{
  "abstract": "We prove the corrected Bessis--Moussa--Villani pinching conjecture for all symmetrized word averages. For Hermitian matrices $A,B$ and $D=E_A(B)$, we construct a positive compactly supported measure $ζ_{A,B}$ on $\\mathbb R^2$ such that \\[ \\Tr f(xA+yB)-\\Tr f(xA+yD) =y^2\\int_{\\mathbb R^2}f''(xa+yb)\\,dζ_{A,B}(a,b). \\] Its total mass is $\\frac12\\|B-D\\|_2^2$. This representation proves the corrected conjecture, including its equality cases, and gives a positive bivariate moment representation for the coefficient differences. We also derive complete monotonicity of normalized exponential pinching defects and a comparison with Lie--Trotter approximations. A one-dimensional second-order loss measure is obtained for trace-preserving conditional expectations on finite tracial von Neumann algebras. Finally, we relate $ζ_{A,B}$ to Heinävaara's tracial joint spectral measure by an explicit positive radial transform.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31851",
  "author_total": 3,
  "authors": [
    {
      "name": "Trung Hoa Dinh"
    },
    {
      "name": "Cong Trinh Le"
    },
    {
      "name": "Trung Dung Vuong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y0xjpv40j52n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31851",
  "fulltext_url": null,
  "id": "5y0xjpv40j52n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31851",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7223681929",
  "pdf_url": "https://arxiv.org/pdf/2610.31851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y0xjpv40j52n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Positive Planar Measures for Spectral Pinching and the Corrected BMV Conjecture",
  "title_text": "Positive Planar Measures for Spectral Pinching and the Corrected BMV Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/5y0xjpv40j52n",
  "venue": "arXiv",
  "versions": []
}