{
  "abstract": "Convexity of the density-fixed adiabatic-connection integrand is widely observed but is not fixed by the variational structure of density-functional theory. We show that it is not universal for ordinary three-dimensional electrons with the bare Coulomb interaction. Equal-step third differences of the Levy functional give a derivative-free classification into convex, affine, concave, and mixed classes, while an exact response identity determines the local sign at regular fixed-density points. Opposite exactly solvable seeds—a closed-shell Hubbard ring and two-electron spherium—are transferred to smooth confining potentials in ordinary space. The resulting full-interval positive, negative, and mixed densities have N = 2, 6, and 8, respectively. For two distinct densities with the same particle number N = 6, one fixed four-point certificate is obtained with either sign. These deliberately engineered existence constructions do not imply that violations are common in molecular densities. Thus convexity is a property of density-preserving many-body response, not a universal exact condition.",
  "abstract_shown": true,
  "affiliations": [
    "College of Materials Science and Engineering",
    "Hohai University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Jian Wu",
      "orcid": "0009-0004-0700-0342"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvegcj2rrb472.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15008317/v1",
  "fulltext_url": null,
  "id": "fvegcj2rrb472",
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  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008317/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7208788183",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15008317/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/fvegcj2rrb472.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "10.26434/chemrxiv.15008317",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008317/v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Advanced Chemical Physics Studies",
      "subfield": "amo"
    }
  ],
  "title": "Breakdown and Classification of Adiabatic-Connection Convexity in Coulomb Systems",
  "title_text": "Breakdown and Classification of Adiabatic-Connection Convexity in Coulomb Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:17Z",
  "url": "https://research.draconitic.com/paper/fvegcj2rrb472",
  "venue": "ChemRxiv",
  "versions": []
}