{
  "abstract": "The exact multi-resolvent hierarchy of dense many-body spectra encodes higher-order spectral-weight correlations, but closing it predictively for interacting Hamiltonians remains a challenge. We introduce the multi-resolvent self-consistency (MRSC) equations, which separate an exact algebraic hierarchy from an approximate finite-parameter closure. The exact Feshbach geometric identity organizes r-resolvent cumulants into a ladder over irreducible vertices Gamma^(r), and the projected hierarchy expresses those vertices as functionals of the cumulants. The closure works in finite parameters: a connectivity basis organizes a general Hamiltonian's seed into class amplitudes, and a causal r-fold Stieltjes representation with a moment-field identity reduce moment matching to a finite-dimensional problem closed at a predictive fixed point. On the free-fermion benchmark the tested exact identities are reproduced and the Faddeeva closure is recovered at r=1. In a blind test on the interacting Ising chain, with the exact two-resolvent data withheld, the Hamiltonian-derived closure predicts the tested probes to 0.35%-0.97%. At the observable level the exact two-resolvent sector supplies a sign-correct, energy-resolved correction to the single-resolvent baseline for the off-diagonal eigenstate-thermalization-hypothesis (ETH) variance, of order one relative to it. Closure errors organize hierarchically: a level-by-level deficit decomposition, anchor measurements of the isolatable terms, and an explicit propagation bound. The same moments further yield a diagnostic chain for the window conditions of local rotational invariance -- an exact drift-kernel identity, a proven single-state identifiability boundary, and a transferability census over couplings and realizations -- a finite-order framework, not a proof of universal emergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28031",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiqiang Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2w7400bbxmcng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28031",
  "fulltext_url": null,
  "id": "2w7400bbxmcng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28031",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7223141718",
  "pdf_url": "https://arxiv.org/pdf/2610.28031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2w7400bbxmcng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28031"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Microscopically informed self-consistent multi-resolvent closure for dense many-body spectra",
  "title_text": "Microscopically informed self-consistent multi-resolvent closure for dense many-body spectra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/2w7400bbxmcng",
  "venue": "arXiv",
  "versions": []
}