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  "problem_id": "vibemathed:faber-harris-isolation-lemma-conjecture",
  "title": "Faber-Harris Conjecture on the Isolation Lemma",
  "canonical_statement": "For an inclusion-free hypergraph on $n$ vertices, a weight assignment $w:[n]\\to[d]$ is isolating when a unique edge attains minimum weight. Faber and Harris conjectured that the number of isolating assignments is at least $n\\sum_{j=0}^{d-1} j^{n-1}$, attained by the hypergraph of $n$ singleton edges. The bound holds, and extends to a more general class of objective functions.",
  "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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      "type": "proved",
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      "occurred_at": "2026-07-07T00:00:00.000Z",
      "title": "arXiv:2607.06171 - The singleton hypergraph is extremal for the Isolation Lemma",
      "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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      "model": "ChatGPT",
      "provider": "OpenAI",
      "attempted_at": "2026-07-07T00:00:00.000Z",
      "human_collaborators": [
        "Vance Faber",
        "David G. Harris"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement credits the model with one specific and load-bearing step: the proof benefited from its assistance in discovering the fractional charging argument. The authors are the pair who stated the conjecture in 2018.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
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