{
  "abstract": "We study persistence modules obtained from the $A$-fundamental groupoids of finite graphs. Moreover, we verify the categorical properties needed to form generalized persistence diagrams, and describe a quotient that identifies equivalent groupoids. A normalized linear presheaf construction places these modules in an essentially small abelian category, where Patel's Continuity Theorem gives a $1$-Lipschitz estimate in erosion distance. Explicit graph filtrations illustrate the groupoid-valued construction, and so we suggest a new approach to interpret persistence diagrams and large data sets in topological data analysis, based on recent works of A-homotopy theory of the last years.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00799",
  "author_total": 3,
  "authors": [
    {
      "name": "Yanga Bavuma"
    },
    {
      "name": "Martin Mijangos"
    },
    {
      "name": "Francesco G. Russo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rp7bdhdvakkd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00799",
  "fulltext_url": null,
  "id": "0rp7bdhdvakkd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00799",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.CT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rp7bdhdvakkd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A result of continuous stability for generalized persistence diagrams",
  "title_text": "A result of continuous stability for generalized persistence diagrams",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0rp7bdhdvakkd",
  "venue": "arXiv",
  "versions": []
}