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  "problem_id": "vibemathed:lions-maximal-regularity-half-holder",
  "title": "Lions' Maximal Regularity Problem at the Half-Holder Endpoint",
  "canonical_statement": "Lions asked whether the variational solution of a non-autonomous divergence-form problem has maximal L2-regularity under Holder continuity in time of the coefficients. Disproved at the half-Holder endpoint: a bounded, uniformly elliptic, real scalar coefficient, half-Holder in time and arbitrarily close to the heat equation, whose Lions solution has a time derivative that is not square integrable.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "type": "disproved",
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      "occurred_at": "2026-08-11T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Tensorisation and parabolic rescaling carry the one-dimensional example to real symmetric isotropic counterexamples on R^d and on every bounded domain, in every dimension.",
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      "provider": "OpenAI",
      "attempted_at": "2026-08-11T00:00:00.000Z",
      "human_collaborators": [
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      "outcome": "The Declaration of AI Use: \"During an exploratory analysis, a first counterexample was found by OpenAI's GPT-5.5 Pro in two dimensions and on the full space. It was then verified and studied by the author, who simplified it and reduced it to the one-dimensional interval counterexample presented here.\" GPT-5.6 Sol was separately used for drafting and revision of the exposition.",
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          "url": "https://arxiv.org/abs/2608.11194",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}