A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game

Short summary

This paper formalizes the mean-field derivation of the Vlasov equation in Lean 4 by framing AI-assisted theorem proving as a strategy game where a mathematician directs and an AI agent executes. The complete axiom-clean formalization covers existence, uniqueness, stability, and mean-field limit, completed in about a month. The optimal-transport machinery separates into a self-contained layer (49 of 299 declarations) that compiles against Mathlib alone, demonstrating reusable AI-assisted formalization methodology.

• •AI-assisted Lean 4 formalization of Vlasov equation framed as a strategy game
• •Mathematician directs scope and decomposition; AI agent executes proofs
• •Full development completed in ~1 month; reusable OT layer compiles against Mathlib

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