{
  "abstract": "We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups and thinness for a third case. These are the three open cases called C-32, C-47, and C-55 in the paper [BDN25] by Bajpai--Dona--Nitsche. This hence settles thinness of primitive integral symplectic hypergeometric monodromy groups of degree-six, according to the tabulation by Bajpai--Dona--Singh--Singh [BDSS21]. The arithmeticity certificates were found with AlphaEvolve and the thinness certificate is a ping pong table found by a harness that was configured to run ChatGPT 5.5. These certificates are then independently verified with exact matrix arithmetic over Q using a computer. We also include illustrations of limit sets of several degree-six symplectic hypergeometric monodromy groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25935",
  "author_total": 4,
  "authors": [
    {
      "name": "J. Maxwell Riestenberg"
    },
    {
      "name": "Diaaeldin Taha"
    },
    {
      "name": "Steve Trettel"
    },
    {
      "name": "Anna Wienhard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1c63q9m6rr8pn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25935",
  "fulltext_url": null,
  "id": "1c63q9m6rr8pn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25935",
  "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.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7162430942",
  "pdf_url": "https://arxiv.org/pdf/2605.25935",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1c63q9m6rr8pn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2605.25935",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25935"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups",
  "title_text": "Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/1c63q9m6rr8pn",
  "venue": "arXiv",
  "versions": []
}