{
  "abstract": "Variational second-order reduced-density-matrix calculations can dissociate molecules into fractionally charged fragments; Part I largely removed this failure with integer electron-count conditions on fixed partitions. Building on the realizability theory of point processes, we place these conditions in a convergent hierarchy of rigorous relaxations, defined by finite occupation linear programs (LPs) on spatial partitions, for real-space pair densities at fixed one-particle density. Every level contains all representable pair densities, the levels tighten under nested refinement, and their intersection characterizes pair densities admitting a symmetric $N$-particle probability-measure extension. In a fixed orbital basis the levels give monotonically increasing lower bounds to the full configuration-interaction energy, which they need not reach, even for the Coulomb repulsion. The spin-summed real-space cuts of Part I are its two-cell members. The LP optimum is also a measure: at fixed one-particle density it equals the $L^1$ distance of the coarse-grained candidate from representability and increases under refinement to that of the candidate, with a vanishing coarse-graining error; its primal law constructs a representable approximation, and its dual a violated valid inequality, used as a cut in molecular calculations. The count conditions are not implied by the usual positivity conditions: moment data that satisfy all three-particle positivity conditions, including $T_1$ and $T_2$, give through Gaussian orbitals a smooth pair density that violates an integer count. For atoms at fractional electron number, ensemble relaxations with the integer-count condition lie closer to the exact piecewise-linear energy than the zero-variance fixed-$N$ form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.11707",
  "author_total": 1,
  "authors": [
    {
      "name": "Maho Nakata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16ay56jm67qjm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.11707",
  "fulltext_url": null,
  "id": "16ay56jm67qjm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.11707",
  "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",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.11707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16ay56jm67qjm.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:23Z",
      "native_id": "2611.11707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.11707"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Integer electron-count cuts in variational second-order reduced-density-matrix theory. II. A convergent hierarchy of rigorous relaxations for real-space pair-density representability",
  "title_text": "Integer electron-count cuts in variational second-order reduced-density-matrix theory. II. A convergent hierarchy of rigorous relaxations for real-space pair-density representability",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:34Z",
  "url": "https://research.draconitic.com/paper/16ay56jm67qjm",
  "venue": "arXiv",
  "versions": []
}