{
  "abstract": "Let $E$ be an $n$-dimensional rigid adelic space over a number field $K$. We study the minimum number $g_E(R)$ of proper $K$-subspaces needed to cover the projective height ball of radius $R$, together with the maximum cardinality $h_E(R)$ of a subset in linear general position. We show that, once $R$ is sufficiently large compared with the last Roy--Thunder minimum of $E$, both quantities have order $Ψ_E(R)^{[K:\\mathbb Q]}$, where $Ψ_E(R)$ is an explicit expression in the Roy--Thunder minima. The comparison constants are effectively computable and uniform in $E$. For the standard adelic space $K^n$, this gives order $R^{[K:\\mathbb Q]n/(n-1)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00988",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruida Di"
    },
    {
      "name": "Runjie Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65rhqq7ebxvr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00988",
  "fulltext_url": null,
  "id": "65rhqq7ebxvr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00988",
  "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": "W7206174297",
  "pdf_url": "https://arxiv.org/pdf/2609.00988",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65rhqq7ebxvr6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00988",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00988"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces",
  "title_text": "Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/65rhqq7ebxvr6",
  "venue": "arXiv",
  "versions": []
}