{
  "abstract": "We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of $Π_1^0$ degrees. This result relies on the construction of a rigid hierarchical structure in a graph model of the hyperbolic plane, and on the fact that every such group admits a representation in $\\operatorname{PSL}_2(\\mathbb{R})$ such that the matrices in the image have coefficients that are computable real numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04353",
  "author_total": 3,
  "authors": [
    {
      "name": "Sebastián Barbieri"
    },
    {
      "name": "Nicanor Carrasco-Vargas"
    },
    {
      "name": "Paul Toussaint"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/es1xj1zx2w96g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04353",
  "fulltext_url": null,
  "id": "es1xj1zx2w96g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04353",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7211900604",
  "pdf_url": "https://arxiv.org/pdf/2609.04353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/es1xj1zx2w96g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Medvedev degrees of SFTs on cocompact Fuchsian groups",
  "title_text": "Medvedev degrees of SFTs on cocompact Fuchsian groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/es1xj1zx2w96g",
  "venue": "arXiv",
  "versions": []
}