{
  "abstract": "Let $μ$ denote the irrationality exponent. Bruiltet proved in 2002 that $μ(Γ(1/4))\\le 10^{143}$ and $μ(Γ(1/3))\\le 10^{151}$. We prove $μ(Γ(1/4))\\le 3.24\\cdot 10^{26}$ and $μ(Γ(1/3))\\le 1.74\\cdot 10^{26}$, with explicit thresholds $h(p/q)\\ge 5.4\\cdot 10^{7}$ and $h(p/q)\\ge 4.7\\cdot 10^{7}$ respectively, against $10^{75}$ and $10^{79}$ in the published statements. The proof keeps the architecture of Bruiltet's argument -- Philippon's transcendence criterion together with a zero estimate in commutative algebraic groups -- and replaces three of its ingredients. First, an approximate Schwarz principle based on Hermite interpolation replaces the gravitation estimate of Reyssat; on a lattice point set its cost per node is governed by a lattice energy and drops from about 3.7 to about 1.0. Second, a summation lemma for the failure of Diaz's approximation lemma sharpens the passage from an approximation measure to an irrationality measure. Third, the auxiliary point is taken at a torsion point of order 4, respectively 3, which lowers the degree of the base field from 8d to 2d. All numerical constants are produced by a verifier run in interval arithmetic, supplied as ancillary files.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01711",
  "author_total": 1,
  "authors": [
    {
      "name": "David Niedbala Giraudin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6zfvr1s1t7p57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01711",
  "fulltext_url": null,
  "id": "6zfvr1s1t7p57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01711",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6zfvr1s1t7p57.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Irrationality measures for $Γ(1/4)$ and $Γ(1/3)$",
  "title_text": "Irrationality measures for Γ(1/4) and Γ(1/3)",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/6zfvr1s1t7p57",
  "venue": "arXiv",
  "versions": []
}