{
  "abstract": "We formulate a unified conjecture: for topological solitons of charge $B$ in a nonlinear field theory, the quantum spectrum on the moduli space $M_B$ is given by the class-1 representations of the global symmetry $\\tilde{G}$ with respect to the residual stabilizer $H_B$, with admissible representations selected by topological constraints (Finkelstein-Rubinstein sign for $SU(2)$, Wess-Zumino-Witten triality for $SU(3)$). We verify this conjecture in six cases spanning four qualitative regimes of $H_B$, with quantitative agreements $< 1\\%$ where data exist. We identify the Hopf fibration as the geometric origin of $U(1)_{\\text{EM}}$ and propose a concrete program for local gauge emergence via Berry phase holonomy and Hull-Spence gauging of moduli isometries. The $\\eta$-invariant on the Atiyah-Hitchin manifold ($B=2$) is identified as a potentially original computation. The moduli structure identified here determines which representations enter the trace of the heat kernel $K(\\tau) = \\mathrm{Tr}(e^{-\\tau \\mathcal{D}^2})$; companion papers address the chirality emerging from the UV topological limit (Emergence Paper II [30]) and the baryon masses generated by the full proper-time integral (Emergence Paper III [29]).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xh78gpq6w6vg.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "9xh78gpq6w6vg",
  "issns": [],
  "landing_url": "https://hal.science/hal-05751208v4",
  "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.phys"
    ],
    [
      "hal",
      "1.math.math-mp"
    ],
    [
      "hal",
      "1.phys.hthe"
    ],
    [
      "hal",
      "1.phys.nucl"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05751208/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xh78gpq6w6vg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05751208",
      "source": "hal",
      "url": "https://hal.science/hal-05751208v5"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.hthe",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.nucl",
      "subfield": "nuclear"
    }
  ],
  "title": "Spectral Emergence from Topological Solitons: A Unified Conjecture for Gauge Representations",
  "title_text": "Spectral Emergence from Topological Solitons: A Unified Conjecture for Gauge Representations",
  "type": "preprint",
  "updated_at": "2026-11-08T12:20:49Z",
  "url": "https://research.draconitic.com/paper/9xh78gpq6w6vg",
  "venue": "HAL",
  "versions": []
}