{
  "abstract": "The heat kernel $K(\\tau) = \\mathrm{Tr}(e^{-\\tau \\mathcal{D}^2})$ of the Dirac operator in a topological soliton background is a single mathematical object from which baryon observables emerge as different functionals. The chiral quark-soliton model is recovered as the mean-field (Hartree-Fock) evaluation of $K(\\tau)$ in a self-consistent hedgehog soliton background. The constituent quark mass $M_q$ is not an external input but an emergent fixed point: the instanton liquid parametrization of the QCD vacuum ($\\rho = 0.33$ fm, $n = 1$ fm$^{-4}$) predicts $M_q = 362$ MeV, and the self-consistent Hartree-Fock iteration converges to a stable nucleon mass $M_N = 923$ MeV ($-1.7\\%$) with $F_\\pi = 91.5$ MeV ($-1.6\\%$), with no adjustable parameter beyond $\\Lambda_\\mathrm{QCD}$ (*Note.* $F_\\pi = 91.5$ MeV uses the normalization $F_\\pi^\\mathrm{exp} \\approx 92.2$ MeV; some references use $f_\\pi = \\sqrt{2} F_\\pi \\approx 130$ MeV (chiral convention); our convention follows Christov et al. [12]). At this point, the full proper-time integral also yields the $N$-$\\Delta$ splitting $\\Delta = 295$ MeV ($+0.7\\%$), and the axial coupling $g_A = 1.174$ ($-7.3\\%$). At this emergence point, the isovector form factor $G_M^{(1)} = 2.815$ yields $\\mu_p = 1.740$ n.m. ($-37.7\\%$) and $\\mu_n = -1.075$ n.m. ($-43.8\\%$). For comparison, matching $F_\\pi = 93.0$ MeV ($M_q = 375$ MeV) gives $G_M^{(1)} = 2.79$ and $\\mu_p = 1.73$ n.m. The proper-time decomposition of $K(\\tau)$ reveals a systematic spectral anatomy: the nucleon mass is UV-dominated (66% from $|\\varepsilon| > 500$ MeV) and well-captured by the gradient expansion, while $g_A$ (97% IR) and the magnetic moments (99% IR) require the full Dirac sea. The hierarchy of deviations — $0.1\\%$ ($M_N/F_\\pi$), $0.7\\%$ ($\\Delta$), $1.7\\%$ ($M_N$, $F_\\pi$), $7.3\\%$ ($g_A$), $37.7\\%$ ($\\mu_p$) (at the zero-parameter point $M_q = 362$ MeV) — correlates with the infrared spectral weight of each observable, identifying the two-body meson exchange current as the dominant missing mechanism. The Skyrme model is the UV sector of $K(\\tau)$; its structural blindness to IR-dominated observables is a consequence, not a deficiency. This is Emergence Paper III of the emergence programme. Together with Emergence Paper I (gauge structure from moduli) and Emergence Paper II (chirality from the UV topological sector), these papers demonstrate that gauge symmetry, chirality, and baryon masses are projections of a single spectral object determined by $\\Lambda_\\mathrm{QCD}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ase9tjr9qh05z.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "ase9tjr9qh05z",
  "issns": [],
  "landing_url": "https://hal.science/hal-05751221v4",
  "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.phys"
    ],
    [
      "hal",
      "1.phys.hphe"
    ],
    [
      "hal",
      "1.phys.mphy"
    ],
    [
      "hal",
      "1.phys.nucl"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05751221/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ase9tjr9qh05z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05751221",
      "source": "hal",
      "url": "https://hal.science/hal-05751221v4"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.hphe",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.nucl",
      "subfield": "nuclear"
    }
  ],
  "title": "Baryon Observables as Projections of a Single Heat Kernel",
  "title_text": "Baryon Observables as Projections of a Single Heat Kernel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/ase9tjr9qh05z",
  "venue": "HAL",
  "versions": []
}