{
  "abstract": "We prove that there is no uniform description of $\\mathrm{LG}^{(n)}$ in terms of colored Jones polynomials for all knots, even when allowing infinitely many colors and arbitrary operations. We prove the $n=1$ case, using an existing cabling formula and the separation of the Conway and Kinoshita--Terasaka knots by $\\mathrm{LG}^{(2)}$. We develop an odd cabling formula and use a Vandermonde argument to show that for each $n\\geq 2$ some satellite of each of these knots is distinguished by $\\mathrm{LG}^{(n)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12352",
  "author_total": 2,
  "authors": [
    {
      "name": "Matthew Harper"
    },
    {
      "name": "Ben-Michael Kohli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8achxhm71kvpx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12352",
  "fulltext_url": null,
  "id": "8achxhm71kvpx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12352",
  "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",
      "math.GT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221129554",
  "pdf_url": "https://arxiv.org/pdf/2610.12352",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8achxhm71kvpx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12352",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12352"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Colored Jones Function does not determine any colored Links--Gould polynomial",
  "title_text": "The Colored Jones Function does not determine any colored Links--Gould polynomial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/8achxhm71kvpx",
  "venue": "arXiv",
  "versions": []
}