{
  "abstract": "Let $G$ be a definable group in an NIP theory. We prove that every minimal proximal definable $G$-flow is strongly proximal. Consequently, the universal minimal proximal definable $G$-flow $Π^{\\mathrm{def}}(G)$ coincides with the minimal strongly proximal definable $G$-flow $Π^{\\mathrm{def}}_{\\mathrm{s}}(G)$. Furthermore, for a $p$-adic definable group $G$, we can compute $Π^{\\mathrm{def}}(G)$ explicitly. We show that $Π^{\\mathrm{def}}(G)$ is exactly $Π^{\\mathrm{def}}(S)$ where $S$ is the semisimple part of the definably amenable-semisimple decomposition of $G$. In addition, $Π^{\\mathrm{def}}(S)\\cong S^*_\\mathcal{F}(\\mathbb{Q}_p)$, the space of types of full dimension on $\\mathbf{F}$, where $\\mathcal{F}=\\mathbf{F}(\\mathbb{Q}_p)$ for a flag variety $\\mathbf{F}$ constructed from $S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03873",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhentao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2dr39762e5nvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03873",
  "fulltext_url": null,
  "id": "2dr39762e5nvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03873",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7208767835",
  "pdf_url": "https://arxiv.org/pdf/2609.03873",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2dr39762e5nvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.03873",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03873"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Minimal proximal definable flows over the $p$-adics",
  "title_text": "Minimal proximal definable flows over the p-adics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2dr39762e5nvq",
  "venue": "arXiv",
  "versions": []
}