{
  "abstract": "We show that there exists $c > 0$ such that any subset of $\\{1,\\ldots,N\\}$ having size $\\gg N / \\exp( (\\log\\log\\log N)^c )$ contains a nontrivial pattern of the form $x,x+y,x+2y,x+y^3$. It is the first configuration of complexity strictly greater than $0$, other than refinements of arithmetic progressions, for which quantitative bounds over integers were obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12032",
  "author_total": 3,
  "authors": [
    {
      "name": "Bartłomiej Bychawski"
    },
    {
      "name": "Bartosz Głowacki"
    },
    {
      "name": "Ivan Spyrydonov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnz0ftb2dggyn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12032",
  "fulltext_url": null,
  "id": "fnz0ftb2dggyn",
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  "landing_url": "https://arxiv.org/abs/2610.12032",
  "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.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221112029",
  "pdf_url": "https://arxiv.org/pdf/2610.12032",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnz0ftb2dggyn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12032",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12032"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Further bounds in the polynomial Szemerédi theorem",
  "title_text": "Further bounds in the polynomial Szemerédi theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/fnz0ftb2dggyn",
  "venue": "arXiv",
  "versions": []
}