Formalizing Carleson's Theorem in Lean

2026-09-25

AI Summary

Carleson’s theorem is a cornerstone of harmonic analysis, yet the intricacy of its proof renders traditional verification insufficient for guaranteeing absolute rigor. This project addresses this challenge by formally verifying the theorem using the Lean proof assistant through a large-scale open-source collaborative framework. By employing systematic mathematical content organization, blueprint design, and rigorous formalization decisions, the team completed the core code development. Ultimately, this work successfully constructs and publicly releases a complete formalized proof system for Carleson’s theorem. Beyond achieving a machine-verifiable proof of a classical mathematical result, this study establishes a scalable collaborative paradigm for the formalization of complex mathematical theories.

Abstract

We present the formalization of Carleson's theorem in the proof assistant Lean. This paper describes the mathematical content, organization of the project, the blueprint, and the main design decisions behind the formalization. It is the result of a large collaborative effort, written and developed in public.

Problem

• Carleson's theorem
• formalization
• Lean
• proof assistant

Innovation

• Carleson's theorem
• formalization
• Lean
• proof assistant
• blueprint