AI4Math

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Today's Scan

Start with MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize, then Teaching Geometric Proof with Tech: Pitfalls and Possibilities. 18 fresh useful item(s) are inside the 21-day content window.

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arXiv18

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Open only the first lane during a busy morning. Older recurring seeds are kept below the daily scan instead of competing with fresh items.

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

core score 7.9 2026-08-26 arXiv

MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

Jiaxin Yuan, Connor Martinez Lockhart, Xiaoyu Liu et al.

Formal theorem proving enables machine-verifiable evaluation of mathematical reasoning, yet existing benchmarks often emphasize aggregate proof accuracy, concentrate on a narrow range of mathematics, and provide limited evidence of robustness to equivalent...

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

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Read if Read if you have 5 minutes and want a direct AI4Math signal.

AI math reasoningLean proof agents

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core score 6.5 2026-08-25 arXiv

Teaching Geometric Proof with Tech: Pitfalls and Possibilities

Hwei-Shin Harriman, Wode Ni, Yuchen Jin et al.

Geometric proof is a foundational yet challenging topic in mathematics, requiring students to integrate visual, logical, and notational skills. While technology has enhanced learning in other mathematical domains, its impact on geometric proof remains limit...

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

Skim cue Skim the search loop: proposal source, verifier call, retry strategy, and stopping rule.

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Lean proof agentsverifier feedback

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core score 6.5 2026-08-24 arXiv

A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates

Ludovic Tagnon

Hermite asked in 1848 for a representation of real numbers whose eventual periodicity characterizes cubic irrationals. The totally real case was solved by Karpenkov's $\sin^2$-algorithm; the complex case, signature (1,1), is his Problem 4. We study a determ...

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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Worth Opening

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

core score 6.5 2026-08-21 arXiv

A Lean 4 Verification Report for Subregular Affine Cells and the Level $-1$ Vertex Algebra of Type $D$

Sihai Jin

We report a Lean 4 formal verification accompanying the paper "Subregular Affine Cells and the Level -1 Vertex Algebra of Type D" (arXiv:2608.11997). The formalization kernel-checks substantial internal parts of the proof architecture, including the Section...

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

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

Read if Read if you have 5 minutes and want a direct AI4Math signal.

Lean proof agentsverifier feedback

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core score 6.5 2026-08-20 arXiv

ProofJudge: Tool-Grounded LLM Evaluation of Formal Proof Quality in Mathlib

Shane Caldwell

Formal proofs in Lean 4 that pass the kernel's type checker can nonetheless vary widely in quality. We introduce ProofJudge, an agentic LLM-as-judge system that scores formal proof quality along five dimensions beyond correctness: library leverage, automati...

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

Skim cue Skim the search loop: proposal source, verifier call, retry strategy, and stopping rule.

Read if Read if you have 5 minutes and want a direct AI4Math signal.

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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 2026-08-25 arXiv

The Kernel Deficit Dominates Twice the Hull Deficit: A Sharp Strengthening of Nakano's Inequality

Dakota Charles Baker

A point lies in the kernel of a polygon if it can see the entire polygon. Thus the kernel measures how much of the polygon is available to a single guard, while the convex hull measures how far the polygon is from being convex. We prove that these two losse...

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

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adjacent score 3.5 2026-08-25 arXiv

Designability of RNA Targets with Up to Two Length-2 Helices

Ashutosh S. Jogalekar

RNA inverse folding asks for an RNA sequence whose prescribed secondary structure is the unique maximum-base-pair compatible fold. In the four-letter Watson-Crick model (A-U and C-G pairs only, no pseudoknots, and zero minimum base-pair span), Hales et al....

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 2026-08-25 arXiv

A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness

Ludovic Tagnon

We develop the structure theory of the deterministic $\sin^2$-type algorithm for complex cubic fields introduced in the companion paper, addressing the complex-signature case of Karpenkov's Problem 4. The selection rule is shown to be, exactly, the minimiza...

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 2026-08-24 arXiv

Relative formalization in Isabelle/HOL of a result in inverse problems

Cătălin I. Cârstea

This reports on an experiment in autoformalization of arxiv:2606.15977, an inverse problems result for piecewise polynomial anisotropic conductivities, using Isabelle/HOL. The proof of the result is relative to a number of external results which were deemed...

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

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

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autoformalization

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adjacent score 3.5 2026-08-24 arXiv

Multi-Winner Voting with Argumentative Ballots

Ryuta Arisaka, Hirotaka Ono

We introduce multi-winner voting with argumentative ballots (MVArg) and investigate theoretical properties. As our conceptual contribution, we generalise approval ballots to argumentative ballots, thereby allowing voters to express defeasible preferences ov...

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 2026-08-24 arXiv

Improved bounds for the smallest 4-chromatic graph of girth six

Glauco Rampone

For integers $k,g \ge 3$ let $n_g(k)$ denote the minimum order of a graph with chromatic number $k$ and girth at least $g$. Exoo and Goedgebeur (DMTCS 2019) proved $26 \le n_6(4) \le 66$; their 66-vertex witness has remained the smallest known 4-chromatic g...

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

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Watch Later

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

adjacent score 3.5 2026-08-22 arXiv

ATHENA: Knowledge-guided agentic neural architecture search for AutoFormer-based electronic health record modeling

Deyi Li, Qi Xu, Lingyao Li et al.

Transformer-based models are widely used for clinical prediction from electronic health records (EHRs), yet their architectures require manual tuning, and the optimal configuration may vary across tasks and hospitals. Neural architecture search (NAS) automa...

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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verifier feedback

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adjacent score 3.5 2026-08-21 arXiv

AI with Authority, from Application to Silicon

Jason Hickey

For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI inverts this relationship: at AI speed, machine verification is not only economical but essential to productiv...

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

Skim cue Skim the search loop: proposal source, verifier call, retry strategy, and stopping rule.

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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.

Skim cue Skim the task definition, metric, and whether the benchmark has Lean-checkable artifacts.

Read if Save for later unless the title matches your current proof-agent work.

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.

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

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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 1.9 2026-08-22 arXiv

The General Subgroup Permanental-Dominance Conjecture in Order Four

Siwei Zeng

The general subgroup permanental-dominance conjecture was previously known only through matrix order three. This paper proves its complete order-four case: for every subgroup $H\leq S_4$, every irreducible complex character $χ$ of $H$, and every $4\times 4$...

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

negative score 0.8 2026-08-28 GitHub

leanprover-community/mathlib4: fix(cache): retry transport errors, improve transfer robustness (#43145)

Marcelo Lynch

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 2026-08-27 GitHub

leanprover/lean4: refactor: new LRAT checker (#14842)

Henrik Böving

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 2026-08-27 GitHub

leanprover/lean4: perf: initialize only the core modules `leanchecker-paranoid` needs (#14936)

Sebastian Ullrich

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.

Open Semantic Scholar

negative score 0.8 2026-08-27 GitHub

leanprover/lean4: fix: avoid exposing Fin.foldl implementation (#14554)

Salkutsan Aleksey

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.

Open Semantic Scholar

negative score 0.8 2026-08-27 GitHub

leanprover/lean4: feat: sane `rwa` (#14937)

Julia Markus Himmel

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.

Open Semantic Scholar

negative score 0.8 2026-08-27 GitHub

leanprover/lean4: feat: lake: read persisted code quality entries in `lake lint --code-quality` (#14933)

Wojciech Różowski

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.

Open Semantic Scholar

negative score 0.8 2026-08-27 GitHub

leanprover/lean4: chore: update stage0

Lean stage0 autoupdater

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 2026-08-27 GitHub

leanprover-community/mathlib4: refactor: definition and notation for `EventuallyEq` on `Set` (#41533)

Yaël Dillies

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

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