{
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  "source": "vibemath",
  "problem_id": "vibemathed:covering-number-c-12-6-4",
  "title": "The Covering Number $C(12,6,4)$",
  "canonical_statement": "A $t$-$(v,k,\\lambda)$ covering is a family of $k$-subsets of a $v$-set meeting every $t$-subset at least $\\lambda$ times, and $C(v,k,t)$ is the least number of blocks. The recorded bounds for $C(12,6,4)$ were $40 \\le C(12,6,4) \\le 41$. No $4$-$(12,6,1)$ covering with $40$ blocks exists, so $C(12,6,4) = 41$.",
  "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",
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      "type": "proved",
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      "occurred_at": "2026-07-26T00:00:00.000Z",
      "title": "arXiv:2607.23766 - The covering number C(12, 6, 4) is 41",
      "summary": "closes a one-block gap in the covering tables; the analogous next case is not reachable by this method",
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      "provider": "OpenAI / Anthropic",
      "attempted_at": "2026-07-26T00:00:00.000Z",
      "human_collaborators": [
        "Charlie Krug"
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        },
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          "label": "VibeMathed: The Covering Number $C(12,6,4)$",
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      "verifier": "VibeMathed (source-reported label)",
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      "note": "The non-existence argument is a forced-structure search: a counting argument pins every point to degree exactly 20 and forces each point link to be an optimal 3-(11,5,1) covering, collapsing the search space. Single-author arXiv preprint, not peer-reviewed.",
      "sources": [
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    {
      "label": "VibeMathed: The Covering Number $C(12,6,4)$",
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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."
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  "generated_at": "2026-09-13T16:28:40.178Z"
}