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  "slug": "almost-equilateral-banach-logarithmic-dimension-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The MathOverflow page has zero answers. Checked literature gives the logarithmic bound for classical l_p spaces and a general log-squared-type bound, while no source located in the dated search establishes the stated uniform logarithmic bound for all norms. Exact unresolved remainder: Prove the existence of C(epsilon) with the displayed universal quantifiers, or construct a fixed epsilon and a sequence of d-dimensional Banach spaces whose largest epsilon-almost-equilateral sets have subexponential size in d. A quantitative result must state all dependencies on epsilon and may rescale a constructed set only by a single common factor.",
  "relevance": "For Logarithmic dimension for almost-equilateral sets in Banach spaces, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The MathOverflow page has zero answers. Checked literature gives the logarithmic bound for classical l_p spaces and a general log-squared-type bound, while no source located in the dated search establishes the stated uniform logarithmic bound for all norms.\n\nExact unresolved remainder: Prove the existence of C(epsilon) with the displayed universal quantifiers, or construct a fixed epsilon and a sequence of d-dimensional Banach spaces whose largest epsilon-almost-equilateral sets have subexponential size in d. A quantitative result must state all dependencies on epsilon and may rescale a constructed set only by a single common factor.",
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    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1016/j.ejc.2003.08.003",
      "locator": "main low-dimensional embedding theorem and coding construction for finite ultrametrics in classical l_p spaces"
    },
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  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.ejc.2003.08.003",
    "locator": "main low-dimensional embedding theorem and coding construction for finite ultrametrics in classical l_p spaces"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1283",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
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    },
    {
      "slug": "almost-equilateral-banach-logarithmic-dimension",
      "title": "almost equilateral banach logarithmic dimension",
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      "relation": "recorded_for",
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}