{
  "abstract": "A stationary scalar correlation energy admits an exact one-mode terminal representation even when the microscopic correlated return is strongly multimode. We test predictive realizations built from specified stationary information carriers in two complementary two-electron systems with the same Coulomb repulsion but different confinement: He-like ions and harmonium (Hooke's atom). For the Coulomb sequence, canonical RHF supplies the symmetry-faithful information carrier. The repeated same-mode return gives a He correlation error of $+0.1164$ m$E_{\\mathrm h}$ and no more than $0.0157$ m$E_{\\mathrm h}$ for Li$^+$--Ar$^{16+}$; H$^-$ is nevertheless bound and $93.3\\%$ of its conventional correlation energy is recovered even though the RHF carrier is qualitatively strained. The dimensionless confinement factor $R_{CC}=D_{CC}/Z$ tends to $1.092394$. For harmonic confinement, an independently constructed response-compressed one-mode return gives $R_H=D_H/\\sqrtω$; for $ω\\ge0.1$ it agrees with reference-inferred values within $0.21\\%$ and tends to the literature high-density limit $1.309283$. Cioslowski and Pernal locate the qualitative crossover to the radially localized strongly correlated harmonium regime at $ω_{\\rm crit}\\simeq0.04012$, below the quantitative domain used here. The H$^-$ endpoint and $ω_{\\rm crit}$ are therefore complementary carrier-validity boundaries: they limit the predictive realization, not exact terminal one-mode representability. A broad helium Bethe--Goldstone spectrum confirms that this terminal statement is not microscopic one-pole dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02090",
  "author_total": 1,
  "authors": [
    {
      "name": "Itai Panas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/en21kt70nzy27.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02090",
  "fulltext_url": null,
  "id": "en21kt70nzy27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02090",
  "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",
      "cond-mat.supr-con"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7216318858",
  "pdf_url": "https://arxiv.org/pdf/2610.02090",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/en21kt70nzy27.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.02090",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02090"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.supr-con",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Stationarity as a One-Mode Constraint on Quantum Correlation",
  "title_text": "Stationarity as a One-Mode Constraint on Quantum Correlation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/en21kt70nzy27",
  "venue": "arXiv",
  "versions": []
}