{
  "abstract": "We study integral Newton rings attached to symmetric quantum colors. We show that their boundary values at a deleted node are exactly the elements of Habiro's cyclotomic completion, and we describe their quantum neighborhoods at $q=1$ uniformly in the rank. The symmetric-color $\\mathfrak{sl}_n$ invariants of a knot are the values of an element of such a ring. In its expansion at $q=1$, the coefficient of $(q-1)^m$ has denominator dividing the $(n-1+2m)$th power of the Alexander polynomial, with integral numerator, and this exponent is sharp. For $5_2$ and $6_1$ at $q=i$, the period matrices of the rank-two coefficient recurrences have spectral modules of exact order three in the Picard group of an affine elliptic curve.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21102",
  "author_total": 1,
  "authors": [
    {
      "name": "Honghuai Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frf1cmqdgk044.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21102",
  "fulltext_url": null,
  "id": "frf1cmqdgk044",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21102",
  "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.GT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7222535994",
  "pdf_url": "https://arxiv.org/pdf/2610.21102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frf1cmqdgk044.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quantum Color Newton Rings",
  "title_text": "Quantum Color Newton Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/frf1cmqdgk044",
  "venue": "arXiv",
  "versions": []
}