{
  "abstract": "We construct an infinite family of rectangular \\(T\\)-meshes whose conformality-vector-space dimension is constant over all structurally similar geometric realizations, although the meshes are not diagonalizable. For every integer \\(d\\ge 2\\), the construction has \\(2(d+2)\\) \\(\\Tl\\)-edges and intersection graph \\(K_{d+2,d+2}\\). Every \\(\\Tl\\)-edge contains at least \\(d+2\\) vertices, so no edge is vanishable under the usual vertex-count criterion for bidegree \\((d,d)\\) and smoothness \\((d-1,d-1)\\). We prove that the conformality-vector space is one-dimensional throughout the structural similarity class. Its generator is the outer product of two vectors of barycentric interpolation weights, extended by four zero coordinates. Non-diagonalizability follows by examining the last edge in any proposed diagonalizing ordering. Thus, for the geometric structural similarity class specified here, diagonalizability is not a necessary condition for dimensional absolute stability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05923",
  "author_total": 1,
  "authors": [
    {
      "name": "Mao Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ce912dnep1a69.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05923",
  "fulltext_url": null,
  "id": "ce912dnep1a69",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05923",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05923",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ce912dnep1a69.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05923",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05923"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Dimensionally absolutely stable but non-diagonalizable $T$-meshes",
  "title_text": "Dimensionally absolutely stable but non-diagonalizable T-meshes",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/ce912dnep1a69",
  "venue": "arXiv",
  "versions": []
}