{
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  "source": "vibemath",
  "problem_id": "vibemathed:espuny-diaz-lichev-wesolek-conjecture",
  "title": "The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs",
  "canonical_statement": "Espuny Diaz, Lichev and Wesolek conjectured that a Dirac-type minimum degree condition forces Hamiltonicity in spanning subgraphs of cycle powers. Asymptotically true: for every $\\varepsilon > 0$ and all large $k$, any spanning subgraph of the $k$th power of a cycle with minimum degree at least $(1+\\varepsilon)k$ has a Hamilton cycle.",
  "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",
  "solution_events": [
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      "problem_id": "vibemathed:espuny-diaz-lichev-wesolek-conjecture",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-06-05T00:00:00.000Z",
      "title": "arXiv:2606.07471 - Dirac subgraphs of powers of cycles are Hamiltonian",
      "summary": "asymptotic in k; the paper also shows the analogous statement is false for d = 2",
      "ai_contribution": "ai_co_developed",
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        "vibemathed:espuny-diaz-lichev-wesolek-conjecture:attempt"
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      "model": "ChatGPT 5.5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-06-05T00:00:00.000Z",
      "human_collaborators": [
        "Richard Lang",
        "Alp Muyesser",
        "Mathias Schacht",
        "Carl Schneider"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The credit is specific and negative-result shaped: the authors show the analogous statement fails for $d = 2$, and say the crucial construction behind that was suggested to them by ChatGPT 5.5 Pro, with a dedicated appendix discussing it.",
      "failed_routes": [],
      "artifacts": [],
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          "label": "VibeMathed: The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs",
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      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs",
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      "label": "arXiv:2606.07471 - Dirac subgraphs of powers of cycles are Hamiltonian",
      "url": "https://arxiv.org/abs/2606.07471",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs",
      "url": "https://vibemathed.com/problem/espuny-diaz-lichev-wesolek-conjecture",
      "kind": "source-assertion",
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  "opportunity_signals": [
    {
      "id": "vibemathed:espuny-diaz-lichev-wesolek-conjecture:signal:recent_partial_result",
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      "kind": "recent_partial_result",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}