{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:uniform-witnesses-k3-question",
  "title": "Uniform Witnesses for Uniform Set Systems: the k=3 Question",
  "canonical_statement": "In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the $k=3$ case of a witness construction question. ChatGPT 5.4 Pro answered it; the published construction generalizes the model's response, and the conversation transcript is public.",
  "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.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:uniform-witnesses-k3-question:event",
      "problem_id": "vibemathed:uniform-witnesses-k3-question",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-03-01T00:00:00.000Z",
      "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.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:uniform-witnesses-k3-question:attempt"
      ],
      "method_family_ids": [
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      ],
      "source_assertion_ids": [
        "vibemathed:uniform-witnesses-k3-question:assertion"
      ]
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  "attempts": [
    {
      "id": "vibemathed:uniform-witnesses-k3-question:attempt",
      "problem_id": "vibemathed:uniform-witnesses-k3-question",
      "model": "ChatGPT 5.4 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-03-01T00:00:00.000Z",
      "human_collaborators": [
        "Ting-Wei Chao",
        "Zixuan Xu",
        "Dmitrii Zakharov"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "\"In an earlier arXiv version of this paper, Theorem 1.6 was stated as a question in the special case k=3. ChatGPT 5.4 Pro managed to successfully answer this question and the construction in Section 3.2 is a generalization of its response\" - with the chat transcript linked in the paper.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "The ChatGPT conversation that answered the k=3 question",
          "url": "https://chatgpt.com/share/69b8e49c-6df0-8009-8180-52161f034bc2",
          "kind": "transcript",
          "license": null
        }
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          "url": "https://arxiv.org/abs/2602.17459",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Uniform Witnesses for Uniform Set Systems: the k=3 Question",
          "url": "https://vibemathed.com/problem/uniform-witnesses-k3-question",
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      "solution_event_id": "vibemathed:uniform-witnesses-k3-question:event",
      "level": "unreviewed",
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": null,
      "sources": [
        {
          "label": "VibeMathed: Uniform Witnesses for Uniform Set Systems: the k=3 Question",
          "url": "https://vibemathed.com/problem/uniform-witnesses-k3-question",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
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          "label": "arXiv",
          "url": "https://arxiv.org/abs/2602.17459",
          "kind": "primary-mathematical-source",
          "license": null
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  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2602.17459",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Uniform Witnesses for Uniform Set Systems: the k=3 Question",
      "url": "https://vibemathed.com/problem/uniform-witnesses-k3-question",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:uniform-witnesses-k3-question:signal:watch_only",
      "problem_id": "vibemathed:uniform-witnesses-k3-question",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}