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  "problem_id": "vibemathed:density-large-dilates",
  "title": "Density Thresholds for Large Dilates of Point Configurations",
  "canonical_statement": "Near-optimal density thresholds forcing a measurable set in $\\mathbb{R}^d$ to contain all sufficiently large similar copies of every $n$-point configuration, answering a question from the Euclidean density theorem literature up to logarithmic factors.",
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      "occurred_at": "2026-04-20T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Near-optimal rather than optimal: the bounds match up to logarithmic-type factors.",
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      "outcome": "ChatGPT 5.4 Pro \"was used to suggest and draft approaches to Proposition 5\"; in particular the random pattern thinning argument, \"somewhat novel in this context,\" was suggested by the model. Main ideas and final proofs are the authors'.",
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          "url": "https://arxiv.org/abs/2604.18544",
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}