{
  "abstract": "For a third-order symmetric tensor, the Comon rank gap is the difference between its CP rank and its symmetric rank. We study direct sums of Lovitz's rational $27$-dimensional tensor, whose two ranks are $55$ and $56$. Two copies have ranks $110$ and $112$, and three copies have ranks $165$ and $168$, over both the real and the complex fields. Thus direct sums yield concise cubic tensors on spaces of dimensions $54$ and $81$ with Comon rank gaps two and three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01660",
  "author_total": 1,
  "authors": [
    {
      "name": "Jianze Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/984sfqanp8gw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01660",
  "fulltext_url": null,
  "id": "984sfqanp8gw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01660",
  "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.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7215718415",
  "pdf_url": "https://arxiv.org/pdf/2610.01660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/984sfqanp8gw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Comon Rank Gap of a Third-Order Symmetric Tensor Can Exceed One",
  "title_text": "The Comon Rank Gap of a Third-Order Symmetric Tensor Can Exceed One",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/984sfqanp8gw8",
  "venue": "arXiv",
  "versions": []
}