a22f517ce88f68fffb2c5aef127706516f487054"
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      "age_days": 0,
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        "mathlib-nolints[bot]"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:2da3ab0a20dc",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(scripts): update nolints.json (#44719)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/2da3ab0a20dc0c66f56a557e37df39f7d36cb953"
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      "age_days": 0,
      "authors": [
        "user202729"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:fa89eff14f58",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Topology): fix some spelling errors (#44752)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/fa89eff14f58e554df4001c58e3d3b8adb64ebb5"
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      "age_days": 0,
      "authors": [
        "Snir Broshi"
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      "content_date": "2026-10-11",
      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:051bc081081f",
      "kind": "github_update",
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      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(Order/SuccPred/Relation): use `to_dual` (#44412)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/051bc081081f2bb77b81d47ee69146c4cef28bbe"
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      "freshness": "fresh",
      "id": "github:leanprover-community/mathlib4:feefa3237dfe",
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      "matched_signals": [],
      "published": "2026-10-11",
      "repo": "leanprover-community/mathlib4",
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      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(LinearAlgebra/Matrix/DualNumber): automated extraction from #44776 (#44779)",
      "updated": "2026-10-11",
      "url": "https://github.com/leanprover-community/mathlib4/commit/feefa3237dfed481db898e96db56d47f6f992c15"
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        "Sofia Rodrigues"
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      "freshness": "fresh",
      "id": "github:leanprover/lean4:07c4dc383411",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-10",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: share error and promise helpers in the libuv bindings (#15594)",
      "updated": "2026-10-10",
      "url": "https://github.com/leanprover/lean4/commit/07c4dc383411a38473a390bd4351d184a43efecc"
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    {
      "age_days": 1,
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      "freshness": "fresh",
      "id": "github:leanprover/lean4:50541c319404",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-10",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: embed libuv handles in the uv socket, timer and signal objects (#15545)",
      "updated": "2026-10-10",
      "url": "https://github.com/leanprover/lean4/commit/50541c3194040b253c3e835340683227a5c462f0"
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    {
      "age_days": 1,
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        "Sofia Rodrigues"
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      "content_date": "2026-10-10",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:ca7a383af084",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-10",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: add RAII-based scoped lock guard (#15547)",
      "updated": "2026-10-10",
      "url": "https://github.com/leanprover/lean4/commit/ca7a383af084133dcf631c6b4db41d4ed958bfab"
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    {
      "age_days": 1,
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        "Leonardo de Moura"
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      "content_date": "2026-10-10",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:62801e856156",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-10",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: validate `finish?` suggestions at the goal before its parameters are asserted (#15606)",
      "updated": "2026-10-10",
      "url": "https://github.com/leanprover/lean4/commit/62801e856156a7485568696a868d3b4b49ec1e7c"
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    {
      "age_days": 1,
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        "Leonardo de Moura"
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      "content_date": "2026-10-10",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d285f8dd8efc",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-10",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: queue solver callbacks replayed during `grind` internalization (#15599)",
      "updated": "2026-10-10",
      "url": "https://github.com/leanprover/lean4/commit/d285f8dd8efc8f29d839ce91fd1a15beb8751761"
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      "kind": "github_update",
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      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: make the export file reader more robust (#15542)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/8fc4172a7f2bdae17e2685149767936336b54f35"
    },
    {
      "age_days": 2,
      "authors": [
        "Wojciech Nawrocki"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:ea247feb4a54",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: handling of 0 in JsonNumber.lt (#15571)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/ea247feb4a54affc68e4b7664ca6f5f73d02b768"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b70afe029893",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: evaluate `cond` lazily in `cbv` (#15582)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/b70afe0298938afe3c8354b045103ef2ce52957d"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:00f086c65ccb",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: do not export realizations triggered only from proofs (#15559)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/00f086c65ccbdee1573c00bcf33b9a64c3cb712d"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:88396769e026",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: do not export `MapDeclarationExtension` entries of private declarations (#15558)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/88396769e0267e48d45fb59c5e4859cea35199b9"
    },
    {
      "age_days": 2,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:c1f2fc66e14c",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: builtin component instances in the `grind` canonicalizer (#15588)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/c1f2fc66e14cf8632e9dd0e0702d407fdc67b9c6"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:d10dc23fa535",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: guard WP.Frames by the ambient precondition (#15497)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/d10dc23fa5351c1d09cfccb7ae4609fdd9f83806"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:91c127243f5d",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: remove leftovers of the old code generator from `Environment` (#15561)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/91c127243f5d1ff33f17ca1b8542e2470a47e80f"
    },
    {
      "age_days": 2,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:87efbbc10605",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: rebalance `libleanshared` DLL split on Windows to avoid symbol limit (#15573)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/87efbbc1060504496cb284ed460d5e5b24e9d707"
    },
    {
      "age_days": 2,
      "authors": [
        "Julia Markus Himmel"
      ],
      "content_date": "2026-10-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:2d3120b46ca4",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: code action to add the deprecation date (#15572)",
      "updated": "2026-10-09",
      "url": "https://github.com/leanprover/lean4/commit/2d3120b46ca4c115aa1cc467c8ab88c19ef4a738"
    },
    {
      "age_days": 3,
      "authors": [
        "Sebastian Ullrich"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:0bb12a87a834",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: assorted `compiler.postponeCompile` fixes (#15565)",
      "updated": "2026-10-08",
      "url": "https://github.com/leanprover/lean4/commit/0bb12a87a8347e45560bc4b4f21c9abd83bbca0a"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12234",
      "authors": [
        "Baiying Liu"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12234",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-08",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Recently, a uniform $\\frac{7}{8}$ zero-free half-plane for finite-order Hecke $L$-functions over $\\mathbb Q(\\sqrt{-3})$ and its transfer to Dirichlet $L$-functions was given by OpenAI in [1]. In its proof, there are two chosen parameters $b=\\frac{1}{8}, \\ell=\\frac{1}{6}$. In this note, via varying $b$ and $\\ell$, following the same strategy, we slightly improve the bound $\\frac{7}{8}=0.875$ to be $$B_{\\mathrm r}=\\frac{34999}{40000}=0.874975, (\\text{when }b_{\\mathrm r}=\\frac{1}{8}, \\ell_{\\mathrm r}=\\frac{1}{6} + \\frac{1}{10000});$$ and \\[ \\begin{gathered} B_{\\mathrm{new}}=\\frac{1507-2\\sqrt{921}}{1653} =0.874957069799\\ldots, (\\text{when }b_{\\mathrm{new}}=-\\frac{4}{29}+\\frac{230\\sqrt{921}}{26709}, \\ell_{\\mathrm{new}}=\\frac{33+8\\sqrt{921}}{1653}). \\end{gathered} \\] This result has been formalized by Lean ([15]).",
      "title": "Slightly improved zero-free half-planes for the quasi-Riemann hypothesis",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12234"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12168",
      "authors": [
        "Lars Simon",
        "Holger Eble",
        "Manuel Radons"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12168",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-08",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We introduce a self-improvement loop for reasoning models based on the following observation: Even when the difficulty of a problem exceeds the model's current solving abilities, an additionally supplied solution might enable the model to extract useful solution ideas in hindsight. We operationalize this by jointly training the same model to exhibit the following three capabilities: predicting solution ideas from problems alone, reverse-engineering ideas from problems and known solutions, and solving problems using provided ideas. The loop alternates between reverse engineering such ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities. We give a formal specification of our method and a concrete instantiation for interactive theorem proving in the Lean theorem prover; empirical evaluation remains future work.",
      "title": "Learning to Plan by Looking Back: Hindsight Hierarchies for Training Reasoning Models",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12168"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.11879",
      "authors": [
        "Scott Armstrong",
        "Benny Avelin",
        "Tuomo Kuusi",
        "Aatu Turpeinen"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.11879",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-08",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We extend the theory of De Giorgi-Nash-Moser to elliptic equations with symmetric coefficients $\\mathbf{a}(x)$ which are possibly degenerate and unbounded but satisfy a coarse ellipticity condition. We prove local upper bounds for weak subsolutions, a weak Harnack inequality for nonnegative supersolutions, and a Harnack inequality for nonnegative solutions. The coarse ellipticity hypothesis requires spatial moments of coarse-grained matrices, suitably discounted and summed across scales, to be finite. In particular, it holds if, for some $α,β\\geq0$ and $1<p,q<\\infty$, $$\\mathbf{a}\\in W^{-α,p}\\cap L^1, \\quad \\mathbf{a}^{-1}\\in W^{-β,q}\\cap L^1 \\quad\\text{and}\\quad \\frac{α+β}{2}+\\frac{d-1}{2}\\Big(\\frac1p+\\frac1q\\Big)<1.$$ We show that the coefficient range is sharp, including its boundary, in every dimension $d\\geq3$, for $α=β=0$ and for the corresponding Besov-type quasi-norms of negative order when $α,β>0$. For $α=β=0$, it corresponds to the results of Bella and Schäffner [8].",
      "title": "Coarse ellipticity and De Giorgi-Nash-Moser theory in the optimal range",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.11879"
    },
    {
      "age_days": 3,
      "arxiv_id": "2610.12335",
      "authors": [
        "Scott Armstrong",
        "Ahmed Bou-Rabee",
        "Tuomo Kuusi"
      ],
      "content_date": "2026-10-08",
      "freshness": "fresh",
      "id": "arxiv:2610.12335",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-08",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We study a Brownian particle in $\\mathbb{R}^d$, $d\\geq2$, with drift given by the gradient of a log-correlated Gaussian potential. At weak disorder, we prove convergence to a scaling limit whose law is singular with respect to Brownian motion and whose invariant measure is given by Gaussian multiplicative chaos. The proof uses a renormalization group induction: at each scale, the elliptic operator is well approximated by a Laplacian with effective diffusivity decaying as a power of scale. We compute this exponent exactly in dimension two.",
      "title": "Anomalous scaling limit of a Brownian particle in a log-correlated potential",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.12335"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.09258",
      "authors": [
        "Arjun Pemmasani"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.09258",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We observe a ball bouncing down a Galton board with any number of directions. At each peg it either keeps its direction with some fixed probability or randomly turns to one of the other directions. Its bin measures how often it went each way, a point of a simplex. When the ball rarely turns, the most likely bins are the corners, which only a ball that never turns can reach. We ask when the best bin of each face of the simplex becomes as likely as a corner. To first order every face catches up at the same moment. We break this tie at second order, with an explicit constant for each face. Hence on a long board, as the expected number of turns grows to any fixed multiple of the length's logarithm, the most likely bin jumps once, from the corners straight to the center. A nonuniform start or a weak external field changes the constants, potentially allowing an intermediate face to win.",
      "title": "Vertex crossings in a symmetric Markov multinomial model",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.09258"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10397",
      "authors": [
        "Angelina Blahodatna",
        "Lauren Detmold",
        "Daniel Glasscock",
        "Anh N. Le"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10397",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The regionally proximal and equicontinuous structure relations are fundamental relations in topological dynamics that capture the equicontinuous behavior in a topological dynamical system and its factors. For minimal actions of abelian groups, these relations are known to be equivalence relations and are known to coincide. In this paper, we generalize these facts to semigroup actions: for minimal actions of commutative semigroups, the regionally proximal and equicontinuous structure relations are equivalence relations and the two coincide. We also develop the machinery of natural extensions for commutative semigroup actions that act by surjections, concluding that the maximal equicontinuous factor of a minimal action of a commutative semigroup is the same as the maximal equicontinuous factor of the group action into which it embeds. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.",
      "title": "The regionally proximal relation for commutative semigroup actions",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10397"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10416",
      "authors": [
        "Angelina Blahodatna",
        "Lauren Detmold",
        "Daniel Glasscock",
        "Anh N. Le"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10416",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "In this paper, we strengthen the connection between the combinatorics of difference sets and the dynamics of group rotations. Our main result shows that sets which have non-empty intersection with all difference subsets of a commutative semigroup possess local Bohr structure. This generalizes results of Bergelson, Furstenberg, and Weiss and Host and Kra from the integers to arbitrary commutative semigroups. We accomplish this by A) utilizing a recent result showing that the regionally proximal relation is an equivalence relation for minimal actions of commutative semigroups and by B) describing a new, DeMorgan-type algebra on Furstenberg families that allows for efficient manipulation and computation. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.",
      "title": "The local dynamical structure of $Δ^*$ sets via a new Furstenberg family algebra",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10416"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10162",
      "authors": [
        "Ahmed Bou-Rabee",
        "Yuval Peres"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10162",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "A centrally excited random walk on ${\\mathbb Z}^d$ moves like simple random walk, except that its first step from each site has a drift of fixed size toward the origin. Kozma (2007) conjectured that after $n$ steps the visited set approximates a ball with radius of order $n^{ 1/(d+1)}$. We prove this in every dimension $d\\geq2$ and show that the rescaled numbers of visits converge uniformly to a cone, which is the potential generated by the drift on a ball. The same argument shows that a drift opposite to a subgradient of a norm produces the ball of that norm. In the plane, the outer and inner radii of the visited set differ by at most $ n^{1/6}$ times a power of $\\log n$, and the exponent $1/6$ cannot be lowered.",
      "title": "Kozma's centrally excited walk converges to a Euclidean ball",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10162"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.09733",
      "authors": [
        "Seunghan Kim",
        "Minyeong Choe",
        "Hyunil Kim",
        "Haehyun Cho"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.09733",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Multilingual LLMs answer the same multi-hop reasoning question across languages, but we lack a mechanistic account of whether they share an internal circuit. We identify Bridge Routing Heads (BRH) in two large multilingual LLMs through a three-stage pipeline. The resulting language-specific head sets exhibit near-complete mutual exclusivity across the five languages, with a mean Jaccard similarity of only 0.017 for Llama 3.1 70B and 0.057 for Qwen 2.5 72B, revealing language-idiosyncratic circuits. Ablating general BRH increases two-hop Negative Log-Likelihood (NLL) by 39-89x the random-head baseline, providing direct causal evidence of their role. Amplifying these heads in a failing target-language pass rescues up to 51.7% of cross-lingual failures, with no training. The two models share this dual-circuit pattern but allocate heads differently: Llama concentrates chaining in a large general pool, while Qwen leans on larger language-specific pools. Together these results show that activation-level intervention alone can recover correct answers from cross-lingual reasoning failures.",
      "title": "Bridge Routing Heads: Where Multilingual Multi-hop Reasoning Lives in LLMs",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.09733"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.11014",
      "authors": [
        "Hanyue Shen",
        "Pavel B. Dubovski"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.11014",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We determine the minimum volume product of centrally symmetric polytopes obtained by adding facet apices to a cube while fixing their total outward height. Heights and tangential coordinates vary subject to a product condition on the polar-cap denominators. In every dimension at least two, the minimum has an explicit formula, attained by concentrating the height at one opposite pair of corner apices. For positive height in dimensions at least three, every minimizing array has this structure. The product condition strictly extends coordinatewise quadratic constraints. We also obtain two bounds without that condition: a four-dimensional Mahler bound for a specified height range, and a correction measuring volume generated jointly by two apices. The latter certifies a continuous family outside the preceding sufficient conditions. The proof combines known cap volumes with a sharp aggregate height estimate and a double-pyramid construction. Lean~4 verifies the actual-volume minimum, the necessary equality structure and both extensions.",
      "title": "A sharp minimum for cube-apex bodies in every dimension",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.11014"
    },
    {
      "age_days": 5,
      "arxiv_id": "2610.09206",
      "authors": [
        "Hazar Yueksel"
      ],
      "content_date": "2026-10-06",
      "freshness": "fresh",
      "id": "arxiv:2610.09206",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Loss-difference conditional mutual information (ld-CMI) uses the smallest of the standard observations in the supersample hierarchy of generalization bounds: it measures what a learner's loss differences reveal about which candidate of each pair it was trained on. Accuracy is known to force information into the model; data processing does not carry such lower bounds to losses. We show, by bounding three moments of the loss differences, that accuracy also forces ld-CMI. For linear predictors with a smooth convex loss of nonzero slope at zero, such as the logistic loss, plus a regularizer whose curvature and growth are both of power $r\\ge2$, on product distributions over a scaled sign cube in dimension at least linear in $n$, every proper learner with expected excess risk at most $\\varepsilon$ on these distributions at the optimal sample size $n\\asymp\\varepsilon^{-2+2/r}$ has worst-case ld-CMI of order $n$ bits, and $Θ(n/(1+(τ/\\varepsilon)^2))$ bits under Gaussian noise of standard deviation $τ$ on the loss differences. The same holds without a regularizer, at $n\\asymp\\varepsilon^{-2}$. Consequently, range-scaled ld-CMI bounds cannot vanish on these distributions, although every proper learner's generalization gap is $O(n^{-1/2})$. We also show that model-level information does not determine noisy loss-difference information, and that the growth, slope and dimension conditions are needed, the last up to a logarithm.",
      "title": "An Accuracy-Information Tradeoff for Loss-Difference Conditional Mutual Information",
      "updated": "2026-10-08",
      "url": "https://arxiv.org/abs/2610.09206"
    },
    {
      "age_days": 5,
      "arxiv_id": "2610.09093",
      "authors": [
        "Nathaniel Craig"
      ],
      "content_date": "2026-10-06",
      "freshness": "fresh",
      "id": "arxiv:2610.09093",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-10-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "We nonperturbatively construct a gauge-invariant measure for overlap fermions on four-dimensional Euclidean lattices in a class of nonabelian chiral gauge theories that includes the Standard Model. On admissible gauge fields, comparing chiral projectors at successive lattice spacings yields an exponentially local current and establishes the global properties needed for Lüscher's reconstruction of a smooth, gauge-invariant fermion measure. This provides a candidate nonperturbative lattice definition of the Standard Model.",
      "title": "A gauge-invariant measure for lattice chiral fermions",
      "updated": "2026-10-06",
      "url": "https://arxiv.org/abs/2610.09093"
    },
    {
      "age_days": 4,
      "arxiv_id": "2610.10673",
      "authors": [
        "Alfredo Guevara"
      ],
      "content_date": "2026-10-07",
      "freshness": "fresh",
      "id": "arxiv:2610.10673",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [
        "negative:vision_world_models"
      ],
      "published": "2026-10-07",
      "score": -2.5,
      "source": "arxiv-ai4math-core",
      "summary": "We argue that the scattering amplitude of a single minus helicity gluon with arbitrarily many positive helicity gluons is topological. The amplitude is constant in chambers of kinematic space, its resonances are located at walls and its factorization is determined by wall-crossing. Yangian invariance dictates the amplitude to be determined by a 2d null Wilson loop that can be lifted into a positive and transverse 3d link. By reinterpreting wall-crossing and the Weinberg soft theorem as skein relations and Reidemeister moves of the subknots, we construct a state-counting description consisting of adding the `corners' of their HOMFLY-PT polynomials. Beyond the classical limit, we argue that this provides a conjectured but precise connection to topological field and string theory. The new formula is rigorously derived via a Lean-formalized dependency graph (DAG) as detailed in a companion paper, laying out the precise assumptions including Reidemeister III invariance. It is further tested exhaustively, including novel `star' kinematics where the amplitude and state count are shown to become Catalan numbers, in agreement with knot theory literature.",
      "title": "Gluons and Knots",
      "updated": "2026-10-07",
      "url": "https://arxiv.org/abs/2610.10673"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}