{
  "abstract": "We establish sharp mixed spectral Barron regularity for eigenfunctions of molecular Coulomb Hamiltonians. The mixed norm is a Fourier $L^1$ norm with one isotropic weight and coordinate-product weights, and therefore detects regularity invisible to the isotropic Barron scale. For a nonempty set $I$ of electron indices on which the wave function is antisymmetric, we derive an explicit admissible region for the isotropic order $s$ and the coordinate orders $α,β$. This region is optimal as a uniform statement over the class of clamped-nuclei Coulomb Hamiltonians. For fixed-spin components with two occupied spin blocks, it reduces to $s+α+β<1$; in the fully spin-polarized class it reduces to $s+α<1$. In particular, if $\\mathcal I_σ$ denotes the family of occupied same-spin blocks determined by $σ$, then every fixed-spin spatial component $ψ_σ$ satisfies, for every $0\\leqα<1$, \\[ \\left(\\sum_{I\\in\\mathcal I_σ}\\prod_{i\\in I}\\langleξ_i\\rangle^α\\right)\\widehat{ψ_σ}\\in L^1(\\mathbb{R}^{3N}). \\] For a fully spin-polarized state, $\\mathcal I_σ=\\{\\{1,\\ldots,N\\}\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00872",
  "author_total": 2,
  "authors": [
    {
      "name": "Pingbing Ming"
    },
    {
      "name": "Hao Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxykr689cax57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00872",
  "fulltext_url": null,
  "id": "bxykr689cax57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00872",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7206189257",
  "pdf_url": "https://arxiv.org/pdf/2609.00872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxykr689cax57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions",
  "title_text": "Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/bxykr689cax57",
  "venue": "arXiv",
  "versions": []
}