{
  "abstract": "We prove that the centroid Banach--Mazur diameter of planar convex bodies is strictly less than $4$, (slightly) improving the prior upper bound $69/17\\approx 4.05882$ due to Lassak. The proof combines a sharp covariance-ellipse sandwich, whose equality cases in any single direction occur only for triangles, with a compactness argument: an extremal pair at distance $4$ would consist of two triangles, which are linearly equivalent and hence must in fact be at distance $1$. The resulting gap below $4$ is uniform but nonquantitative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13952",
  "author_total": 1,
  "authors": [
    {
      "name": "Scott Duke Kominers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d65k0rhqfpgxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13952",
  "fulltext_url": null,
  "id": "d65k0rhqfpgxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13952",
  "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.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.13952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d65k0rhqfpgxn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Breaking the Fourth Wall: The Planar Centroid Banach--Mazur Diameter Is Strictly Less than $4$",
  "title_text": "Breaking the Fourth Wall: The Planar Centroid Banach--Mazur Diameter Is Strictly Less than $4$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/d65k0rhqfpgxn",
  "venue": "arXiv",
  "versions": []
}