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  "problem_id": "vibemathed:furthest-pair-seth-hardness",
  "title": "Quadratic-Time Hardness of Furthest Pair in Superconstant Dimension",
  "canonical_statement": "Furthest Pair and its relatives admit $f(d)\\,n^{2-\\Theta(1/d)}$ algorithms, making them the standard examples of barely subquadratic computation, and whether that is optimal in superconstant dimension was open. Under SETH it is: Furthest Pair requires quadratic time once the dimension is superconstant.",
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      "title": "arXiv:2606.25887 - Furthest Pair Requires Quadratic Time in Superconstant Dimension under SETH",
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        "Barna Saha",
        "Yinzhan Xu",
        "Christopher Ye"
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      "outcome": "The paper states the proof was initially discovered by ChatGPT 5.5 Pro, that the initial prompt was essential, and that other systems were used to generate feedback on it. The authors validated and substantially edited the proof to improve it.",
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      "kind": "primary-mathematical-source",
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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"
}