{
  "abstract": "We investigate the approximation of elements of the middle-third Cantor set by dyadic rationals, and natural extensions. We prove a conjecture of Velani, completing the metric theory for the Cantor measure. Our key method enables a quantitative study of the incommensurability of binary and ternary expansions of integers, initiated by Furstenberg. The method has other applications, e.g. $\\sum_{k} |\\hatμ(2^k)|^σ< \\infty$ for any $σ> 0$, where $μ$ is the Cantor measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28839",
  "author_total": 2,
  "authors": [
    {
      "name": "Sam Chow"
    },
    {
      "name": "Han Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6afvavxbrv39a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28839",
  "fulltext_url": null,
  "id": "6afvavxbrv39a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28839",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223206276",
  "pdf_url": "https://arxiv.org/pdf/2610.28839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6afvavxbrv39a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On a conjecture of Velani",
  "title_text": "On a conjecture of Velani",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/6afvavxbrv39a",
  "venue": "arXiv",
  "versions": []
}