AI4Math

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Today's Scan

Start with CircuitProver: Agentic Lean 4 Theorem Proving with Reusable Circuit Proof Library for Hardware Verification, then When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation. 20 fresh useful item(s) are inside the 21-day content window.

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arXiv20

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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 2026-07-29 arXiv

CircuitProver: Agentic Lean 4 Theorem Proving with Reusable Circuit Proof Library for Hardware Verification

Ziyi Yang, Wenji Fang, Chen Chen et al.

Modern integrated circuits (ICs) are becoming increasingly complex, making functional verification a major bottleneck. The dominant hardware formal verification methodology, model checking, verifies each design instance separately and exposes only pass/fail...

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

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 2026-07-25 arXiv

When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation

Mojtaba Soltanalian

When can additional low-bit residual computation replace missing numerical precision for a fixed input-output map? We model a quantized residual system over a fixed horizon as a pure schedule selecting fields from a declared low-bit operation library, and u...

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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adjacent score 4.9 2026-07-26 arXiv

A counterexample to the zero forcing versus independence conjecture for cubic and subcubic graphs

Mikko Fischer

We exhibit a connected graph on 24 vertices with maximum degree 3, independence number 9 and zero forcing number 11, refuting a 2017 conjecture of TxGraffiti recorded as Conjecture 2 of the survey of Davila, Brimkov and Pepper. The same construction with a...

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 3.5 2026-07-30 arXiv

BlueprintRepair: Typed Local Edits for Failed Lean Proof Blueprints

Ruslan Khrulev

LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operat...

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 2026-07-29 arXiv

Machine-Checked Certificates for the Geometric Half of the Minimum Kochen-Specker Bound

Shayaan Siddique, Ibrahim Mian

The best known lower bound for the minimum Kochen-Specker vector system in $\mathbb{R}^3$ -- 24 vectors -- rests on a computational proof whose combinatorial half emits DRAT proofs but whose geometric half does not: the non-embeddability of thousands of can...

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 2026-07-29 arXiv

Estimating Size of the Union of Sets in Streaming Model

Kuldeep S. Meel, N. V. Vinodchandran, Sourav Chakraborty

We study estimating the size of the union of sets $S_1,\dots,S_M$, where each $S_i\subseteqΩ$ is presented implicitly and arrives in a stream. We introduce Delphic sets, a class of streaming problems in which membership, sampling, and counting queries to ea...

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 2026-07-29 arXiv

Counterexamples, Spectral Obstructions, and Deletion Stability for WOW-284

Samuil Petkov

WOW-284 asserts that the minimum dual degree of every connected graph of order at least three and girth at least five does not exceed the negative of its least distance eigenvalue. We refute it with exact counterexamples of orders $38,39,40,42$, and $50$, a...

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 2026-07-28 arXiv

Kernel-Checked Exclusions for the Erdős-Selfridge Odd Covering Problem: Any Odd Covering of $\mathbb{Z}$ Has lcm Exceeding 10000

Ibrahim Mian, Shayaan Siddique

The Erdős-Selfridge odd covering problem (Erdős problem #7) asks whether a covering system of $\mathbb{Z}$ exists whose moduli are all odd, distinct, and greater than 1. The problem is open. We present a Lean 4 formalization, checked end to end by the proof...

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 2026-07-28 arXiv

Foundational Refinement Proofs for Deployed Bytecode, at the Price of Tokens

Lefteris Lazaropoulos, Zoe Paraskevopoulou

Relating low-level executable code to a high-level account of its behavior has been a central concern of programming-language research for decades. From formally verified compilers to translation validators, certifying compilers, and proof-carrying code, ea...

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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verifier feedback

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adjacent score 3.5 2026-07-28 arXiv

Formally certifying number field invariants

Alain Chavarri Villarello, Sander R. Dahmen

Number fields, which generalize the rational numbers, are fundamental objects in number theory. Many of their key arithmetic properties are captured by invariants whose computation is among the central tasks of computational algebraic number theory and a fo...

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 2026-07-28 arXiv

Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks

Xin Xu, Siru Tao, Kaizhen Tan

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of th...

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 2026-07-27 arXiv

The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon

Alexander Temerev, Alessio Doria

We solve Bellman's lost-in-a-forest problem for the golden gnomon $G$, the isosceles triangle with equal sides $1$ and apex angle $108^\circ$: the shortest curve guaranteed to reach the boundary of $G$ from an unknown starting position and heading is a symm...

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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Watch Later

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

adjacent score 3.5 2026-07-27 arXiv

Consensus In Asynchrony: Strictly Formal

Ivan Klianev

In this paper, we resolve the apparent contradiction between the proven possibility of deterministic crash-tolerant consensus in a fully asynchronous environment and the reconfirmation of the FLP impossibility result by Attiya, Castañeda, and Rajsbaum. With...

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

Skim cue Skim the abstract first; open the paper only if the method touches proof agents or formal verification.

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adjacent score 3.5 2026-07-27 arXiv

Classifying Capabilities (Extended Version)

Cao Nguyen Pham, Oliver Bračevac, Yichen Xu et al.

Capture checking in Scala 3 enables lightweight and practical effect and resource tracking by recording capabilities in types. However, the system offers no way to reason about kinds of capabilities. Natural constraints such as "retaining only the control-f...

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 2026-07-26 arXiv

Formally Verified Synthesizable Floating-Point Data Types in ARCH HDL

Shuqing Zhao

We report the design and end-to-end verification of first-class IEEE-754 binary32 (FP32) and bfloat16 (BF16) arithmetic for ARCH, a hardware description language intended to be generated by language models. Every operator - comparisons, conversions, add, su...

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 2026-07-26 arXiv

A Frozen 12B Beats Frontier Models on Verified Work: 100% Accuracy, 0 Tokens, Bit-Exact, Forever

Sietse Schelpe

Improving a language model today means retraining it: enormous compute, a new opaque model each cycle, non-deterministic output. We take the opposite path: the model stays frozen, and a persistent memory of verified solutions grows beside it. Once a problem...

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 2026-07-30 arXiv

FaithEyes: Towards Faithful Tool Use via Multi-Agent Process-Image Verification

Haoqing Wang, Xingrun Xing, Wei Xia et al.

Agentic vision-language models (VLMs), which interleave textual reasoning with explicit tool calls such as cropping and code-based image manipulation, have emerged as a compelling paradigm for reliable and interpretable multimodal reasoning. However, recent...

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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downweight: vision world modelstool-use agentsverifier feedback

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adjacent score 1.9 2026-07-28 arXiv

The 2-Domination Number and the Upper Median Degree: A Proof of Graffiti.pc Conjecture 387

Jun Qing

Let G be a nonempty finite simple graph of order n, and let m(G) be the upper median of its degree sequence. We prove that the 2-domination number satisfies gamma_2(G) <= n - m(G) + 1. This proves Graffiti.pc Conjecture 387. In fact, the argument establishe...

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

negative score 0.8 2026-08-01 GitHub

leanprover/lean4: chore: remove deprecated `toCtorIdx` alias for `ctorIdx` (#14627)

Robin Arnez

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 2026-08-01 GitHub

leanprover/lean4: chore: check the structure name when comparing projections in the kernel (#14631)

Leonardo de Moura

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 2026-08-01 GitHub

leanprover-community/mathlib4: feat(MeasureTheory): pushforward of Hausdorff measure under a homothety (#41798)

Francesco Chotuck

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.

Open Semantic Scholar

negative score 0.8 2026-08-01 GitHub

leanprover-community/mathlib4: feat(LinearAlgebra/Dimension/Free): division version of tower law (#41488)

Artie Khovanov

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.

Open Semantic Scholar

negative score 0.8 2026-08-01 GitHub

leanprover-community/mathlib4: feat(Algebra/Homology): homotopy equivalences satisfy the two out of three property (#42321)

Joël Riou

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.

Open Semantic Scholar

negative score 0.8 2026-08-01 GitHub

leanprover-community/mathlib4: feat(Algebra/DirectSum): equivalence between direct sum indexed by ι₁ and double sum indexed by ι₂ and fibres of f : ι₁ → ι₂ (#39607)

Marcus Zibrowius

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.

Open Semantic Scholar

negative score 0.8 2026-08-01 GitHub

leanprover-community/mathlib4: chore: update Mathlib dependencies 2026-08-01 (#42268)

mathlib-update-dependencies[bot]

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.

Open Semantic Scholar

negative score 0.8 2026-08-01 GitHub

leanprover-community/mathlib4: chore: fix various typos (#42232)

Felix Pernegger

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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