{
  "abstract": "We establish that structural stabilization via nonlinear self-trapping (Structural Stabilization Requirement, SSR) is a necessary condition for the existence of robust localized structures in dispersive substrates (Theorem 1), that a soliton's self-generated potential well supports exactly the eigenmode that generates it — perfect self-consistency (Theorem 2) — and that the linearity of the Hilbert space formalism axiomatically screens any such nonlinearity from the descriptive level (Theorem 3). We demonstrate the complete chain — self-trapping, emergent eigenmodes, heat kernel spectral decomposition, and structural screening — in an exactly solvable model (the one-dimensional cubic Soler equation [3]), extracting the spectral mass gap from $K(\\tau) = \\mathrm{Tr}(e^{-\\tau D^2})$ with four-digit precision and proving that the screening is exact (eigenvalue difference = 0.00). A formal classification theorem (the Dynamical Ledger, Theorem 4) eliminates twenty-one candidate field theories by systematic application of four independently motivated predicates — topological localization, emergent spinorial structure, descriptive linearity, and CPT conjugation — leaving exactly three surviving classes: nonlinear Dirac (Soler), chiral sigma (Skyrme), and their self-consistent coupling, the Chiral Quark Soliton Model (CQSM). This provides the mathematical foundations for a programme of ten companion papers (Emergence Papers I–X [13–22]) in which the self-consistent mean-field limit of these dynamics — the chiral quark-soliton model (CQSM) of Diakonov and Petrov — is recovered as a benchmark and tested against hadronic observables spanning five orders of magnitude in energy, with no adjustable parameters beyond $\\Lambda_\\mathrm{QCD}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4sj6kq5xp1emv.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4sj6kq5xp1emv",
  "issns": [],
  "landing_url": "https://hal.science/hal-05787457v3",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.nlin"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-mp"
    ],
    [
      "hal",
      "1.nlin.nlin-ps"
    ],
    [
      "hal",
      "1.phys.nucl"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05787457/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4sj6kq5xp1emv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05787457",
      "source": "hal",
      "url": "https://hal.science/hal-05787457v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.nucl",
      "subfield": "nuclear"
    },
    {
      "field": "physics",
      "origin": "hal:0.nlin",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Structural Stabilization and Spectral Screening in Nonlinear Wave Substrates: Proof of Concept for a Spectral Emergence Programme",
  "title_text": "Structural Stabilization and Spectral Screening in Nonlinear Wave Substrates: Proof of Concept for a Spectral Emergence Programme",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/4sj6kq5xp1emv",
  "venue": "HAL",
  "versions": []
}