{
  "abstract": "We study operator systems arising from Peter-Weyl and Dirac spectral truncations of $\\mathrm{SU}(2)$ in the sense of Connes-Van Suijlekom. We determine operator system invariants for these systems, including the $C^*$-envelope and uniform bounds on the propagation number. For Peter-Weyl truncations, we find $\\mathrm{prop} \\leq 2$ for all connected compact Lie groups, generalizing known results for the torus. We also carry out an analysis of the spectral localizer by Loring and Schulz-Baldes on $\\mathrm{SU}(2)$. In this analysis, we find numerical evidence that an index map for operator systems previously proposed by Van Suijlekom only captures the right information in a suitable interval of the parameter $κ$, instead of the limit $κ\\downarrow 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19791",
  "author_total": 1,
  "authors": [
    {
      "name": "Matt Verhoeven"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50kmjm7vsm8j6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19791",
  "fulltext_url": null,
  "id": "50kmjm7vsm8j6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19791",
  "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.KT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222046632",
  "pdf_url": "https://arxiv.org/pdf/2610.19791",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50kmjm7vsm8j6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19791",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19791"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral truncations of SU(2) and the spectral localizer",
  "title_text": "Spectral truncations of SU(2) and the spectral localizer",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/50kmjm7vsm8j6",
  "venue": "arXiv",
  "versions": []
}