{
  "abstract": "Let $(a_n)$ be a positive null sequence with $\\liminf_{n\\to\\infty}a_{n+1}/a_n>0$. For every $η>0$, we construct a compact set $E\\subset[0,1]$ with Lebesgue measure greater than $1-η$ containing no nontrivial affine copy of $\\{a_n:n\\ge1\\}$. No monotonicity is assumed. The proof adapts a finite-tree construction for geometric sequences to grids chosen from a subsequence with two-sided ratio bounds. We also obtain one such set for any prescribed countable family of sequences, with infinitely many distinct points omitted from every affine copy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11449",
  "author_total": 2,
  "authors": [
    {
      "name": "Kan Jiang"
    },
    {
      "name": "Lifeng Xi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33ft0bexax5d6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11449",
  "fulltext_url": null,
  "id": "33ft0bexax5d6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11449",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221192482",
  "pdf_url": "https://arxiv.org/pdf/2610.11449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33ft0bexax5d6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11449"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Erdős similarity problem for null sequences with adjacent ratios bounded below",
  "title_text": "The Erdős similarity problem for null sequences with adjacent ratios bounded below",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/33ft0bexax5d6",
  "venue": "arXiv",
  "versions": []
}