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Equilibria of the Vlasov-Maxwell-Landau System

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vlasov-maxwell-landau-equilibriaDifferential equationsposed by 2026recorded: solved

1 attempt · 1 machine check · no person has looked

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?

Context

A concrete equilibrium statement from the formalization project itself.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGemini Deep Think, Claude Code, Aristotle ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Gemini Deep Think, Claude Code, Aristotle

    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.

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      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.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

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