{
  "abstract": "We develop a finite-corner framework for convex cones of normal maps between \\(\\mathcal B(\\mathcal H)\\) and \\(\\mathcal B(\\mathcal K)\\). The basic structural assumption is stability under finite cut--pad operations. We prove that every point-ultraweakly closed cut--pad stable cone is completely determined by its finite-dimensional corner cones, and conversely that every coherent family of closed finite-dimensional corner cones admits a unique global realization of this type. For a cut--pad stable cone that is not necessarily point-ultraweakly closed, reconstruction from the norm closures of its corner cones yields exactly its point-ultraweak closure. Combining this reconstruction principle with finite-dimensional separation and the Choi representation, we show that non-membership in a global cone is always detected on a single finite-dimensional corner by a finite-dimensional witness. We illustrate the framework for completely positive and decomposable maps; in the decomposable case, the Hermitian parts of the finite-corner witnesses are PPT.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04889",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohsen Kian"
    },
    {
      "name": "Fuad Kittaneh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0aarpd0dk08cy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04889",
  "fulltext_url": null,
  "id": "0aarpd0dk08cy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04889",
  "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": "W7211892156",
  "pdf_url": "https://arxiv.org/pdf/2609.04889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0aarpd0dk08cy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:14Z",
      "native_id": "2609.04889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Finite-Corner Reconstruction and Separation for Cones of Normal Maps",
  "title_text": "Finite-Corner Reconstruction and Separation for Cones of Normal Maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/0aarpd0dk08cy",
  "venue": "arXiv",
  "versions": []
}