{
  "abstract": "We investigate the maximal total quantum dimension at a bounded categorical rank cutoff $R$ in three-dimensional Dijkgraaf--Witten theories. This optimization problem physically governs the maximal state-optimized torus topological entanglement entropy at a fixed torus ground-state degeneracy, while providing a quantitative constraint on the search space required to classify these topological order phases. We analyze how topological twists (3-cocycles) and gauge-group structures independently govern this trade-off. For elementary-Abelian gauge groups at a fixed prime $p$, we prove that introducing cocycle twists elevates the maximum total quantum dimension from square-root growth $Θ_p(R^{1/2})$ to linear growth $Θ_p(R)$ in the rank cutoff, driven by the geometric protection of cyclic holonomies. For untwisted theories, we establish sharp envelopes for symmetric and alternating gauge groups, and derive group-theoretic bounds across almost-simple, solvable, and radical-free families. In particular, almost-simple groups and their direct products obey a quadratic-logarithmic upper envelope: $\\log\\mathcal{D} = O((\\log R)^2)$. Finally, we compare these scales against WZW models and discuss the status of the general quadratic-logarithmic envelope conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26914",
  "author_total": 1,
  "authors": [
    {
      "name": "Ce Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74xhhwq60gxnj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26914",
  "fulltext_url": null,
  "id": "74xhhwq60gxnj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26914",
  "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",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214174655",
  "pdf_url": "https://arxiv.org/pdf/2609.26914",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74xhhwq60gxnj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.26914",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26914"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Maximal Total Quantum Dimension at Bounded Rank in Dijkgraaf-Witten Theories",
  "title_text": "Maximal Total Quantum Dimension at Bounded Rank in Dijkgraaf-Witten Theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/74xhhwq60gxnj",
  "venue": "arXiv",
  "versions": []
}