{
  "abstract": "An $r$-uniform hypergraph $H$ is uniformly dense with respect to $j$-graphs if, up to a small error, at least a prescribed proportion of the $r$-cliques of every $j$-uniform hypergraph on the same vertex set are edges of $H$. For a forbidden hypergraph $F$, its uniform Turán density at level $j$ is the supremum of these density bounds over arbitrarily large $F$-free hypergraphs with the error tending to zero. For every $r\\ge4$ and $1\\le j\\le r-3$, this paper proves that this Turán density is zero precisely when $F$ admits a vertex ordering in which every $(j+1)$-set shared by two edges occupies the same positions in both edges. This generalizes the zero-density characterizations of Erdős at $j=0$ and of Reiher, Rödl, and Schacht at $j=r-2$, and establishes the latter authors' proposed extension to the remaining nontrivial levels. Consequently, at level $j$, every positive uniform Turán density of a possibly infinite forbidden family is at least $N^{-N}$, where $N=\\binom r{j+1}$. The proof combines hypergraph regularity with adjacent exchanges in spreadable random hypergraphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06964",
  "author_total": 2,
  "authors": [
    {
      "name": "Heng Li"
    },
    {
      "name": "Xizhi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1gnhqex4zw60.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06964",
  "fulltext_url": null,
  "id": "a1gnhqex4zw60",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06964",
  "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/2611.06964",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1gnhqex4zw60.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.06964",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06964"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hypergraphs with zero uniform Turán density at intermediate levels",
  "title_text": "Hypergraphs with zero uniform Turán density at intermediate levels",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/a1gnhqex4zw60",
  "venue": "arXiv",
  "versions": []
}