{
  "abstract": "For a fixed $k$-uniform hypergraph $F$, let $\\mathrm{ex}_k(n,F)$ denote the maximum number of edges in an $F$-free $k$-uniform hypergraph on $n$ vertices. We prove that for every integer $k\\ge2$ and every rational $r\\in[0,1]$ there exists a $k$-uniform hypergraph $F_{k,r}$ such that \\begin{equation*} \\mathrm{ex}_k(n,F_{k,r})=Θ(n^{k-r}). \\end{equation*} The case $k=2$ is the rational exponents conjecture of Erdős and Simonovits \\cite{Erdos1988}, also known as Erdős problem \\#571 \\cite{BloomErdoswebsite}; a proof was announced in September 2026 and is expounded by Conlon et al.\\ \\cite{Conlon-Janzer-Jiang-Kim-Lee-Liu-Longbrake-Yepremyan}. For $k\\ge3$ the theorem extends their result to $k$-uniform hypergraphs. In the single-hypergraph setting, this strengthens Fitch's finite-family theorem \\cite{Fitch} by realizing each exponent with a single forbidden $k$-uniform hypergraph for $0\\le r\\le1$. We also show, via an explicit two-edge construction, that for $k\\ge4$ this strengthening fails for $\\lceil k/2\\rceil<r\\le k-1$: no single $k$-uniform hypergraph $F$ then satisfies $\\mathrm{ex}_k(n,F)=Θ(n^{k-r})$. The main result of this paper has been formalized in Lean 4, conditional on two explicitly stated axioms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07290",
  "author_total": 2,
  "authors": [
    {
      "name": "Chang Liu"
    },
    {
      "name": "Jue Dai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/evmyfrjxd7fkn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07290",
  "fulltext_url": null,
  "id": "evmyfrjxd7fkn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07290",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/evmyfrjxd7fkn.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07290"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Rational Turán exponents of a single $k$-uniform hypergraph",
  "title_text": "Rational Turán exponents of a single k-uniform hypergraph",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/evmyfrjxd7fkn",
  "venue": "arXiv",
  "versions": []
}