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Equilibria of the Vlasov-Maxwell-Landau System

Differential equations · posed by 2026 · solved

2 comments

Statement

Under smoothness, positivity, decay and score assumptions, are all steady solutions of the Coulomb Vlasov-Maxwell-Landau system on T3×R3\mathbb{T}^3 \times \mathbb{R}^3 necessarily spatially uniform Maxwellians?

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    Gemini Deep Think, Claude Code, Aristotle

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    A full AI-assisted loop: Gemini Deep Think generated the proof, Claude Code translated it into Lean from natural-language prompts, and Aristotle closed 111 lemmas - one supervising mathematician, zero hand-written lines of code.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    The main theorem is formally verified end to end by the Lean 4 kernel; arXiv preprint documents the pipeline.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.