Problem detail · source-aware

Equilibria of the Vlasov-Maxwell-Landau System

resolvedconfidence 70%

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Precise statement

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

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

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.

Provider: Google DeepMind / Anthropic / Harmonic · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

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

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

  1. arXiv:2603.15929 - Semi-autonomous formalization of the Vlasov-Maxwell-Landau equilibrium

    VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

  • VibeMath has not independently verified the mathematical claim.
  • AI-attempt independence and training-data exposure are unknown unless explicitly documented.
  • VibeMath has not independently audited the mathematical statement, proof, or novelty claim.