{
  "abstract": "For Hermitian matrices $α,β$ let $\\A_{n,m}(e^α,e^β)$ be the average of the traces of all words with $n$ letters $e^α$ and $m$ letters $e^β$. The refined Bessis--Moussa--Villani conjecture contains the lower bound $\\A_{n,m}(e^α,e^β)\\ge\\Tr e^{nα+mβ}$ (Tr denotes the trace), which for $n=m=1$ is the Golden--Thompson inequality. We prove this lower bound for all $n+m\\le7$ when the matrices have size at most three, and for $\\min(n,m)\\le2$ in every dimension. In all these cases we prove the stronger inequality $\\A_{n,m}(A,B)\\ge\\Tr(A^{n/m}B)^m$ for positive semidefinite $A,B$, or its mirror image with the roles of $A$ and $B$ exchanged; the lower bound of the refined conjecture follows from the Araki--Lieb--Thirring inequality. The cases with three letters $B$ in dimension three, $(n,m)=(3,3)$ and $(4,3)$, are reduced by an exact identity and the inequality of arithmetic and geometric means to a polynomial inequality in two variables, which is certified in exact rational arithmetic by Bernstein expansion on three boxes. The certificate is a short program in the ancillary files.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00129",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Hägele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74grybbztkme7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00129",
  "fulltext_url": null,
  "id": "74grybbztkme7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00129",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74grybbztkme7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On the lower bound of the refined Bessis--Moussa--Villani conjecture: proof of the cases S_{6,3} and S_{7,3} for 3x3 matrices",
  "title_text": "On the lower bound of the refined Bessis--Moussa--Villani conjecture: proof of the cases S_{6,3} and S_{7,3} for 3x3 matrices",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/74grybbztkme7",
  "venue": "arXiv",
  "versions": []
}