{
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  "problem_id": "vibemathed:auslander-reiten-smalo-perfect-fields",
  "title": "Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields",
  "canonical_statement": "For a perfect field $k$ and a representation-infinite finite-dimensional $k$-algebra $A$, the Auslander–Reiten quiver of $A$ has infinitely many connected components. This establishes a conjecture of Auslander, Reiten and Smalø, for finite-dimensional algebras over perfect fields.",
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      "occurred_at": "2026-07-27T00:00:00.000Z",
      "title": "arXiv",
      "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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      "attempted_at": "2026-07-27T00:00:00.000Z",
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        "Quanyu Tang"
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      "outcome": "The authors credit ChatGPT with the technical construction and verification of the semilinear twist argument in Lemma 4, and say it was used more substantially in extending the result from algebraically closed fields to arbitrary perfect fields - the step that gives the paper its stated generality.",
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          "label": "arXiv",
          "url": "https://arxiv.org/abs/2607.24466",
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          "label": "VibeMathed: Infinitely Many Components in Auslander–Reiten Quivers over Perfect Fields",
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    {
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  "generated_at": "2026-09-13T16:28:40.178Z"
}