{
  "abstract": "Eigenstate thermalization fixes the smooth energy-resolved envelope of few-body observables but not the microscopic overlap statistics that realize it. In the multi-resolvent hierarchy, this missing information appears in a two-resolvent fluctuation sector. We solve that sector exactly in a tractable benchmark, random free fermions, obtaining a non-Porter-Thomas intensity hierarchy, a structured channel-distance covariance, and an exact overlap kernel that closes the two-resolvent covariance. We then reconstruct the same sector without using its exact solution: a projected self-consistency scheme fixes the irreducible vertex through independently computable projections, while unconstrained residuals identify the sectors missed by a minimal ansatz and are completed exactly by a finite-size Weingarten evaluation, without fitting. For interacting deformations, we prove a model-independent moment identity showing that the deep-plane coefficients are fixed by Hamiltonian-moment covariances. This yields an exact rigidity law: pair-hopping interactions freeze the sector, dense perturbations add only an isotropic layer, and density-density interactions produce an explicit polynomial deformation in channel geometry. By contrast, the bulk sector requires the interacting eigenstate-overlap kernel and exhibits a logarithmically divergent perturbative response. The fluctuation sector therefore splits into a rigid moment-determined part and an intrinsically nonperturbative eigenstate-resolved part.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17037",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhiqiang Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6cbpk3zx4kw95.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17037",
  "fulltext_url": null,
  "id": "6cbpk3zx4kw95",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17037",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213438343",
  "pdf_url": "https://arxiv.org/pdf/2609.17037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6cbpk3zx4kw95.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.17037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17037"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Beyond the ETH envelope: exact two-resolvent fluctuation structure, projected microscopic closure, and rigid versus nonperturbative sectors",
  "title_text": "Beyond the ETH envelope: exact two-resolvent fluctuation structure, projected microscopic closure, and rigid versus nonperturbative sectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/6cbpk3zx4kw95",
  "venue": "arXiv",
  "versions": []
}