Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium

• URL: http://arxiv.org/abs/2603.15929v1
• Date: Mon, 16 Mar 2026 21:21:53 GMT
• Title: Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium
• Abstract summary: We present a complete Lean 4 formalization of the equilibrium characterization in the Vlasov-Maxwell-Landau (VML) system.<n>Project demonstrates the full AI-assisted mathematical research loop.
• Score: 0.564046562677526
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a complete Lean 4 formalization of the equilibrium characterization in the Vlasov-Maxwell-Landau (VML) system, which describes the motion of charged plasma. The project demonstrates the full AI-assisted mathematical research loop: an AI reasoning model (Gemini DeepThink) generated the proof from a conjecture, an agentic coding tool (Claude Code) translated it into Lean from natural-language prompts, a specialized prover (Aristotle) closed 111 lemmas, and the Lean kernel verified the result. A single mathematician supervised the process over 10 days at a cost of \$200, writing zero lines of code. The entire development process is public: all 229 human prompts, and 213 git commits are archived in the repository. We report detailed lessons on AI failure modes -- hypothesis creep, definition-alignment bugs, agent avoidance behaviors -- and on what worked: the abstract/concrete proof split, adversarial self-review, and the critical role of human review of key definitions and theorem statements. Notably, the formalization was completed before the final draft of the corresponding math paper was finished.

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