{
  "abstract": "Let $K\\subset\\mathbb{C}$ be the attractor of $n\\ge2$ similarities $z\\mapstoλz+b_k$, $0<|λ|<1$, whose fixed points are evenly spaced on a line, and suppose that $K$ does not lie in a line. We prove that $K$ can be a dendrite only if $n\\le6$, and that such dendrites exist for every $2\\le n\\le6$; no separation or finite-intersection hypothesis is imposed. Hence, for $n\\ge7$, every connected $K$ of this kind has interior points or separates the plane. Neighboring pieces of $K$ meet in similar copies of a single contact set. In a dendrite exactly one first-level piece meets this set, whereas for $n\\ge7$ at least $n-\\lceil2\\sqrt{n-1}\\rceil\\ge2$ do, a bound attained by explicit quadratic parameters. The proof combines a planar translation obstruction for replicated contact arcs with an estimate based on Jensen's formula. After normalizing to $z\\mapsto t+z/c$, $t\\in\\{-n+1,-n+3,\\ldots,n-1\\}$, the connectedness locus is the closure, outside the unit disk, of the roots of monic integer polynomials of height at most $n-1$. The same estimate shows that, for $n\\ge7$, every such polynomial with a non-real root $c$ satisfying $|c|^2\\ge\\lceil2\\sqrt{n-1}\\rceil+1$ has subleading coefficient of absolute value at most $\\lceil2\\sqrt{n-1}\\rceil$, and that this bound is sharp. Accordingly, for $n\\ge7$, at every non-real boundary point $c$ of the locus with $|c|>1$, each expansion $c=\\sum_{j\\ge0}d_jc^{-j}$ with integer digits $|d_j|\\le n-1$ has $|d_0|\\le\\lceil2\\sqrt{n-1}\\rceil$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01291",
  "author_total": 1,
  "authors": [
    {
      "name": "Bernat Espigule"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16sm5f371vkx7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01291",
  "fulltext_url": null,
  "id": "16sm5f371vkx7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01291",
  "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.MG"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01291",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16sm5f371vkx7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01291",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01291"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Contact multiplicity and a sharp six-map bound for collinear self-similar dendrites",
  "title_text": "Contact multiplicity and a sharp six-map bound for collinear self-similar dendrites",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/16sm5f371vkx7",
  "venue": "arXiv",
  "versions": []
}