{
  "abstract": "We prove the Gromov-Hausdorff convergence of the state spaces, equipped with Connes' distance function, of the operator systems associated with spectral truncations for noncommutative $n$-tori, $n\\ge 2$. The action of the $n$-torus on the noncommutative $n$-torus, together with an appropriate use of Bochner integrals, enables us to construct an $C^1$-approximate order isomorphism that establishes the convergence. The earlier convergence result for the classical case of tori [20] follows as a special case of our result. We conclude by studying the $C^*$-envelopes and propagation numbers of the truncated operator systems and show that the structural properties of the truncated operator systems for tori persist under deformation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01132",
  "author_total": 3,
  "authors": [
    {
      "name": "Vibhor Bhatt"
    },
    {
      "name": "Satyajit Guin"
    },
    {
      "name": "Palash Sharma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8epxysvw29vwc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01132",
  "fulltext_url": null,
  "id": "8epxysvw29vwc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01132",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7216218969",
  "pdf_url": "https://arxiv.org/pdf/2610.01132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8epxysvw29vwc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Gromov-Hausdorff Convergence of Spectral Truncations for Noncommutative Tori",
  "title_text": "Gromov-Hausdorff Convergence of Spectral Truncations for Noncommutative Tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8epxysvw29vwc",
  "venue": "arXiv",
  "versions": []
}