{
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  "problem_id": "vibemathed:bounded-circumference-cycle-counting",
  "title": "Counting Fixed Cycles in Graphs with Bounded Circumference",
  "canonical_statement": "Zhu, Gyori, He, Lv, Salia and Xiao conjectured the maximum number of copies of a fixed cycle in an $n$-vertex graph of bounded circumference, attained by the join of a clique with an independent set. For every fixed $s \\ge 3$ and $L \\ge 2s+2$ and all large $n$, $\\mathrm{ex}(n, C_{2s+1}, \\mathcal{C}_{\\ge L+1}) = N(C_{2s+1}, H(n,L))$. Together with the companion even-cycle result this settles the conjecture.",
  "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",
      "status": "resolved",
      "occurred_at": "2026-07-12T00:00:00.000Z",
      "title": "arXiv:2607.10779 - Counting Odd Cycles in Graphs with Bounded Circumference",
      "summary": "the odd-cycle half; the even-cycle half is a companion paper by the same authors",
      "ai_contribution": "ai_assisted",
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      "model": "GPT-5.6",
      "provider": "OpenAI",
      "attempted_at": "2026-07-12T00:00:00.000Z",
      "human_collaborators": [
        "Xiamiao Zhao",
        "Yuanpei Wang"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The declaration credits the model with solving one case of Theorem 1.2, in particular the calculations in that proof, and with rewriting the Section 2.4 argument in the language of directed graphs; the rest is readability and exposition. The authors reviewed and verified the proofs and take sole responsibility.",
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          "label": "arXiv:2607.10779 - Counting Odd Cycles in Graphs with Bounded Circumference",
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      "label": "arXiv:2607.10779 - Counting Odd Cycles in Graphs with Bounded Circumference",
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      "kind": "primary-mathematical-source",
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    {
      "label": "VibeMathed: Counting Fixed Cycles in Graphs with Bounded Circumference",
      "url": "https://vibemathed.com/problem/bounded-circumference-cycle-counting",
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    "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."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}