{
  "abstract": "We prove uniqueness of q-rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modular symmetry. We prove that there are exactly two deformations which deliver the usual q-integers: the original q-rationals defined by Morier-Genoud and Ovsienko, and another new one. Although the new family can be obtained by conjugacy from the old one, new positivity properties appear. In addition, this new family provides a direct computation of the Jones polynomial of rational knots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22308",
  "author_total": 3,
  "authors": [
    {
      "name": "Perrine Jouteur"
    },
    {
      "name": "Olga Paris-Romaskevich"
    },
    {
      "name": "Alexander Thomas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72dsbvzy6cmrf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22308",
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  "id": "72dsbvzy6cmrf",
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  "landing_url": "https://hal.science/hal-05717044v2",
  "language": "en",
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  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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      "arxiv",
      "math.GT"
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      "math.QA"
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      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7171376827",
  "pdf_url": "https://hal.science/hal-05717044/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72dsbvzy6cmrf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05717044",
      "source": "hal",
      "url": "https://hal.science/hal-05717044v2"
    },
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2607.22308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Nuancing the uniqueness of q-rationals",
  "title_text": "Nuancing the uniqueness of q-rationals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/72dsbvzy6cmrf",
  "venue": "HAL",
  "versions": []
}