{
  "abstract": "Let ${R^\\ast}(n)$ be the least radius of a central circle to which nonoverlapping circles of radii $1,\\ldots,n$ are externally tangent. We prove that ${R^\\ast}(n)={C_\\ast} n^2+o(n^2)$ and characterize ${C_\\ast}$ by finite linear programs with an explicit error tending to zero. The reduction preserves arbitrary orders and all pairwise constraints: the limiting problem places marked points on a line at pairwise separation at least the geometric mean of their marks. Concatenation with a bounded boundary cost proves existence, and balanced finite-word programs supply matching effective upper and lower bounds. Their certified gap is $(1/k+1/r)/π$, before directed arithmetic error, for $k$ mark types and words of length $r$. A quantitative reflected-block recovery theorem supplies genuine permutations and full ring geometry, with a countable extension and a strict four-block improvement. The explicit interval is $C_{\\mathrm{term}}+η_{\\mathrm{width}}\\le{C_\\ast}\\le U_4$; neither endpoint is asserted sharp. In particular, the coefficient $1/8$ proposed in the preceding finite study is false. An elementary expression for ${C_\\ast}$, efficient high-precision evaluation and global floating-circle structure remain open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13630",
  "author_total": 1,
  "authors": [
    {
      "name": "Maurizio Falconi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m6ynt74j9pm3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13630",
  "fulltext_url": null,
  "id": "6m6ynt74j9pm3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13630",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7213223348",
  "pdf_url": "https://arxiv.org/pdf/2609.13630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m6ynt74j9pm3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimum central circles: an effective characterization of the global asymptotic constant",
  "title_text": "Minimum central circles: an effective characterization of the global asymptotic constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6m6ynt74j9pm3",
  "venue": "arXiv",
  "versions": []
}