{
  "abstract": "We prove that a relation obtained by composing arbitrary functions of arity $\\leq k$ with a relation definable in an $n$-dependent structure is $kn$-dependent. This confirms a conjecture of Chernikov and Hempel. We also demonstrate optimality of the result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01230",
  "author_total": 2,
  "authors": [
    {
      "name": "Artem Chernikov"
    },
    {
      "name": "Yuyan He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zaz635gyg9kq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01230",
  "fulltext_url": null,
  "id": "5zaz635gyg9kq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01230",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
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      "openalex",
      "2608|Advanced Topology and Set Theory"
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  ],
  "openalex": "W7206188919",
  "pdf_url": "https://arxiv.org/pdf/2609.01230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zaz635gyg9kq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01230"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The Composition Lemma for $n$-dependence",
  "title_text": "The Composition Lemma for n-dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/5zaz635gyg9kq",
  "venue": "arXiv",
  "versions": []
}