{
  "abstract": "Every scalar ordinary differential equation of order at least three with rational right-hand side that is locally linearizable by a point transformation admits a linear form with rational coefficients over the same coefficient field. We prove this by restricting the derived symmetry algebra to a coordinate line and recovering a scalar differential operator from rational symmetry-jet data. The construction uses differential elimination and linear algebra; it does not require the symmetry generators or a linearizing transformation to be solved for. A single integer parameter suffices to choose the line.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01338",
  "author_total": 1,
  "authors": [
    {
      "name": "Dmitry Lyakhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xsz7hpdengda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01338",
  "fulltext_url": null,
  "id": "2xsz7hpdengda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01338",
  "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",
      "cs.SC"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7215971368",
  "pdf_url": "https://arxiv.org/pdf/2610.01338",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xsz7hpdengda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01338",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01338"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Rational linear forms of linearizable ordinary differential equations",
  "title_text": "Rational linear forms of linearizable ordinary differential equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/2xsz7hpdengda",
  "venue": "arXiv",
  "versions": []
}