{
  "abstract": "We prove the lower bounds \\[ B_\\infty>0.51,\\qquad L>0.51, \\] where $B_\\infty$ is the locally univalent Bloch constant and $L$ is Landau's constant, improving the bound $\\frac{1}{2}+2\\cdot10^{-8}$ of Chen and Shiba. The argument passes to the logarithm $g=\\log f'$ of a normalized locally univalent Bloch function, where the Bloch condition becomes a one-sided linear constraint on $\\operatorname{Re} g$; positive Toeplitz moment matrices then provide a finite-dimensional outer relaxation for the low logarithmic coefficients, and any non-negative dual vector for a linear program over that relaxation certifies a bound. Floating-point linear programming is used only to discover such dual vectors; the same duality also certifies the second-derivative bounds that control the Taylor allowances and the coefficient caps that contract the cover. An independent arbitrary-precision interval-arithmetic program reconstructs every witness and checks a finite cover of the normalized coefficient body by $1179$ boxes, the smallest certified radius being $0.51003$. All numerical premises were verified with Arb at $80$ decimal digits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23236",
  "author_total": 1,
  "authors": [
    {
      "name": "Frank Wikström"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4n60cq260d9m1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23236",
  "fulltext_url": null,
  "id": "4n60cq260d9m1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23236",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7214017898",
  "pdf_url": "https://arxiv.org/pdf/2609.23236",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4n60cq260d9m1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23236",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23236"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A computer-assisted lower bound for Landau's constant",
  "title_text": "A computer-assisted lower bound for Landau's constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/4n60cq260d9m1",
  "venue": "arXiv",
  "versions": []
}