{
  "abstract": "We prove a version of topological recursion for the correlation differentials of colored HOMFLY-PT polynomials of torus knots on the corresponding augmentation curves, following the proposal of Gu, Jockers, Klemm, and Soroush. To this end, we explicitly construct the spectral curve from the so-called auxiliary curve of Brini, Eynard, and Mariño and prove that it coincides with the augmentation curve for every torus knot with coprime $(r,s)$. Finally, our version of topological recursion proves the higher-genus closed-string prediction of the Aganagic--Vafa conjecture for all torus knot augmentation curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21585",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Hock"
    },
    {
      "name": "Sergey Shadrin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56xk3v95bfej2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21585",
  "fulltext_url": null,
  "id": "56xk3v95bfej2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21585",
  "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",
      "hep-th"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.AG"
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      "arxiv",
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      "arxiv",
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7222428752",
  "pdf_url": "https://arxiv.org/pdf/2610.21585",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56xk3v95bfej2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21585",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21585"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Augmentation curve for torus knots",
  "title_text": "Augmentation curve for torus knots",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/56xk3v95bfej2",
  "venue": "arXiv",
  "versions": []
}