{
  "abstract": "We revisit the feasibility and convergence claims for the polarization hierarchy of Plávala, Ligthart and Gross [Linear Algebra Appl.\\ 723 (2025) 15--32]. Counterexamples show that the stated assumption is insufficient for the feasibility characterization and for convergence of the hierarchy with the polarization constraint. We establish corrected results under a stronger algebraic condition and supply a missing compactness argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24542",
  "author_total": 1,
  "authors": [
    {
      "name": "Julius A. Zeiss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bxgfqq29q756.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24542",
  "fulltext_url": null,
  "id": "8bxgfqq29q756",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24542",
  "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",
      "math.OC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223070162",
  "pdf_url": "https://arxiv.org/pdf/2610.24542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bxgfqq29q756.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Comment on \"The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank\"",
  "title_text": "Comment on \"The polarization hierarchy for polynomial optimization over convex bodies, with applications to nonnegative matrix rank\"",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/8bxgfqq29q756",
  "venue": "arXiv",
  "versions": []
}