{
  "abstract": "We introduce a dynamical version $\\operatorname{rc} (A, α)$ of the radius of comparison $\\operatorname{rc} (A)$ of a unital C*-algebra, based on the dynamical Cuntz semigroup. We also give an intrinsic ordered semigroup definition, which agrees with $\\operatorname{rc} (A, α)$ when $A$ is residually stably finite, and is lower semicontinuous for equivariant direct limits with injective unital maps. We construct actions $α$ of $G = \\mathbb{Z} / 2 \\mathbb{Z}$ on simple unital AH~algebras for which $\\operatorname{rc} (A, α)$ lies strictly between $\\operatorname{rc} (A)$ and $\\operatorname{rc} (A) / \\operatorname{card} (G)$, and actions $α$ of a finite group $G$ on unital C*-algebras for which $\\operatorname{rc} (A, α)$ lies strictly between $\\operatorname{rc} (A)$ and $\\operatorname{rc} (C^* (G, A, α))$. For a minimal action of a countable discrete group $G$ on a zero dimensional compact metrizable space $X$, we prove that $\\operatorname{rc} (C (X), α) = 0$ if and only if the action has dynamical comparison as defined by Kerr. For finite group actions on simple unital stably finite C*-algebras, assuming the weak tracial Rokhlin property, we get $\\operatorname{rc} (A, α) \\leq \\operatorname{rc} (A) / \\operatorname{card} (G)$, and assuming weak tracial strict approximate innerness, we get $\\operatorname{rc} (A, α) = \\operatorname{rc} (A)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30211",
  "author_total": 2,
  "authors": [
    {
      "name": "M. Ali Asadi-Vasfi"
    },
    {
      "name": "N. Christopher Phillips"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akrpwb7erhee1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30211",
  "fulltext_url": null,
  "id": "akrpwb7erhee1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30211",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214367084",
  "pdf_url": "https://arxiv.org/pdf/2609.30211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akrpwb7erhee1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30211"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Dynamical Radius of Comparison for C*-Dynamical Systems",
  "title_text": "The Dynamical Radius of Comparison for C*-Dynamical Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/akrpwb7erhee1",
  "venue": "arXiv",
  "versions": []
}