{
  "abstract": "Let $P_d$ be the elliptope of $d \\times d$ correlation matrices, and, for a standardised law $F$, let $S_d^F$ be the set of correlation matrices of random vectors with all margins $F$. We give two short proofs. First, an eleven-term representation of $|x|^4$ as a sum of fourth powers of linear forms on $\\mathbb{R}^4$ yields $S_{11} \\neq P_{11}$ for uniform margins. Second, the six diagonals of the regular icosahedron yield $S_6^F \\neq P_6$ for arcsine margins. Together with a result of Devroye and Letac, this gives $S_d^F = P_d$ if and only if $d \\le 5$, settling a conjecture of theirs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14610",
  "author_total": 1,
  "authors": [
    {
      "name": "Cedric Phillips"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zccp62e2r3mp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14610",
  "fulltext_url": null,
  "id": "8zccp62e2r3mp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14610",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7213249054",
  "pdf_url": "https://arxiv.org/pdf/2609.14610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zccp62e2r3mp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Two short proofs of incompatibility for correlation matrices",
  "title_text": "Two short proofs of incompatibility for correlation matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/8zccp62e2r3mp",
  "venue": "arXiv",
  "versions": []
}