{
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  "problem_id": "vibemathed:wegner-rectangle-piercing-conjecture",
  "title": "Wegner's Piercing Conjecture for Rectangles",
  "canonical_statement": "Wegner conjectured in 1965 that every finite family $\\mathcal{R}$ of axis-parallel rectangles satisfies $\\tau(\\mathcal{R}) \\le 2\\nu(\\mathcal{R}) - 1$, where $\\tau$ is the minimum number of piercing points and $\\nu$ the largest pairwise-disjoint subfamily. False, by an explicit triangle-free counterexample.",
  "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": "disproved",
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      "occurred_at": "2026-06-16T00:00:00.000Z",
      "title": "arXiv:2606.17854 - Counterexamples to Wegner's Conjecture for Rectangles",
      "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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      "model": "GPT-5.5 Pro, Codex",
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      "attempted_at": "2026-06-16T00:00:00.000Z",
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        "Deepak Ajwani",
        "Rishikesh Gajjala",
        "Rajiv Raman"
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      "note": "The refutation is an explicit finite family of rectangles, so it reduces to a finite piercing computation. arXiv preprint, not peer-reviewed.",
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      "label": "arXiv:2606.17854 - Counterexamples to Wegner's Conjecture for Rectangles",
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    {
      "label": "VibeMathed: Wegner's Piercing Conjecture for Rectangles",
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
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