{
  "abstract": "We close the spectral chain initiated in Emergence Papers I–III by investigating the inverse problem: to what extent does the heat-kernel trace $K(\\tau)$ of the Dirac operator in the soliton framework [Emergence Paper III] constrain the effective Lagrangian $\\mathcal{L}_\\mathrm{eff}$ and, through it, the hedgehog profile $F(r)$? Four numerical results are established. (N1) The Seeley–DeWitt asymptotic expansion of $K(\\tau)$ saturates the Skyrme Lagrangian at $O(p^4)$ to better than 0.02%, confirming that UV spectral data constrain $\\mathcal{L}_\\mathrm{eff}$ but do not fully determine $F(r)$. (N2) An inverse spectral reconstruction from phase-shift data recovers the self-consistent profile to 0.98% (L2), supporting a topological Borg–Marchenko conjecture within the B=1 sector. (N2+) The Fréchet Jacobian of the spectral map $\\Phi: F \\to \\{\\delta_\\kappa(\\varepsilon)\\}$ has full rank 11/11 at the Hartree–Fock fixed point, establishing local injectivity via the implicit function theorem; the singular-value spectrum reveals a three-tier hierarchy with condition number $\\kappa \\approx 10^6$ that quantitatively explains the reconstruction residual. (N3a) A self-consistent fixed-point scan shows that 6 out of 7 initial profiles converge to the same F* under Anderson mixing (<0.41% L2), providing a numerical substitute for the Hohenberg–Kohn uniqueness theorem. A detailed parallel with density-functional theory — sharing reduced descriptor, self-consistent cycle, and Anderson/DIIS acceleration — is developed. Taken together, these results demonstrate that the spectral chain $K(\\tau) \\to \\mathcal{L}_\\mathrm{eff} \\to F(r) \\to \\{\\varepsilon_n, \\delta_\\kappa(\\varepsilon)\\} \\to F^*(r)$ is self-consistently closed at Level A (local, K=0 channel), and identify precise routes toward a global uniqueness theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gb9zds3wkbs3.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4gb9zds3wkbs3",
  "issns": [],
  "landing_url": "https://hal.science/hal-05787614v3",
  "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"
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      "hal",
      "1.phys.hthe"
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      "hal",
      "1.phys.nucl"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05787614/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gb9zds3wkbs3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05787614",
      "source": "hal",
      "url": "https://hal.science/hal-05787614v3"
    }
  ],
  "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": "Self-consistency of the chiral soliton: the heat kernel constrains the Lagrangian",
  "title_text": "Self-consistency of the chiral soliton: the heat kernel constrains the Lagrangian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/4gb9zds3wkbs3",
  "venue": "HAL",
  "versions": []
}