{
  "abstract": "We introduce a class of extensions of unital operator systems satisfying a certain Toeplitz type property and show that these extensions induce corresponding extensions of the $C^*$-algebras they generate. We prove that an extension in this class is hyperrigid in the $C^*$-algebra it generates if and only if both operator systems from which it is constructed are hyperrigid in the $C^*$-algebras they generate. We then introduce the quantum double suspension of operator systems as a special case of this construction and show that its iterates yield the Hong-Szymański quantum double suspensions at the $C^*$-algebra level, including the Vaksman-Soibelman quantum spheres. In particular, we construct hyperrigid operator systems that generate the $C^*$-algebras of these quantum spheres. As a further application, we show that every counterexample to Arveson's hyperrigidity conjecture gives rise to a sequence of counterexamples. We identify the Šilov ideal and the $C^*$-envelope of these extensions and derive a $K$-theoretic condition under which each such sequence contains infinitely many pairwise non-isomorphic counterexamples. In particular, Scherer's counterexample gives rise to infinitely many pairwise non-isomorphic counterexamples. Finally, we compute the propagation number, an invariant of operator systems introduced by Connes and van Suijlekom, for this class of extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18129",
  "author_total": 3,
  "authors": [
    {
      "name": "Vibhor Bhatt"
    },
    {
      "name": "Satyajit Guin"
    },
    {
      "name": "Palash Sharma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e00npzzrzgvmv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18129",
  "fulltext_url": null,
  "id": "e00npzzrzgvmv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18129",
  "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": "W7221776527",
  "pdf_url": "https://arxiv.org/pdf/2610.18129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e00npzzrzgvmv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.18129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extensions of Operator Systems, Hyperrigidity and Quantum Double Suspension",
  "title_text": "Extensions of Operator Systems, Hyperrigidity and Quantum Double Suspension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/e00npzzrzgvmv",
  "venue": "arXiv",
  "versions": []
}