AI4Math

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Today's Scan

Start with Does the Proof Prove It That Way? Faithful Formalization of Elements Proofs, then Grading the Graders: Verification Autonomy Levels (L0-L5) for LLM Reasoning. 18 fresh useful item(s) are inside the 21-day content window.

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arXiv18

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The top few items most likely to matter for formal proof agents or Lean-facing AI4Math work.

core score 12.5 2026-08-15 arXiv

Does the Proof Prove It That Way? Faithful Formalization of Elements Proofs

Tadd Mao, Tianjun Zhong, Dhruva Arekar et al.

In formal verification, both the autoformalization of statements and automated proof search have been studied extensively. While automated proof search can produce a formal proof that compiles, the generated proof does not necessarily reflect how the natura...

Why it matters Most relevant if you are tracking proof-search loops that use verifier feedback instead of treating Lean as a binary oracle.

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autoformalizationLean proof agentsverifier feedback

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core score 6.5 2026-08-19 arXiv

Grading the Graders: Verification Autonomy Levels (L0-L5) for LLM Reasoning

Yajie Yin

Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors. Yet the verification literature uses the word "level" t...

Why it matters Most relevant if you are tracking proof-search loops that use verifier feedback instead of treating Lean as a binary oracle.

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Lean proof agentsverifier feedback

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core score 6.5 2026-08-15 arXiv

A Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving

Ian D'Ambrosio

Huang, Lou, and Xiao introduced Dynamic Mixture-of-Experts Serving and gave an O(sqrt(log k))-competitive randomized algorithm for its integral primal problem, where k is the number of replica GPUs beyond the mandatory copy of each expert. Their matching lo...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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Worth Opening

Good candidates after the first three. These are plausible paper-tab opens, not a mandatory reading list.

adjacent score 4.9 2026-08-19 arXiv

The Equality Cases of the Weak Simplex Conjecture

Mengwei Su, Kaiwen Yang, Hao Xu et al.

Among $n+1$ equiprobable equal-energy signals in $\R^n$ under additive white Gaussian noise with maximum-likelihood decoding, which arrangement maximizes the probability of correct decoding? The question is Shannon's, recorded by Rice in 1950. Mulgund prove...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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AI math reasoningLean proof agents

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adjacent score 3.5 2026-08-20 arXiv

FormalTCS: Benchmarking End-to-End Frontier Formal Theoretical Computer Science Research of Large Language Models

Dingzirui Wang, Xuanliang Zhang, Keyan Xu et al.

Large language models (LLMs) have shown growing potential for automated theoretical computer science (TCS) research, yet existing benchmarks remain far from realistic research settings. We introduce \ourbenchmark, an expert-validated benchmark for evaluatin...

Why it matters Useful for the informal-to-formal bottleneck: it is about preserving mathematical intent across the translation boundary.

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autoformalization

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adjacent score 3.5 2026-08-20 arXiv

A Fixed-Penalty Linearized Augmented Lagrangian Method with Classical Multiplier Updates

Benqi Liu, Kangkang Deng, Zichen Wang et al.

Augmented Lagrangian methods are effective for nonlinear equality-constrained optimization, but solving their nonlinear primal subproblems can be expensive. For smooth nonconvex problems with deterministic or stochastic objectives, we propose a nonlinear-re...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-19 arXiv

The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers

Mahadee Al Mobin, Md. Shariful Islam

We state and prove the Theorem: for primes $p < 10^n$ with base-$10$ expansion $p = \sum_{k=0}^{n(p)-1} d_k(p) 10^k$, the positional digit probabilities $P_n(d \mid k)$ satisfy \[ \lim_{n \to \infty} P_n(d \mid k) = \begin{cases} 1/10, & k \ge 1,\ d \in \{0...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-19 arXiv

Budget-First Tariff Recommendation (BFTR): A Complete Algorithmic Framework for Telecom Plan Recommendation without Overcharging

Ghislain Dorian Tchuente Mondjo

Telecom operators traditionally offer predefined tariff grids, forcing users to choose from a limited set of plans. This paper proposes BFTR (Budget-First Tariff Recommendation), a complete algorithmic framework integrating eight Budget-First strategies, in...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-18 arXiv

Weak Typicality of von Neumann Entanglement Entropy in Gaussian Boson Sampling

Hongru Zhao

We study the von Neumann entanglement entropy generated by a Haar distributed passive interferometer acting on $n$ equally squeezed input modes with fixed nonzero squeezing strength $s$. Previous work established proportional weak typicality for integer R'e...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-18 arXiv

Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits

Olga Mashkova, Asaad Mohammedsaleh, Fernando Zhapa-Camacho et al.

OWL 2 DL ontologies, grounded in the description logic $\mathcal{SROIQ}$, express large knowledge bases in biomedicine and the Semantic Web. Neuro-symbolic (NeSy) learners over description logics either embed the ontology in a continuous space, abandoning c...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-18 arXiv

Graph Surgery and the Do-Operator: A Precise Correspondence for Acyclic Structural Causal Models

Satpreet Makhija

The $\operatorname{do}$-operator is described graphically by deleting arrows into its targets and functionally by replacing their mechanisms with constants. To call these operations equivalent is not yet a mathematical statement: one returns a graph and rem...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-18 arXiv

A Kernel-Checked Exclusion Certificate for Erdős Problem 647

Ibrahim Mian, Shayaan Siddique

Erdős problem 647 asks whether any $n > 24$ satisfies $\max_{m<n}(m + τ(m)) \le n + 2$, where $τ$ is the divisor-count function. Computational searches have excluded solutions up to $10^{12}$ by direct sieve and up to roughly $9.17 \times 10^{18}$ within a...

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

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Adjacent formalization or infrastructure signals. Keep them in peripheral vision unless they match an active project.

adjacent score 3.5 2026-08-17 arXiv

Bounds on the real tensor rank of octonion multiplication

Hardik Jain

The tensor rank of a bilinear map is the least number of multiplications any bilinear algorithm needs to compute it; for the multiplication of an algebra it measures how cheaply the algebra can be multiplied at all. For the even-dimensional real normed divi...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-16 arXiv

Pricing the Risk of Runtime Compression: Anytime-Valid Admission and a Served-Output Law for Compressed Serving State

Fanzhe Wei, Li Liu

Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-level risk by a union bound over a pre-declared event cou...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

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adjacent score 3.5 2026-08-16 arXiv

Absorption cutoff and stationary singularities for rounded Gaussian random dynamical systems

Benny Avelin

We study Gaussian random dynamical systems with coordinatewise $\tanh$ nonlinearity, where finite precision is modeled by nearest-grid rounding after each step. Gaussian symmetry reduces the dynamics to an exact Markov chain for the normalized squared radiu...

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

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adjacent score 3.5 2026-08-15 arXiv

The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation

Michele Caprio

We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows. For the standard cellular flow in dimension two $V_A(x_1,x_2)=A(-\sin x_1\cos x_2,\...

Why it matters Direct Lean signal: likely relevant to the formalization or theorem-proving environment around AI4Math agents.

Skim cue Skim which definitions entered Lean and whether the work adds reusable library surface.

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adjacent score 1.9 2026-08-18 arXiv

An equidistribution conjecture for quotient-closed and submodule-closed subcategories

Haruhisa Enomoto

We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules. We propose the quotient--submodule equidistribution conjecture: over a representation-finite algebra, the number of quotient-closed...

Why it matters Adjacent signal: scan the abstract for a concrete connection to formal proof, verification, or proof-agent evaluation.

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AI math reasoning

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adjacent score 1.9 2026-08-15 arXiv

Algebraic geometric framework of Rogers--Ramanujan identities

Yifeng Huang, Kenny Lau, Ken Ono et al.

The Rogers--Ramanujan identities equate a $q$-series whose exponents are governed by a quadratic form with an infinite product supported on two residue classes modulo~$5$. Identities of this shape are scarce, and a central problem is to identify the structu...

Why it matters Adjacent signal: scan the abstract for a concrete connection to formal proof, verification, or proof-agent evaluation.

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Older but Useful

0 relevant item(s) are outside the 21-day content window. Keep them for context, but do not let them drive today's scan.

No older useful items were retained in this run.

Downweighted 68 low-priority match(es), folded for daily reading.

negative score 0.8 2026-08-22 GitHub

leanprover/lean4: fix: apply specs to goals with a registered WP instance in vcgen (#14883)

Sebastian Graf

Recent commit on leanprover/lean4.

Why it matters Toolchain signal: open only if the commit touches proof search, elaboration, tactics, Lake, or mathlib behavior you depend on.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

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negative score 0.8 2026-08-22 GitHub

leanprover/lean4: feat: lake: add --fail-fast build option (#14797)

Dennj

Recent commit on leanprover/lean4.

Why it matters Toolchain signal: open only if the commit touches proof search, elaboration, tactics, Lake, or mathlib behavior you depend on.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

Read if Open only if you are debugging Lean or mathlib locally.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: feat: the Levi-Civita connection on a manifold (#36845)

Michael Rothgang

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

Read if Open only if you are debugging Lean or mathlib locally.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: feat: immersions in the sense of differentials (#35078)

Michael Rothgang

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

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Read if Open only if you are debugging Lean or mathlib locally.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: feat: an immersion is an immersion in the sense of differentials (#41796)

Michael Rothgang

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

Read if Open only if you are debugging Lean or mathlib locally.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: feat(Mathlib/Order/SuccPred/Limit): more `WithTop` lemmas about `IsMin`/`CovBy`/`IsSuccLimit` (#38841)

Snir Broshi

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

Read if Open only if you are debugging Lean or mathlib locally.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: feat(Geometry/Euclidean/Angle): the unoriented angle at the center in terms of the angle at the circumference (#41123)

Li Jiale

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

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negative score 0.8 2026-08-22 GitHub

leanprover-community/mathlib4: chore(Algebra/QuadraticAlgebra): rename Discr to Discriminant (#42975)

Xavier Roblot

Recent commit on leanprover-community/mathlib4.

Why it matters Infrastructure signal: this may improve premise discovery, dependency retrieval, or library navigation for agents.

Skim cue Skim only the changed subsystem and whether it affects your Lean workflow.

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Warnings are preserved so failed sources do not silently disappear from the brief.

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