{
  "abstract": "We prove that conjugacy of minimal homeomorphisms of the Cantor space is Borel bireducible with isomorphism of countable graphs, answering the Cantor minimal case of a question of Foreman. We obtain the lower bound by encoding countably based profinite groups. Finite quotient homomorphisms are represented by factor maps between a common family of minimal subshifts. Amalgamation makes the resulting inverse limit independent, up to conjugacy, of the quotient presentation. Conversely, finite-stage factorization recovers the group from any conjugacy of these inverse limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12031",
  "author_total": 5,
  "authors": [
    {
      "name": "Xinan Dai"
    },
    {
      "name": "Wenhao Deng"
    },
    {
      "name": "Yingdong Shi"
    },
    {
      "name": "Tailin Wu"
    },
    {
      "name": "Yuchen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83gyaqcg3y6kw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12031",
  "fulltext_url": null,
  "id": "83gyaqcg3y6kw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12031",
  "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.DS"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7212953379",
  "pdf_url": "https://arxiv.org/pdf/2609.12031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83gyaqcg3y6kw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The Borel complexity of conjugacy for Cantor minimal systems",
  "title_text": "The Borel complexity of conjugacy for Cantor minimal systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/83gyaqcg3y6kw",
  "venue": "arXiv",
  "versions": []
}