{
  "abstract": "Recently, Hilbert's Tenth Problem over the field $\\mathbb Q$ of rational numbers was solved negatively by OpenAI based on a five-contact height estimate and a pole-parity construction. In this paper, we prove further that there is no algorithm to decide for any polynomial $P(x_1,\\ldots,x_{86})$ with integer coefficients whether the equation $P(x_1,\\ldots,x_{86})=0$ has solutions with $x_1,\\ldots,x_{86}\\in\\mathbb Q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20691",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Wei Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fh0t1ts6crq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20691",
  "fulltext_url": null,
  "id": "3fh0t1ts6crq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20691",
  "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.LO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222500688",
  "pdf_url": "https://arxiv.org/pdf/2610.20691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fh0t1ts6crq6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.20691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "86 unknowns for Hilbert's tenth problem over the rationals",
  "title_text": "86 unknowns for Hilbert's tenth problem over the rationals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/3fh0t1ts6crq6",
  "venue": "arXiv",
  "versions": []
}