{
  "abstract": "For fermions in a slowly varying aperiodic potential with random interactions $V_{ij}/|i-j|^α$, the potential fixes the resonance supply $N_0 \\propto L^{2-n}/h$. On crossing $α-2n$, wherever Hartree fragmentation is operative, the resonant-object ensemble reconstructs: turning-point runs fragment into clusters whose intrinsic matching law resolves no logarithmic singularity, while isolated wing bonds survive at finite density and restore a reduced logarithm. The scaling $x^{4-2n-α}_{pair} ln{x_{pair}} \\propto h^2/(V t0)$ is unchanged. Random coefficient fluctuations sustain the $R^{-α}$ coupling; uniform ones cancel to $R^{-α-2}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30746",
  "author_total": 1,
  "authors": [
    {
      "name": "Yogeshwar Prasad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9e3jkh46jcn5m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30746",
  "fulltext_url": null,
  "id": "9e3jkh46jcn5m",
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  "landing_url": "https://arxiv.org/abs/2608.30746",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
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      "arxiv",
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      "2610|Spectral Theory in Mathematical Physics"
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  ],
  "openalex": "W7204930546",
  "pdf_url": "https://arxiv.org/pdf/2608.30746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9e3jkh46jcn5m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30746"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains",
  "title_text": "Hartree Fragmentation and Long-Range Pair Networks in Aperiodic Chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/9e3jkh46jcn5m",
  "venue": "arXiv",
  "versions": []
}