{
  "abstract": "For a set $V$ of $n$ distinct positive integers, let $\\mathrm{ML}(V)=\\max_{t\\in\\mathbb{R}/\\mathbb{Z}}\\min_{v\\in V}\\|vt\\|$, where $\\|x\\|$ is the distance from $x$ to the nearest integer. We prove that there is an absolute constant $c>0$ such that for every $n\\ge2$ and every $V$, \\[ \\mathrm{ML}(V)>\\frac{1+c}{2n}. \\] The proof combines a refinement of the large GCD argument of Green and Walker with a new physical spillover inequality for interval multiplicities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23790",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiyu Hu"
    },
    {
      "name": "Yifan Jing"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ce87523ytxkk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23790",
  "fulltext_url": null,
  "id": "7ce87523ytxkk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23790",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222920391",
  "pdf_url": "https://arxiv.org/pdf/2610.23790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ce87523ytxkk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23790"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Near optimal gap in the Lonely Runner Conjecture",
  "title_text": "Near optimal gap in the Lonely Runner Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/7ce87523ytxkk",
  "venue": "arXiv",
  "versions": []
}