{
  "abstract": "We prove a conjecture of Regts and Sevenster: a complex-valued graph parameter $f$ with $f(\\emptyset)=1$ has exponentially bounded edge-connection rank if and only if it is a mixed partition function. The bound is exact: for a real number $R\\ge 1$, the connection ranks satisfy $\\operatorname{rk} M_{f,t}\\le R^t$ for all $t\\ge 0$ if and only if $f$ has a model on a super vector space $\\mathbb{C}^{k|2\\ell}$ with $k+2\\ell\\le R$. Consequently the base of exponential growth of the connection ranks is the least number of colours of a model, the two dimensions of a minimal model are determined by $f$, and the parameters with a model on a prescribed $\\mathbb{C}^{k|2\\ell}$ are characterised. The proof organises fragments modulo the connection kernel into a rigid symmetric tensor category whose morphism spaces have the connection ranks as dimensions; the rank hypothesis and an argument of Schrijver make its additive idempotent completion semisimple, Deligne's theorem provides a fibre functor to super vector spaces, and the resulting super tensor network is identified with the Regts-Sevenster model exactly, circuit signs included. An appendix shows that in a rigid symmetric $\\mathbb{C}$-linear category with $\\mathrm{End}(\\mathbf{1})=\\mathbb{C}$, exponentially bounded endomorphism growth makes the trace zeta function of every endomorphism rational, with explicit degree bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.27198",
  "author_total": 1,
  "authors": [
    {
      "name": "William Whistler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xjvrybed5y41.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27198",
  "fulltext_url": null,
  "id": "9xjvrybed5y41",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27198",
  "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.CO"
    ],
    [
      "arxiv",
      "math.QA"
    ],
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      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
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  "openalex": "W7171765648",
  "pdf_url": "https://arxiv.org/pdf/2607.27198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xjvrybed5y41.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.27198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Mixed partition functions are exactly the graph parameters of exponentially bounded edge-connection rank",
  "title_text": "Mixed partition functions are exactly the graph parameters of exponentially bounded edge-connection rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/9xjvrybed5y41",
  "venue": "arXiv",
  "versions": []
}