{
  "abstract": "We establish a complete structural classification for cw$_F$-hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw$_F$-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus $\\mathbb{T}^2$ or to a standard hyperelliptic quotient on $\\mathbb{S}^2$ of a hyperbolic affine toral map. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11943",
  "author_total": 4,
  "authors": [
    {
      "name": "Rodrigo Arruda"
    },
    {
      "name": "Bernardo Carvalho"
    },
    {
      "name": "Piotr Oprocha"
    },
    {
      "name": "Alberto Sarmiento"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqhq14wees6xt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11943",
  "fulltext_url": null,
  "id": "cqhq14wees6xt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11943",
  "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.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7164380718",
  "pdf_url": "https://arxiv.org/pdf/2606.11943",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqhq14wees6xt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2606.11943",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11943"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities",
  "title_text": "Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/cqhq14wees6xt",
  "venue": "arXiv",
  "versions": []
}