{
  "abstract": "We show that every vineyard can be decomposed into vines, that is, every path in the space of persistence diagrams $\\mathcal{D}$ can be decomposed into a sequence of paths in $\\mathbb R^2$. Moreover, we characterize which spaces $X$ have the property that every continuous map $X\\to \\mathcal{D}$ has such a decomposition. Our results hold not just for $\\mathcal{D}$, but also for many other spaces of unordered tuples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20046",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Hull"
    },
    {
      "name": "Thomas Payne"
    },
    {
      "name": "Thomas Weighill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxrfsehfr74et.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20046",
  "fulltext_url": null,
  "id": "cxrfsehfr74et",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20046",
  "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.AT"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7222144796",
  "pdf_url": "https://arxiv.org/pdf/2610.20046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxrfsehfr74et.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Real Tree Vineyards have Vines",
  "title_text": "Real Tree Vineyards have Vines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cxrfsehfr74et",
  "venue": "arXiv",
  "versions": []
}