{
  "abstract": "We present an instantiation of the constructive solution to the fermionic quantum marginal problem by building the complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy. Our construction combines positive-semidefinite Gram matrices with explicit linear nullspace constraints that exactly cancel all higher-body contributions following a similar idea to the existing solution but made explicit in open source software. We demonstrate the weighted sum-of-squares construction numerically by solving the associated semidefinite program and recovering the exact ground-state energy of a Richardson Hamiltonian in the three-fermion sector. We further prove that higher-degree particle-number multipliers are unnecessary when the full sum-of-squares generating algebra is used.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20737",
  "author_total": 2,
  "authors": [
    {
      "name": "Nicholas C. Rubin"
    },
    {
      "name": "A. Eugene DePrince III"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51z74pm2cy9cs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20737",
  "fulltext_url": null,
  "id": "51z74pm2cy9cs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20737",
  "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",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7222564988",
  "pdf_url": "https://arxiv.org/pdf/2610.20737",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/51z74pm2cy9cs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.20737",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20737"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A constructive solution to the $n$-representability problem",
  "title_text": "A constructive solution to the n-representability problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/51z74pm2cy9cs",
  "venue": "arXiv",
  "versions": []
}