{
  "abstract": "The integer Chebyshev constant of [0,1] has been bracketed by 0.4213 <= t_Z([0,1]) <= 0.422685 since the work of Pritsker (2005) and of Flammang (2014). We prove 0.4222286000 <= t_Z([0,1]) <= 0.4226846976, narrowing the interval from 1.39e-3 to 4.56e-4. Both bounds are established by explicit certificates. The upper bound is carried by an integer polynomial with 92 factors and explicit integer exponents; the lower bound by a discrete measure on 947 cells together with a library of 206 irreducible polynomials, through an inequality in which the terms paying for divisibility are made explicit. Two self-contained scripts, included as ancillary files, re-derive both bounds from the certificates alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00386",
  "author_total": 1,
  "authors": [
    {
      "name": "David Niedbala Giraudin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6bw2fh06vz18.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00386",
  "fulltext_url": null,
  "id": "e6bw2fh06vz18",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00386",
  "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.NT"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7216027604",
  "pdf_url": "https://arxiv.org/pdf/2610.00386",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6bw2fh06vz18.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.00386",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00386"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "New bounds for the integer Chebyshev constant of [0,1]",
  "title_text": "New bounds for the integer Chebyshev constant of [0,1]",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/e6bw2fh06vz18",
  "venue": "arXiv",
  "versions": []
}