{
  "abstract": "We develop a quantitative approach to quasi-local operators with bounded block-rank. Our main results are a quantitative decomposition for quasi-local operators into block-rank-one pieces and a quantitative finite-propagation approximation in the block-rank-one case, leading to a quantitative proof of the bounded block-rank rigidity result for Roe and quasi-local algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23004",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiawen Zhang"
    },
    {
      "name": "Jingming Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqkt4adq0p90s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23004",
  "fulltext_url": null,
  "id": "dqkt4adq0p90s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23004",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214043123",
  "pdf_url": "https://arxiv.org/pdf/2609.23004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqkt4adq0p90s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantitative decomposition and approximation for quasi-local operators",
  "title_text": "Quantitative decomposition and approximation for quasi-local operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dqkt4adq0p90s",
  "venue": "arXiv",
  "versions": []
}