{
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  "problem_id": "vibemathed:kalton-peck-space-hyperplanes",
  "title": "Kalton-Peck Space and its Hyperplanes",
  "canonical_statement": "Whether the real Kalton-Peck space $Z_2$ is isomorphic to its hyperplanes. It is not: no hyperplane of $Z_2$ is isomorphic to $Z_2$, proved through a rank parity theorem for symplectic spaces applied to the Kalton-Swanson symplectic structure.",
  "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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      "occurred_at": "2026-08-03T00:00:00.000Z",
      "title": "arXiv:2608.02126 - Kalton-Peck space is not isomorphic to its hyperplanes",
      "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_co_developed",
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      "attempted_at": "2026-08-03T00:00:00.000Z",
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        "A. Das",
        "V. Ferenczi",
        "Ch. Rosendal"
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      "outcome": "The AI use and Lean formalization section states that the principal result was first obtained through an extended interaction with ChatGPT using GPT-5.5 with Pro-Extended reasoning, which supplied an ingredient of the argument.",
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    "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"
}