{
  "abstract": "Plate tectonics is described in two registers: a discrete one, in which rigid plates tile the sphere and meet at trivalent junctions, and a continuous one, in which Bercovici and Wessel (1994) replace hard plate outlines by smooth shape functions of finite boundary half-width $δ^*$. We prove that the two registers are connected by a limit theorem. Generalizing the shape functions to a signed-geodesic-distance construction, we show that they converge almost everywhere, exponentially in $1/δ^*$, to the plate indicator functions; that the sharp plate mosaic is a finite regular trivalent CW decomposition of the sphere under an explicit structural hypothesis; and that a component-counted weighted Euler characteristic $χ_w^{δ^*}(τ)$, built from the super-level sets of the shape functions, equals $V-E+F=2$ for all $δ^*$ below an explicit threshold $δ_0(τ)$, with its face, edge and vertex terms converging separately to the numbers of plates, boundary arcs and triple junctions. The theorem is proved unconditionally on the signed-distance offset cover under positive-reach, separation and bounded-sector hypotheses, and transferred to the normalized partition-of-unity field for thresholds $τ<1/3$ by a comparison lemma whose junction-ball step, a planar single-crossing property, is certified numerically. The residual $|χ_w-2|$ defines a topological diffuseness index for diffuse plate boundaries. For the present-day PB2002 network the hypotheses are measured to be non-vacuous, with $δ_0(0.15)\\approx2.8$ km. The theorem is the mathematical foundation of the topological audit of plate reconstructions presented in a companion paper (Kim, 2026, submitted to Geoscience Frontiers).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39187",
  "author_total": 1,
  "authors": [
    {
      "name": "Seung-Sep Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33dc9pm11jgng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39187",
  "fulltext_url": null,
  "id": "33dc9pm11jgng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39187",
  "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",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "1907|Geological and Geophysical Studies"
    ]
  ],
  "openalex": "W7215031474",
  "pdf_url": "https://arxiv.org/pdf/2609.39187",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33dc9pm11jgng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39187",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39187"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    }
  ],
  "title": "A limit theorem linking continuous plate models to the topology of the plate boundary network",
  "title_text": "A limit theorem linking continuous plate models to the topology of the plate boundary network",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/33dc9pm11jgng",
  "venue": "arXiv",
  "versions": []
}