{
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  "problem_id": "vibemathed:mazya-maximal-operator-banach-space",
  "title": "Maz'ya's Question on Distinguishing Two Maximal Operators",
  "canonical_statement": "Maz'ya and Shaposhnikova introduced a non-classical maximal operator $M^\\diamond$, the maximal convolution with the vector-valued signum kernel truncated to centered balls. One of Maz'ya's 75 open problems in analysis asks whether it can be separated from the sharp maximal operator $M^\\sharp$. It can: there is a translation-invariant Banach space of locally integrable functions on which $M^\\diamond$ is bounded but $M^\\sharp$ is not.",
  "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.",
  "current_status": "resolved",
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      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-05-17T00:00:00.000Z",
      "title": "arXiv:2605.17663 - A Banach space that distinguishes two maximal operators",
      "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.",
      "ai_contribution": "ai_assisted",
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        "vibemathed:mazya-maximal-operator-banach-space:attempt"
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      "problem_id": "vibemathed:mazya-maximal-operator-banach-space",
      "model": "ChatGPT 5.4 Pro and ChatGPT 5.5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-05-17T00:00:00.000Z",
      "human_collaborators": [
        "Vjekoslav Kovač"
      ],
      "exposure": "unknown",
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      "outcome": "Instructive in both directions. ChatGPT 5.4 Pro helped rule out candidate examples, specifically the classical function spaces already covered in the literature, which is search-space pruning rather than construction. Then after the author had finalized the proof, ChatGPT 5.5 Pro produced an alternative example the author calls surprisingly simple but not entirely legitimate, and the paper prints it anyway. The formal declaration is unambiguous: the ideas, results, proofs, bibliography and writing are entirely the author's work.",
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          "label": "VibeMathed: Maz'ya's Question on Distinguishing Two Maximal Operators",
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      "label": "arXiv:2605.17663 - A Banach space that distinguishes two maximal operators",
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      "kind": "primary-mathematical-source",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}