{
  "abstract": "We establish degree-dependent irrationality-exponent bounds for logarithms at algebraic arguments and sharper bounds when conjugate logarithms match. A two-torus construction gives an upper bound of three for ratios of logarithms of multiplicatively independent positive rational numbers. We also treat normalized quadratic logarithms and circular logarithms. The rational-logarithm and rational-power exponent-two cases were treated earlier by Liu, Jiang and Zhang; we retain them within the broader framework and its Lean verification. Starting from the interpolation and determinant method in OpenAI's September 24, 2026 preprint on the irrationality exponent of $π$, we track the arithmetic cost of algebraic embeddings and the effects of matching conjugate logarithms. A second, graded Pade construction gives near-optimal measures for powers and bounded-degree polynomial values at sufficiently small logarithmic arguments, with estimates uniform in both coefficient height and rational denominator. We state the branch, independence, parameter-order, and approximation-field hypotheses explicitly. The Lean supplement has reviewed endpoint correspondences for all 62 numbered results: 53 direct checked endpoints or compositions, and nine applications with named classical theorem inputs. Native proofs of those inputs and separate formalizations of every unnumbered assertion are not supplied. Appendix A gives the exact declarations, hypotheses, and verification evidence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28079",
  "author_total": 1,
  "authors": [
    {
      "name": "Gregory V. Chudnovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvae64gcw438m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28079",
  "fulltext_url": null,
  "id": "fvae64gcw438m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28079",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223089607",
  "pdf_url": "https://arxiv.org/pdf/2610.28079",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvae64gcw438m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28079",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28079"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Irrationality exponents of logarithmic numbers: Values, quotients, and graded approximation",
  "title_text": "Irrationality exponents of logarithmic numbers: Values, quotients, and graded approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/fvae64gcw438m",
  "venue": "arXiv",
  "versions": []
}