{
  "abstract": "Recent advances in the classification of certain classes of Yang-Baxter operators through a holistic categorical approach has some of us wondering about ways to identify solutions. In particular the classification of charge conserving solutions in all dimensions inspires the question: \\emph{what fraction of solutions are \\textbf{close to} charge conserving solutions, under any \\textbf{reasonable} notion of equivalence?} Of course \\emph{reasonable} and \\emph{close to} are open to interpretation. Here we suggest some precise notions of both, and prove that in dimension $2$, 10 out of 11 local families of solutions are close to charge conserving, and the one that misses is a singleton.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38290",
  "author_total": 2,
  "authors": [
    {
      "name": "Paul P. Martin"
    },
    {
      "name": "Eric C. Rowell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a18s8twmk7kja.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38290",
  "fulltext_url": null,
  "id": "a18s8twmk7kja",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38290",
  "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.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7215029312",
  "pdf_url": "https://arxiv.org/pdf/2609.38290",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a18s8twmk7kja.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38290",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38290"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Notions of equivalence among constant Yang--Baxter Operators: To $\\infty$-Equivalence and Beyond",
  "title_text": "Notions of equivalence among constant Yang--Baxter Operators: To ∞-Equivalence and Beyond",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/a18s8twmk7kja",
  "venue": "arXiv",
  "versions": []
}