{
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  "source": "vibemath",
  "problem_id": "vibemathed:wow-284-refuted",
  "title": "Written on the Wall II, Conjecture 284",
  "canonical_statement": "WOW-284 asserts that the minimum dual degree of every connected graph of order at least three and girth at least five is at most the negative of its least distance eigenvalue. The paper refutes it with exact counterexamples of orders 38, 39, 40, 42 and 50, and develops a structural theory of the failure.",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-29T00:00:00.000Z",
      "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_assisted",
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      "problem_id": "vibemathed:wow-284-refuted",
      "model": "ChatGPT-5.6 Sol Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-07-29T00:00:00.000Z",
      "human_collaborators": [
        "Samuil Petkov"
      ],
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      "prompt_public": null,
      "outcome": "The author credits ChatGPT-5.6 Sol Pro with adversarial proof checking, proof exploration and Lean formalization, and assumes full responsibility for the mathematics, attribution and conclusions.",
      "failed_routes": [],
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          "label": "Counterexample certificates and Lean sources",
          "url": "https://github.com/SamPetkov/wow284",
          "kind": "lean-proof",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2607.27452",
          "kind": "primary-mathematical-source",
          "license": null
        },
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          "license": "https://vibemathed.com/data-license"
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      "independence": "unknown"
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      "verifier": "VibeMathed (source-reported label)",
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      "sources": [
        {
          "label": "VibeMathed: Written on the Wall II, Conjecture 284",
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      "kind": "primary-mathematical-source",
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      "label": "VibeMathed: Written on the Wall II, Conjecture 284",
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      "kind": "source-assertion",
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      "id": "vibemathed:wow-284-refuted:signal:watch_only",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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    "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"
}