{
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  "problem_id": "vibemathed:erdos-graham-semiprime-unit-fractions",
  "title": "The Erdos-Graham Semiprime Unit Fraction Problem",
  "canonical_statement": "Every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes. This is the $\\omega = 2$ integer case of a problem of Erdos and Graham, left as a conjecture by Butler, Erdos and Graham, who proved the $\\omega = 3$ analogue.",
  "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": "2026-06-13T00:00:00.000Z",
      "title": "arXiv:2606.15159 - Every natural number is a sum of distinct semiprime unit fractions",
      "summary": "the omega = 2 integer case, the one Butler, Erdos and Graham left open",
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      "attempted_at": "2026-06-13T00:00:00.000Z",
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    {
      "label": "VibeMathed: The Erdos-Graham Semiprime Unit Fraction Problem",
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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.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}