{
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  "source": "vibemath",
  "problem_id": "vibemathed:erdos-lovasz-cover-number",
  "title": "The Erdos-Lovasz Cover Number Problem",
  "canonical_statement": "Let $g(r)$ be the fewest edges in an $r$-uniform intersecting hypergraph with cover number $r$. Erdos and Lovasz proved $g(r) \\ge 8r/3 - 3$. An elementary argument gives $g(r) \\ge 3r - 4$, and building on it with Kahn's small-codegree edge-colouring theorem pushes the bound further.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
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    {
      "id": "vibemathed:erdos-lovasz-cover-number:event",
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      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-06-23T00:00:00.000Z",
      "title": "arXiv:2606.24878 - An Improved Lower Bound for the Erdos-Lovasz Cover Number Problem",
      "summary": "an improved lower bound; the true order of g(r) remains open",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:erdos-lovasz-cover-number:attempt"
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      "model": "ChatGPT 5.5 Pro, Aristotle",
      "provider": "OpenAI / Harmonic",
      "attempted_at": "2026-06-23T00:00:00.000Z",
      "human_collaborators": [
        "Varun Sivashankar"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement states the proof was discovered with the help of ChatGPT 5.5 Pro, and that Theorem 1 was then formalized in Lean with Harmonic's Aristotle.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2606.24878 - An Improved Lower Bound for the Erdos-Lovasz Cover Number Problem",
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        },
        {
          "label": "VibeMathed: The Erdos-Lovasz Cover Number Problem",
          "url": "https://vibemathed.com/problem/erdos-lovasz-cover-number",
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        }
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      "independence": "unknown"
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      "solution_event_id": "vibemathed:erdos-lovasz-cover-number:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The Lean formalization is partial by the author's own account: part (i) of Theorem 1 is formalized in full and part (ii) only conditional on Kahn's theorem. We have not compiled it. arXiv preprint, not peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Erdos-Lovasz Cover Number Problem",
          "url": "https://vibemathed.com/problem/erdos-lovasz-cover-number",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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        {
          "label": "arXiv:2606.24878 - An Improved Lower Bound for the Erdos-Lovasz Cover Number Problem",
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      "label": "arXiv:2606.24878 - An Improved Lower Bound for the Erdos-Lovasz Cover Number Problem",
      "url": "https://arxiv.org/abs/2606.24878",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Erdos-Lovasz Cover Number Problem",
      "url": "https://vibemathed.com/problem/erdos-lovasz-cover-number",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:erdos-lovasz-cover-number:signal:recent_partial_result",
      "problem_id": "vibemathed:erdos-lovasz-cover-number",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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"
}