{
  "abstract": "In 2000, Birbrair and Fernandes proved that the Hölder Semicomplex of the branches of a germ of a curve with its contact orders is a complete invariant of outer bi-Lipschitz equivalence of definable sets in polynomially bounded o-minimal structures. They also proved a realization theorem for it, i.e., for each Hölder semicomplex $G$, there is a germ of a semialgebraic curve $(X,x_0)$ such that the Hölder Semicomplex of $(X,x_0)$ coincides with $G$. In 2000, Birbrair proposed the problem of finding and characterizing all the Hölder semicomplexes that can be realized as a Hölder Semicomplex of a real analytic curve. Solving this problem in its full generality is a notoriously hard task; however, in this paper, we provide a complete answer to this problem when we restrict it to tangential nodal curves: curves defined as the union of the zero set of a harmonic function and its tangent cone at a fixed point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36381",
  "author_total": 3,
  "authors": [
    {
      "name": "José Edson Sampaio"
    },
    {
      "name": "Luan Moura Sousa"
    },
    {
      "name": "Emanoel Ferreira de Souza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kwz6w2czw19v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36381",
  "fulltext_url": null,
  "id": "2kwz6w2czw19v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36381",
  "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.CV"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7224088930",
  "pdf_url": "https://arxiv.org/pdf/2610.36381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kwz6w2czw19v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36381"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Outer Lipschitz Geometry of Unions of Tangential Nodal Sets",
  "title_text": "Outer Lipschitz Geometry of Unions of Tangential Nodal Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/2kwz6w2czw19v",
  "venue": "arXiv",
  "versions": []
}