{
  "counts": {
    "adjacent": 14,
    "core": 2,
    "errors": 0,
    "negative": 73,
    "total": 89
  },
  "date": "2026-08-11",
  "errors": [],
  "fresh_content_days": 21,
  "generated_at": "2026-08-11T16:25:44Z",
  "items": [
    {
      "age_days": 4,
      "arxiv_id": "2608.07388",
      "authors": [
        "David Muñoz-Lahoz"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07388",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "autoformalization",
        "lean_formal_proving_agents",
        "mathlib_retrieval"
      ],
      "published": "2026-08-07",
      "score": 9.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present a Lean 4 library for the theory of Banach lattices. Its purpose is to support the systematic formalization of contemporary research in Banach lattices and related areas. As evidence of this, we describe three research-level formalizations built using the library. Writing the library at scale was made possible by the use of LLMs with careful human supervision and planning. Unlike autoformalization, this approach allows for an actual understanding of the code. This, in turn, led to new mathematical insights that are also discussed. Judging by the interest expressed by other researchers, we expect the library to become a communal effort in the near future. For this reason, we also describe several parts of the theory that could be added next.",
      "title": "The Banach lattice Lean library",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07388"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.07407",
      "authors": [
        "Heechang Kim",
        "Ernest K. Ryu",
        "Shuvomoy Das Gupta"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07407",
      "kind": "paper",
      "label": "core",
      "matched_signals": [
        "lean_formal_proving_agents",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-07",
      "score": 6.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present AutoOPT, a domain-specific harness for end-to-end automation of optimization research. AutoOPT organizes the discovery of optimal first-order methods into four stages: numerical design through the BnB-PEP methodology; symbolic discovery of the analytic description and a convergence proof through frontier large language models (LLMs); formal verification in the Lean 4 proof assistant; and human interpretation and write-up. We demonstrate the framework on two case studies, each of independent interest. The first, lemniscate acceleration, is a new accelerated gradient method for minimizing the gradient norm of a smooth convex function: after $N$ gradient steps it reduces the squared gradient norm at the optimal $O(1/N^{4})$ rate, with a constant governed by the lemniscate constant $\\varpi$, a classical elliptic-integral constant. The second is the analytic description of ITEM-f, a method previously known only numerically: for $L$-smooth, $μ$-strongly convex minimization it contracts the function-value gap at an accelerated linear rate with a per-step factor $(1-\\sqrt{μ/L})^{2}$. The convergence theorems of both case studies are formalized and machine-checked in Lean 4.",
      "title": "A Domain-Specific Harness for End-to-End Automation of Optimization Research",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07407"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.08643",
      "authors": [
        "A. Mayeux"
      ],
      "content_date": "2026-08-09",
      "freshness": "fresh",
      "id": "arxiv:2608.08643",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-09",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "The paper \\emph{Conjecture: the set of prime numbers is supernatural} conjectures that no non-constant function built from the identity and constants by finitely many pointwise additions, multiplications, and exponentiations maps every positive integer to a prime. We give a complete Lean~4 formalization of that paper over Mathlib: every definition, example, remark, numbered result, and experimental table row has a machine-checked counterpart, with no \\lcode{sorry}. The conjecture and similar generalizations are stated exactly, as named open problems. So stated, the conjecture becomes a precise target: an automated reasoning system can now attempt a kernel-checked proof.",
      "title": "The set of primes is supernatural: a Lean formalization of the statement of the conjecture",
      "updated": "2026-08-09",
      "url": "https://arxiv.org/abs/2608.08643"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06440",
      "authors": [
        "Abhishek Saigal",
        "Akaash R. Parthasarathy"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06440",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning",
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-06",
      "score": 4.9,
      "source": "arxiv-ai4math-core",
      "summary": "For every odd integer $t\\ge17$, we prove that an explicit circulant graph on $5t-10$ vertices is doubly saturated $R(3,t)$-good. The graph is triangle-free and has independence number $t-1$. Adding any nonedge creates a triangle, whereas deleting any edge creates an independent set of order $t$. This settles Conjecture 2 of Przybocki, Mackey, Heule, and Subercaseaux. A cyclic sumset identity and explicit witnesses prove the local saturation properties. Writing $t=2m+1$, a five-layer reduction proves the independence bound via a uniform affine certificate for $m\\ge30$ and an exhaustive checker for $8\\le m\\le29$. The checker soundness and the complete argument are formalized in Lean 4.32.2. Consequently, $2t-1\\le \\operatorname{DS}(3,t)\\le 5t-10$ for odd $t\\ge17$.",
      "title": "An infinite family of doubly saturated $R(3,t)$-good graphs",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.06440"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.09858",
      "authors": [
        "Ioseph L. Buchbinder",
        "Petr M. Lavrov",
        "Thomas M. Sangy",
        "Ilya L. Shapiro"
      ],
      "content_date": "2026-08-10",
      "freshness": "fresh",
      "id": "arxiv:2608.09858",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-10",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "One-loop divergences in classically conformal theory in curved spacetime is a nontrivial issue if the theory under consideration possesses gauge invariance. In this case, quantization involves introducing the gauge-fixing term and the action of ghosts, both of which are not conformal. The formal proof of the conformal invariant renormalizability in this situation, including interacting theories, has been given in the paper from 1984 by one of the present authors. Owing to BRST symmetry, the contributions of the gauge-fixing and ghost sectors to the conformal variation of the effective action cancel each other. This cancellation does not hold in the finite part of the one-loop and higher-loops effective action, that results in the anomaly. In this paper, we extend the early results on conformal matter fields in external gravitational field and apply them to conformal quantum gravity, including the case of conformal gravity coupled to other conformal matter fields. The gauge-fixing in the Weyl-squared gravity is more complicated, nevertheless, the proof of the one-loop conformal invariant renormalization using BRST symmetry is possible. As a preliminary to conformal quantum gravity, we also present a detailed general proof of conformal invariant one-loop divergences in the corresponding semiclassical theory.",
      "title": "On the Renormalization in Conformal Quantum Gravity",
      "updated": "2026-08-10",
      "url": "https://arxiv.org/abs/2608.09858"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.08421",
      "authors": [
        "Bernardo Subercaseaux",
        "Benjamin Przybocki"
      ],
      "content_date": "2026-08-09",
      "freshness": "fresh",
      "id": "arxiv:2608.08421",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "autoformalization"
      ],
      "published": "2026-08-09",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Tarski's high school algebra problem asks whether every true identity concerning addition, multiplication, and exponentiation of positive integers follows from a list of 11 elementary identities. Surprisingly, Wilkie showed that the following identity is valid over the positive integers and yet does not follow from Tarski's axioms: \\begin{align*} &\\left((1+x)^y + (1+x+x^2)^y\\right)^x \\cdot \\left((1+x^3)^x + (1+x^2+x^4)^x\\right)^y = \\\\ &\\left((1+x)^x + (1+x+x^2)^x\\right)^y \\cdot \\left((1+x^3)^y + (1+x^2+x^4)^y\\right)^x. \\end{align*} Gurevič gave an algebra on 59 elements that satisfies Tarski's axioms but not Wilkie's identity, and over the years several authors whittled down the size of such a countermodel, culminating in a countermodel of size 12 due to Burris and Yeats. On the other hand, Zhang proved that there is no countermodel with fewer than 11 elements. Using SAT, we prove that the smallest countermodels are of size 12, as conjectured by Burris and Yeats. Moreover, we show that there are exactly 8,957,952 countermodels on 12 elements up to isomorphism and provide a simple classification of them. Our SAT approach outperforms dedicated tools for finding countermodels in equational theories, namely Mace4 and SEM. Furthermore, using autoformalization, we prove the correctness of our main result in Lean.",
      "title": "A SAT Attack on Tarski's High School Algebra Problem",
      "updated": "2026-08-09",
      "url": "https://arxiv.org/abs/2608.08421"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.06682",
      "authors": [
        "Mayank Pandey"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.06682",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-07",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We make explicit and formalize a result of the author on squarefree numbers in short intervals, showing that for $0 < \\varepsilon\\le 1/90935 $, $X\\ge \\exp(10^{27}/\\varepsilon^2)$, $H = X^{1/5 - 2/90935 + \\varepsilon}$, we have that \\[ \\biggl|\\sum_{X\\le n\\le X + H } μ(n)^2 - \\frac{6}{π^2}H\\biggr| \\le \\frac{10^{450}}{\\varepsilon} H X^{-\\varepsilon/10^{25}}. \\] This article gives an account of what went into making the exponent explicit. The Github repository linked contains the formalization in Lean 4 as well as an account of what went into the largely automated formalization.",
      "title": "Squarefree numbers in short intervals: explicit and formalized",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.06682"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.07366",
      "authors": [
        "Daniel Goldberg",
        "Antoine Vinciguerra"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07366",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-07",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We formalize the Dirichlet integral and several of its classical applications in the Lean~4 proof assistant. Since the sinc function is not Lebesgue integrable on the positive half-line, the Dirichlet integral must be represented as the limit of integrals over bounded intervals. To avoid the difficulty of removing an exponential factor from a conditionally convergent integral, we instead pass through the absolutely integrable function \\(\\operatorname{sinc}^2\\). We evaluate its integral by differentiation under the integral sign and dominated convergence, and then recover the Dirichlet integral from an identity between truncated integrals. Using these results, we formalize the convergence of the Dirichlet cutoff to the Heaviside function and derive several quadratic and bilinear trigonometric integral identities. Finally, we formalize Lobachevsky's integral formula for continuous periodic functions satisfying a reflection symmetry, using the density of cosine polynomials obtained from Mathlib's Fourier analysis on the additive circle.",
      "title": "From the Dirichlet Integral to Lobachevsky's Formula: A Formalization in Lean 4",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07366"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.07384",
      "authors": [
        "Daniel Goldberg",
        "Antoine Vinciguerra"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07384",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-07",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present a Lean 4 formalization of the Laplace transform for complex-valued functions, its fundamental operational rules, and a Bromwich-type inversion theorem proved through real-variable integration and the Dirichlet integral. As an application, we formalize the Laplace-domain solution of the harmonic oscillator and identify its transform with that of $\\sin(ωt)$. We also discuss the principal analytic and formalization challenges encountered in the development.",
      "title": "A Formalization of the Laplace Transform and Its Inversion in Lean 4",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07384"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06261",
      "authors": [
        "Stefan Dziembowski",
        "Grzegorz Fabiański",
        "Daniele Micciancio",
        "Rafał Stefański"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06261",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We present HOPSCOTCH, a Lean 4 framework for mechanizing computationally sound, game-based cryptographic proofs. Security definitions are expressed as indistinguishability between stateful probabilistic oracles, and proofs follow the standard game-hopping paradigm. HOPSCOTCH uses a shallow embedding: oracles and reductions are ordinary Lean definitions, enabling direct integration with the full Lean ecosystem, including general mathematical theories from Mathlib, such as finite-group theory. A game-hopping proof in HOPSCOTCH is represented as an explicit formal object whose constructors correspond to the standard steps of a game-hopping argument, making proofs easier to construct, automate, and inspect. We prove a general computational soundness theorem that interprets these proof objects by constructing reductions against the assumptions they use and deriving a concrete bound on the advantage of any distinguisher. Observational equivalence between oracles is established using a state-abstraction methodology: a simple yet powerful approach that supports transformations such as adding or forgetting state and replacing eager sampling with lazy sampling. We illustrate the framework with formalized proofs of the IND-CCA security of encrypt-then-MAC, the security of ElGamal encryption from DDH, the implication from one-time secrecy to public-key IND-CPA security, and the GGM pseudorandom-function construction. To the best of our knowledge, the last is the first mechanized proof of GGM for non-constant depth.",
      "title": "Game Hopping in Lean",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.06261"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06531",
      "authors": [
        "Milos Tatarevic"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06531",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove the inequality $R(k+1,s+1) \\ge R(k,s) + 2k + 2s$ for classical Ramsey numbers, valid for all $5 \\le k \\le s$, and formalize the proof in Lean 4. As a consequence, we obtain the new lower bound $R(12,12) \\ge 1641$.",
      "title": "A constructive two-parameter Ramsey increment",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.06531"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06315",
      "authors": [
        "Kevin Morio",
        "Yavor Ivanov",
        "Robert Künnemann"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06315",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "verifier_guided_reasoning"
      ],
      "published": "2026-08-06",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Tamarin and ProVerif are two prominent tools for the formal verification of security protocols. They share the same high-level goal but differ significantly in their underlying formalisms and verification techniques, making a systematic comparison challenging: Tamarin uses multiset rewrite rules with sound and complete verification, whereas ProVerif employs an extension of the applied-pi calculus that provides fast but potentially incomplete results. We present a sound translation from Tamarin to ProVerif that enables a rigorous comparison of the two tools. It introduces techniques for formula rewriting, encoding multiset rewrite semantics, and handling simultaneous events, supporting a large subset of Tamarin's features, including multiset rewrite rules, lemmas, and restrictions, while precisely characterizing the cases where faithful translation is not possible. We provide formal proofs: within the faithful fragment, soundness ensures that any property verified in ProVerif also holds in the original Tamarin model, and completeness ensures that exists-trace properties not involving attacker knowledge are preserved. Best-effort encodings, in particular XOR, are reported separately and are outside these guarantees. Finally, we evaluate our translation on 121 Tamarin models. The ProVerif front end accepts executable translations for 523 of 566 lemma tasks. Among non-XOR tasks with definitive results from both tools, 237 of 238 agree, with the remaining verdict explicitly flagged as using an incomplete model. Among the 344 tasks for which Tamarin returns a Boolean result and ProVerif completes with a logical result, ProVerif is faster in 316 cases (91.9%), with median per-task runtime and peak-memory ratios of 6.74x and 6.13x, respectively.",
      "title": "A Sound Translation from Tamarin to ProVerif: Enabling Comparative Analysis",
      "updated": "2026-08-08",
      "url": "https://arxiv.org/abs/2608.06315"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.04992",
      "authors": [
        "Jaume de Dios Pont",
        "Karlheinz Gröchenig",
        "Lukas Liehr",
        "Irina Shafkulovska",
        "Mitchell A. Taylor"
      ],
      "content_date": "2026-08-05",
      "freshness": "fresh",
      "id": "arxiv:2608.04992",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-05",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "We prove that the set of time-frequency shifts $\\{e^{2πi βl t} g(t-αk) : k,l \\in \\mathbb{Z}\\}$ with a continuous, integrable totally positive function $g$ and lattice parameters $α,β>0$ generates a frame for $L^2(\\mathbb{R})$ if and only if $αβ<1$. This fully settles the so-called frame set problem for the class of totally positive functions. As a closely related result we prove a sharp Kadets-type theorem for every shift-invariant space generated by a continuous totally positive function. The proofs are based on Fredholm theory and limit-operator theory. A formalization of our main result in Lean 4 is also provided.",
      "title": "Gabor Frames of Totally Positive Functions: A Complete Characterization",
      "updated": "2026-08-05",
      "url": "https://arxiv.org/abs/2608.04992"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.05420",
      "authors": [
        "Ahmed Ryan",
        "Md Erfan",
        "Akond Ashfaque Ur Rahman",
        "Md Rayhanur Rahman"
      ],
      "content_date": "2026-08-05",
      "freshness": "fresh",
      "id": "arxiv:2608.05420",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "lean_formal_proving_agents"
      ],
      "published": "2026-08-05",
      "score": 3.5,
      "source": "arxiv-ai4math-core",
      "summary": "Large language models (LLMs) can generate text that resembles a mathematical proof, but resemblance does not establish correctness. A formal proof checker verifies whether each proof step follows established logical rules. Coq bases its rules on the Calculus of Inductive Constructions, a logical framework that defines which proof steps the system may accept. This pilot study evaluated six open-weight LLMs on the same 100 theorems from CoqStoq, a benchmark derived from real Coq projects. Each LLM received one attempt per theorem with the temperature set to 0, and Coq checked every proposed proof in the theorem's original project environment. We counted a proof as successful only if the Coq kernel accepted it. Gemma 4 verified 12 of 100 theorems, Llama 3.3 verified 8, and DeepSeek Coder V2 Lite verified 1. Qwen 3.5, Mistral Small 3.1, and GPT-OSS verified none. The 21 successful model-theorem results covered 15 distinct theorems, 11 of which were not solved by a baseline of standard Coq tactics. All verified theorems had short or medium human-written reference proofs; no model verified a theorem with a long reference proof. Because the proof-length analysis was exploratory, this pattern does not establish that proof length caused the difference. For the three models with at least one success, the total generation cost per verified proof ranged from 741 to 36,193 output tokens, 14.9 to 178.0 seconds, and 0.0167 to 0.2000 aggregate GPU hours. We could not calculate these ratios for models with no verified proofs. Across 600 attempts, the models produced 21 kernel-verified proofs, giving an overall success rate of 3.5%. The study reports descriptive differences among the models but does not statistically test whether one model outperforms another. Therefore, the results do not establish a universal ranking of the six models.",
      "title": "Can Open-Weight LLMs Produce Kernel-Verified Coq Proofs? A Pilot Study",
      "updated": "2026-08-05",
      "url": "https://arxiv.org/abs/2608.05420"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.09277",
      "authors": [
        "Zenan Li",
        "Ziran Yang",
        "Peiyang Song",
        "Zhaoyu Li",
        "Kaiyu Yang"
      ],
      "content_date": "2026-08-10",
      "freshness": "fresh",
      "id": "arxiv:2608.09277",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "seed_author:Kaiyu Yang",
        "seed_author:Ziran Yang"
      ],
      "published": "2026-08-10",
      "score": 2.9,
      "source": "arxiv-ai4math-core",
      "summary": "Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction. The de facto workflow decouples the two halves of the problem: first synthesize a program, then attempt to prove it correct. We observe that this sequential pipeline can be both ineffective and inefficient in practice. A program generated without anticipating its proof can be subtly incorrect or structurally difficult to verify, forcing the LLM into brittle repair loops that alternate between patching the code and patching the proof. Inspired by Dijkstra's view that a program and its correctness argument should be developed hand in hand, we propose $P^3$, an LLM-based agentic workflow that first derives a unified program-and-proof plan from the specification, then elaborates the implementation and proof scaffold under this shared plan. To evaluate verified code generation in realistic settings, we further introduce Lean4Commit0, a repository-derived, library-level benchmark built by extracting core APIs from real-world software repositories and translating their requirements, including relational specifications across APIs, into Lean tasks. Using four frontier LLM backends, we evaluate $P^3$ on Verina, AlgoVeri, and our Lean4Commit0 benchmark, where it achieves the highest solve rate in every benchmark--model setting. Compared with the stronger baseline, it improves solve rates by 4.6--11.2 percentage points and reduces per-task API cost by up to roughly 40\\% and wall-clock time by up to roughly 37\\% on the difficult subset of each benchmark. A targeted ablation further shows gains of 3.3--8.3 points over implementation-only planning, isolating the benefit of planning the program and proof jointly.",
      "title": "P$^{3}$: Joint Program-and-Proof Planning for Verified Code Generation",
      "updated": "2026-08-10",
      "url": "https://arxiv.org/abs/2608.09277"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.05480",
      "authors": [
        "Kenny Lau",
        "Ken Ono"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.05480",
      "kind": "paper",
      "label": "adjacent",
      "matched_signals": [
        "general_ai_math_reasoning"
      ],
      "published": "2026-08-06",
      "score": 1.9,
      "source": "arxiv-ai4math-core",
      "summary": "For coprime $1<a<b$, let $M_n^{a,b}(\\mathbb{F}_q)$ be the set of commuting pairs of nilpotent $n\\times n$ matrices over $\\mathbb{F}_q$ with $X^a=Y^b$. Huang, Jiang, and Oblomkov assembled their orders as an Eulerian $q$-series $Z_{a,b}(q)$. They conjectured that it is an explicit product $P_{a,b}(q)$ involving Jacobi's theta function and Dedekind's eta-function, implying the threefold equality $$\\underbrace{\\prod_{n\\ge1}(1-q^n)\\cdot\\Biggl(\\sum_{n=0}^{\\infty}\\frac{|M_n^{a,b}(\\mathbb{F}_q)|}{|\\mathrm{GL}_n(\\mathbb{F}_q)|}\\Biggr)\\Biggr|_{q\\mapsto q^{-1}}}_{\\text{point count}}\\;=\\;\\underbrace{Z_{a,b}(q)}_{q\\text{-series}}\\;=\\;\\underbrace{P_{a,b}(q)}_{\\text{theta quotient}}$$ If true, the point count on $X^a=Y^b$ is essentially a modular function on $Γ(a+b)$. The conjecture is layered in $a$, with an identity for each $b$. The $a=2$ layer is classical, including identities of Rogers--Ramanujan and Andrews--Gordon. For $a\\geq3,$ nothing was known. We prove the $a=3$ layer in full: a new infinite family of Rogers--Ramanujan identities, and a geometric origin for Warnaar's products. AxiomProver verified these new identities in Lean assuming existing literature.",
      "title": "Modularity of Point Counts for the Curves $X^a=Y^b$: New Rogers--Ramanujan Identities",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.05480"
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        "Sebastian Graf"
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: test: a loop over an iterator states its invariant (#14752)",
      "updated": "2026-08-11",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: refactor: one loop gadget per set of annotations a loop states (#14751)",
      "updated": "2026-08-11",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: typos in diagnostics (#14743)",
      "updated": "2026-08-11",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: step vcgen through specs whose program applies a continuation variable (#14747)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: fold vcgen's symbolic state as it is produced (#14745)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `invariant` and `decreasing` clauses on `repeat` and `while` loops (#14703)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: `grind` reads a loop's measure through the states of the assertions (#14744)",
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      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: chore: update release scripts (#14736)",
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      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: refactor: reorganize Topology/EMetricSpace/Defs to generalise basic results (#40510)",
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      "summary": "Recent commit on leanprover-community/mathlib4.",
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      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-10",
      "repo": "leanprover-community/mathlib4",
      "score": 0.8,
      "source": "mathlib4-github",
      "summary": "Recent commit on leanprover-community/mathlib4.",
      "title": "leanprover-community/mathlib4: chore(AlgebraicTopology/MooreComplex): tidy docs (#42595)",
      "updated": "2026-08-10",
      "url": "https://github.com/leanprover-community/mathlib4/commit/55b267748a771c1a50c2abbeae061e849f8f7373"
    },
    {
      "age_days": 2,
      "authors": [
        "Mac Malone"
      ],
      "content_date": "2026-08-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:b1cd183c9978",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: lake: demote cache failures to `trace` (#14720)",
      "updated": "2026-08-09",
      "url": "https://github.com/leanprover/lean4/commit/b1cd183c9978c3bedddc33baf7c9599baaeca046"
    },
    {
      "age_days": 2,
      "authors": [
        "Mac Malone"
      ],
      "content_date": "2026-08-09",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:7c90644a5f2a",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-09",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: lake: `leanExit` test flakiness (#14721)",
      "updated": "2026-08-09",
      "url": "https://github.com/leanprover/lean4/commit/7c90644a5f2a8a62e0cfc1dcf7a19c0d6c70c6ce"
    },
    {
      "age_days": 3,
      "authors": [
        "Sebastian Graf"
      ],
      "content_date": "2026-08-08",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:f29e9e488ea8",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-08",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: support well-founded and state-dependent termination measures in Spec.repeatM (#14507)",
      "updated": "2026-08-08",
      "url": "https://github.com/leanprover/lean4/commit/f29e9e488ea8242c875806e4b0564820c2d553b2"
    },
    {
      "age_days": 4,
      "authors": [
        "Leonardo de Moura"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:10d40baf2b2b",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: fix: apply beta when canonicalizing types in `grind` (#14709)",
      "updated": "2026-08-07",
      "url": "https://github.com/leanprover/lean4/commit/10d40baf2b2bb80fde528102d0d0eb55b52f526c"
    },
    {
      "age_days": 4,
      "authors": [
        "Henrik Böving"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "github:leanprover/lean4:87e7204456bf",
      "kind": "github_update",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "repo": "leanprover/lean4",
      "score": 0.8,
      "source": "lean4-github",
      "summary": "Recent commit on leanprover/lean4.",
      "title": "leanprover/lean4: feat: bv_decide grind integration (#14713)",
      "updated": "2026-08-07",
      "url": "https://github.com/leanprover/lean4/commit/87e7204456bfca901bdc724c996030e13c2f80c6"
    },
    {
      "age_days": 1,
      "arxiv_id": "2608.09305",
      "authors": [
        "Arnaud Mayeux"
      ],
      "content_date": "2026-08-10",
      "freshness": "fresh",
      "id": "arxiv:2608.09305",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-10",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Given a category $\\calC$ and a center, that is a collection of pairs $(d_i, N_i)$ consisting of a morphism $d_i$ and a sieve $N_i$ over its codomain, the dilatation of $\\calC$ is a new category $\\calC'$ in which every $n \\in N_i$ factors, uniquely and functorially, through $d_i$. This paper presents the theory of dilatations of categories through a full formalization of the construction and its main theorems in the Lean~4 proof assistant, on top of the Mathlib library. An appendix collects a systematic dictionary between the mathematical statements and the Lean declarations that formalize them.",
      "title": "Dilatations of categories, via their lean formalization",
      "updated": "2026-08-10",
      "url": "https://arxiv.org/abs/2608.09305"
    },
    {
      "age_days": 2,
      "arxiv_id": "2608.08897",
      "authors": [
        "Wesley H. Holliday"
      ],
      "content_date": "2026-08-09",
      "freshness": "fresh",
      "id": "arxiv:2608.08897",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-09",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "A common problem in social choice is to determine whether there is a social choice procedure, such as a voting method, satisfying some desired criteria. Computer-aided methods such as SAT solving can sometimes answer these questions. However, under typical encodings, a SAT solver may only synthesize a voting method on a finite domain, while we may want one on an infinite domain, such as the domain of all preference profiles for a fixed number of candidates but any finite number of voters. In this paper, we use an approach based on reasoning with constrained Horn clauses and computation with polyhedra to synthesize a voting method on an infinite domain. We then use SMT and Lean to verify its properties. Our main result is a possibility theorem about four well-known criteria from voting theory: the Condorcet winner and loser criteria, positive involvement, and resolvability. Previous work has shown that for five or more candidates, there is no voting method satisfying these axioms, and that for four candidates, there is no method satisfying these core axioms plus one more invariance axiom. Here we show that for four candidates, there does exist a method satisfying the core axioms and more.",
      "title": "Voting Method Synthesis on an Infinite Domain: A Possibility Theorem for Positive Involvement",
      "updated": "2026-08-09",
      "url": "https://arxiv.org/abs/2608.08897"
    },
    {
      "age_days": 3,
      "arxiv_id": "2608.07979",
      "authors": [
        "William J. Dwyer"
      ],
      "content_date": "2026-08-08",
      "freshness": "fresh",
      "id": "arxiv:2608.07979",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-08",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Testing independence in an R by C table is usually posed as one omnibus statistic against a dense alternative. When the departure is sparse, concentrated in a few cells, the sharp object is instead a detection boundary: the weakest signal any test can find. This paper treats independence through that lens, in three parts. Part I specializes sparse-signal detection theory (Ingster 1997; Donoho and Jin 2004; Chhor, Mukherjee and Sen 2024) to the table: it is a heteroscedastic Gaussian sequence whose variance profile is the expected-count table, fixed by the two margins through the product-CV identity CVe^2 = (1 + CVr^2)(1 + CVc^2) - 1, so marginal heterogeneity is exactly the heteroscedasticity profile; a variance-stabilizing root transform gives the exact standardized amplitude 2 sqrt(m)(sqrt(1 + a) - 1) and a closed-form separation radius, valid under a growing-count condition and provably failing at fixed small counts. Part II casts independence as goodness of fit of the log-linear no-interaction model and shows that higher criticism, with its closed-form Jaeschke-Eicker null, attains that boundary adaptively over the unknown sparsity, while being candid that in the very sparse strong regime the maximum-cell rule dominates and exact-conditional optimality is conjectural. Part III measures the small-count calibration failure (size 0.3 to 0.6, even under uniform margins, so the driver is the per-cell tail, not heterogeneity), removes it with the exact margin-conditional reference laws, and shows conditioning on both margins is the complete treatment for a test (no oracle; size 0.003 to 0.009); a routing rule keyed to the margin profile sends large-count tables to the asymptotic gate and small-count tables to the exact anchor. Two-thirds of a 5,543-table public corpus route to the exact anchor. Every claim is confirmed numerically from openly deposited, deterministically seeded code.",
      "title": "Sparse departures from independence in two-way tables: a heteroscedasticity profile and detection boundary, an adaptive higher-criticism gate, and an assumption-lean exact anchor",
      "updated": "2026-08-08",
      "url": "https://arxiv.org/abs/2608.07979"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.07360",
      "authors": [
        "Zeru Zhu",
        "Jinzheng Li",
        "Yuanjie Ren",
        "Ji Liu"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07360",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Kolokolnikov conjectured that, among finite simple graphs on $n$ vertices with exactly $2(n-2)$ edges, the complete bipartite graph $K_{2,n-2}$ maximizes algebraic connectivity. We prove the conjectured statement for every $n\\ge123$: every such graph has algebraic connectivity at most $2$, while $K_{2,n-2}$ attains $2$. The proof begins with explicit Rayleigh-quotient certificates that exclude several local configurations from a hypothetical counterexample. A global degree count then controls the number and total excess of vertices of degree at least $5$ and bounds the edge excess of the subgraph induced by vertices of degree at most $4$. A Moore-type breadth-first-search criterion uses this excess to guarantee a short cycle, while a spectral criterion excludes cycles in the same length range. An explicit arithmetic estimate shows that the two criteria apply simultaneously once $n\\ge123$. A Lean formalization covering every $n\\ge4$, including the complementary range $4\\le n\\le122$, has been produced with MerLean and checked by the Lean kernel; the present paper gives a self-contained mathematical account of the large-order component.",
      "title": "Maximizing Algebraic Connectivity with $2(n-2)$ Edges: The Large Vertex Number Case",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07360"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.07396",
      "authors": [
        "Jaume de Dios Pont",
        "Lukas Liehr",
        "David Muñoz-Lahoz",
        "Mitchell A. Taylor",
        "Pedro Tradacete"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.07396",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The ability of large language models to assist professional mathematicians has been progressing rapidly. Earlier this year, a group of researchers in Banach lattice theory and phase retrieval began incorporating this technology into their research workflows. Facing challenges about the reliability of these models, they also decided to couple the discovery process with Lean verification. Here, we present a case study of how this has led to a more united community and a deeper understanding of our field.",
      "title": "Banach lattices and phase retrieval: A case study for the use of AI in mathematics",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.07396"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.06996",
      "authors": [
        "Eunkyu Choi",
        "Joonho Seo",
        "Seungmin Lee",
        "Seokhwan Jeong"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.06996",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "This paper presents a sensor-minimal automated assembly system for bidirectional single-row flat ribbon cable harnesses (FRCHs). Unlike conventional peg-in-hole or single-terminal insertion tasks, FRCH assembly involves mechanically coupled multi-terminal insertion under flexible and dense geometric constraints. To address this problem, the proposed system performs the assembly through a purely mechanical sequence consisting of Cable Alignment, Lean & Slide, Weaving, and Clamping, without relying on active sensing or vision. Each mechanism is designed to progressively reduce correlated terminal misalignment, insertion interference, and instability before final locking. Experiments on bidirectional single-row FRCHs achieved an 83.75% end-to-end process success rate over 80 trials, with success rates of 85.0% and 82.5% in the first and second halves, respectively. The cycle time was 33 s under half-speed operation. To the best of our knowledge, this work presents the first automated prototype for FRCH terminal-to-housing assembly for multi-pin housings.",
      "title": "Automated Terminal-to-Housing Assembly System for Flat Ribbon Cable Harness",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.06996"
    },
    {
      "age_days": 4,
      "arxiv_id": "2608.06728",
      "authors": [
        "Jiao-Long Cao",
        "Ye Yuan"
      ],
      "content_date": "2026-08-07",
      "freshness": "fresh",
      "id": "arxiv:2608.06728",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-07",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "For an odd prime $p$, let $m(p)$ be the minimum cardinality of a set $A\\subseteq \\mathbb Z/p\\mathbb Z$, with $|A|\\geq2$, such that no sum in $A+A$ has a unique representation as an unordered pair from $A$, with repetition allowed. Bedert proved \\[ m(p)\\gg \\log p\\, \\frac{\\sqrt{\\log^{(3)}p}}{\\log^{(4)}p}. \\] We prove the stronger lower bound \\[ m(p)\\gg \\log p\\,\\log\\log p. \\] More generally, if $G$ is a finite Abelian group and $q(G)$ is the least prime divisor of $|G|$, then the same explicit estimate holds whenever $q(G)>2$, and in particular every subset $A\\subseteq G$ with $|A|\\geq2$ and no unique sum has cardinality $\\gg \\log q(G)\\,\\log\\log q(G)$ as $q(G)\\to\\infty$. The proof has two structural inputs. First, a maximum subset of $A$ whose distinct-element subset sums of size at most four are all different has cardinality $\\gg\\log p$. This follows from a short-coordinate lemma and a collision-lattice determinant argument. Second, we refine Bedert's density increment. Alternative representations are oriented toward an uncovered endpoint, coalesced by their translation, and separated into wide, exposed, and recurrent batches. A load-sensitive entropy lemma codes the recurrent translations using their actual final fibre multiplicities. The resulting global shift-set complexity is $\\exp(O(K))$, where $K$ is the ratio of $|A|$ to the level-four additive dimension. This forces $K\\gg\\log\\log p$, and the theorem follows. All headline statements and the structural implications used to derive them have also been checked in Lean~4 with explicit integer constants. As a secondary and logically independent result, we construct weakly ternary-balanced sets and obtain \\[ m(p)\\leq \\frac{(\\log p)^2}{2(\\log 3)^2} +\\left(\\frac{2}{\\log 3}+o(1)\\right) \\frac{(\\log p)^2}{\\log\\log p}. \\]",
      "title": "A Second-Logarithm Lower Bound for Sets with No Unique Sums",
      "updated": "2026-08-07",
      "url": "https://arxiv.org/abs/2608.06728"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.05863",
      "authors": [
        "Fanzhe Wei",
        "Li Liu",
        "Ziyang Wang",
        "Chenyu Wang"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.05863",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Modern models no longer keep a plain KV cache: latent caches, learned sparse selectors and recurrent states each carry the model's memory in a different form, and each fails differently under compression. We give a runtime observability contract that covers all four memory classes with three operators, instantiate it on six model configurations across five architecture families, and compose the per-stage bounds into an executable request-level risk ledger. Contracts carry their error metric as a type -- composition is only defined when metrics match, and this check rejected our own first composed chain; the repaired chain crosses metrics through two proved bridges, and whatever no formal system can certify is measured instead, dropping the composed tier to empirical automatically: every claim is certified, partially certified, or empirical, composition inherits the weakest tier, and the tier is decided by the machine. Replayed over $12.4$M entry reads and run under eight-way concurrency with per-request budgets and fail-closed identity attribution, the ledger quantifies the honest trade-off on today's witness and holds its risk budget with zero violations. A fused always-on probe observes a declared one-layer subset under CUDA graphs inside the serving noise floor. Applied to a served DeepSeek-V4 stack with a packed compressed-KV prototype, the same machinery localizes a silent corruption to a precise structural boundary -- exact in the eviction-free, identity-isolated regime, with every observed failure in an eviction or slot-reuse regime -- through a machine-adjudicated discrimination campaign whose calculus rejected two of our own confounded inferences along the way. All artifacts, guards, and the Lean development are released at https://github.com/metask-ai/witprobe-attention-memory; every number in this paper regenerates from the shipped artifacts by one command.",
      "title": "Runtime Observability for Heterogeneous Attention Memory",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.05863"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.07605",
      "authors": [
        "Alexander Kolpakov",
        "Igor Rivin"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.07605",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "A fixed simplex, randomly projected into three dimensions and joined in Hamiltonian order, produces a rich and unusually tractable model of random stick knots. We prove that Gaussian projections and Haar-random Stiefel projections have exactly the same knot-type law, despite having different metric shapes, and that at every stick budget the model gives positive probability to precisely the knot types realizable with that many sticks. Its linear-algebraic structure yields an exact marginal distance law, an exact mean planar-crossing count, and crossing concentration, while in the first nontrivial six-stick case the complete tetrahedral sign pattern gives an exact unknot-versus-handed-trefoil classifier for every generic sample. The result is a direct bridge from random projections and finite sign geometry to the topology of random knots.",
      "title": "Random Knots via Stiefel manifolds",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.07605"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06235",
      "authors": [
        "Zhi Li",
        "Xiaofei Shi"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06235",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "To probe a bipartite quantum system, one may use arbitrary global operators or restrict to product operators acting separately on the two subsystems. We determine the sharp universal comparison between the resulting norms. For every $z\\in M_n\\otimes M_m$, we prove $\\|z\\|_1\\leq\\sqrt{2}\\min\\{n,m\\}\\|z\\|_\\varepsilon$, where $\\|\\cdot\\|_1$ is the trace norm and $\\|\\cdot\\|_\\varepsilon$ is the injective tensor norm associated with the trace norms on $M_n$ and $M_m$. To prove the upper bound, we establish an $L_1$ noncommutative Khintchine inequality whose random coefficients are the entries of a Haar unitary. We also show that the coefficient $\\sqrt{2}$ is sharp. As applications, we show that the same sharp constant governs the gap between bipartite correlation measured in trace norm and that measured by a correlation function, and obtain an improved universal upper bound for quantum data hiding. The upper bound has also been formalized and machine-checked in Lean.",
      "title": "Global vs. Product Observables in Bipartite Quantum Systems: The Sharp Bound",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.06235"
    },
    {
      "age_days": 5,
      "arxiv_id": "2608.06652",
      "authors": [
        "Alexandria Leto",
        "Rohan Das",
        "Juan Vásquez",
        "Abram Handler",
        "Maria Leonor Pacheco"
      ],
      "content_date": "2026-08-06",
      "freshness": "fresh",
      "id": "arxiv:2608.06652",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-06",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Conceptual metaphors guide our thinking and actions by allowing us to reason about more abstract experiences (e.g., paying taxes) in terms of more concrete or embodied experiences (e.g., carrying a physical load) (Lakoff and Johnson, 2011). It follows that different conceptual metaphors can result in different reasoning: framing paying taxes as an investment in a community rather than a physical load leads to a very different outlook on taxation. Identifying the conceptual metaphors guiding a speaker or writer thus helps to reveal their framing of events. Though these metaphors can't be observed directly, groups of linguistic metaphors, metaphorical expressions as they appear in language, serve as evidence for them. Motivated by this, we present an unsupervised method that extracts linguistic metaphors from a corpus and uses a structured clustering approach to form groups corresponding to conceptual metaphors. Using this method, we point to key topical and framing differences in left- vs. right-leaning podcasts. For example, left-leaning podcasts tend to conceptualize media stories as a weapon, while right-leaning sources commonly discuss the economy as a system subject to vertical changes.",
      "title": "Discovering Conceptual Metaphors Across Topics and Media Types",
      "updated": "2026-08-06",
      "url": "https://arxiv.org/abs/2608.06652"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.05451",
      "authors": [
        "Zhengyao Lin",
        "Yi Cai",
        "Milijana Surbatovich"
      ],
      "content_date": "2026-08-05",
      "freshness": "fresh",
      "id": "arxiv:2608.05451",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-05",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "Dataflow architectures have gained renewed interest due to their balance between power efficiency and performance. In (spatial) dataflow architectures, a program is represented as a set of entirely distributed and dynamically scheduled dataflow operators that communicate through asynchronous channels, which greatly improves data locality and parallelism. However, compiling to dataflow architectures remains an error-prone process, in order to maintain determinacy while enabling pipelining. Determinacy means that the result of a dataflow program is deterministic and independent of the schedule of operator execution, and pipelining is an important optimization in spatial dataflow that enables parallelism across loop iterations. In this work, we present Wavelet, the first effort to formally verify a compiler for asynchronous dataflow. We use a mix of techniques to achieve this goal. Our frontend uses a novel capability type system with fences to synchronize conflicting memory accesses and enable pipelining. We then verify a Lean formalization of two core passes of our compiler that translates elaborated programs from the type checker to dataflow graphs, proving important properties of forward simulation and determinacy. Notably, our formalization semantically propagates the soundness guarantees of the frontend type system, ensuring modularity between simulation and determinacy proofs. In evaluation, we show that dataflow graphs compiled by Wavelet have comparable sizes to those produced by an unverified optimizing compiler for the RipTide spatial dataflow architecture.",
      "title": "Let it Flow: A Formally Verified Compilation Framework for Asynchronous Dataflow",
      "updated": "2026-08-05",
      "url": "https://arxiv.org/abs/2608.05451"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.05075",
      "authors": [
        "Peer Saleth",
        "Segun T. Aroyehun",
        "Fabio Carrella",
        "Christoph M. Abels",
        "Stephan Lewandowsky",
        "David Garcia"
      ],
      "content_date": "2026-08-05",
      "freshness": "fresh",
      "id": "arxiv:2608.05075",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-05",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "The spread of misinformation is widely perceived as a threat to democratic deliberation, yet how political elites' rhetorical commitments to truth shift alongside the rise of populist actors remains poorly understood. Analysing 4.5 million tweets and 59,170 parliamentary speeches by German political elites between 2015 and 2025, we measure evidence-based and intuition-based rhetoric using a validated distributed dictionary representation. Across both arenas, intuition-based language has become more prominent, and right-leaning actors consistently exhibit the lowest Evidence Minus Intuition (EMI) scores. The parliamentary entry of the extreme-right Alternative for Germany (AfD) in 2017 coincides with sharp downward shifts in EMI across the broader chamber, while a more gradual decline is observed on Twitter. These findings document an association between far-right visibility and a changing approach to truth in elite discourse in a multiparty European democracy.",
      "title": "German parties shifted towards intuition-based rhetoric after the far right's parliamentary breakthrough",
      "updated": "2026-08-05",
      "url": "https://arxiv.org/abs/2608.05075"
    },
    {
      "age_days": 6,
      "arxiv_id": "2608.05142",
      "authors": [
        "Michal Mogielnicki",
        "Ken Ono",
        "Niels Voss",
        "Jujian Zhang"
      ],
      "content_date": "2026-08-05",
      "freshness": "fresh",
      "id": "arxiv:2608.05142",
      "kind": "paper",
      "label": "negative",
      "matched_signals": [],
      "published": "2026-08-05",
      "score": 0.5,
      "source": "arxiv-ai4math-core",
      "summary": "In 2016, Berkovich and Uncu proved that, for all nonnegative integers $i$, $j$, and $n$, the number of strict partitions of $n$ with $i$ odd-indexed odd parts and $j$ even-indexed odd parts equals the number of strict partitions of $n$ with $i$ parts congruent to $1$ modulo $4$ and $j$ parts congruent to $3$ modulo $4$. Their proof used generating functions, and they asked for a combinatorial proof. We answer their question with an explicit bijection, assembled from three classical ingredients: $2$-modular diagrams, an insertion algorithm of Chen, Gao, Ji, and Li, and Glaisher's bijection. AxiomProver autonomously formalized and verified the proof of the main theorem in Lean.",
      "title": "A bijective proof of a partition theorem of Berkovich and Uncu",
      "updated": "2026-08-05",
      "url": "https://arxiv.org/abs/2608.05142"
    }
  ],
  "lookback_days": 21,
  "schema": "ai4math-radar-run-v1",
  "timezone": "America/Los_Angeles"
}