{
  "abstract": "The heat kernel $K(\\tau) = \\mathrm{Tr}(e^{-\\tau \\mathcal{D}^2})$ of the self-consistent chiral soliton encodes all baryon observables as spectral projections, with systematic deficits ranging from $<2\\%$ (mass, Class A) to $38\\%$ (magnetic moment, Class C). We perform a spectral anatomy of these deficits in the nucleon magnetic moment, using the proper-time decomposition to map the boundary between one-body projections of $K(\\tau)$ and multi-body spectral content. Seven results are established. First, the isovector magnetic form factor $G_M^{T=1}$ has a UV-dominated one-body budget (75\\% UV) that rebalances to 47/53 UV/IR after inclusion of the $(N_c+2)/N_c$ algebraic factor from collective quantization and the leading meson exchange current estimate, yielding $\\mu_p = 2.70$ n.m. ($-3.3\\%$). Second, the isoscalar magnetic form factor $G_M^{T=0,\\mathrm{quark}}$ vanishes exactly through a double cancellation specific to the magnetic operator $\\gamma^0 \\gamma^k$: radial orthogonality within the same angular channel and angular orthogonality across channels. This operator selectivity distinguishes the magnetic zero ($G_M^{T=0} = 0$, Class D) from the non-zero axial isoscalar ($g_A^{(0)} \\approx 0.2$--$0.33$), establishing that the screening structure depends on the Dirac bilinear of the insertion, not merely on isospin. Third, the vanishing of the one-body contribution provides a calibration bound: the residual $\\mu^{T=0} - \\mu^{T=0}_\\mathrm{bos} = 0.13$--$0.19$ n.m. measures pure inter-sector corrections in a channel where the mean-field contribution is rigorously zero. Fourth, the proper-time spectral response $\\delta K(\\tau)$ is computed in 3+1D via the Friedel phase-shift method and compared with the Koopman screening measure $\\Delta K$; the two quantities probe complementary content (one-body Dirac shift vs inter-sector boson-fermion correlations), with anti-correlated profiles in the 1+1D benchmark. Fifth, the self-consistent profile $F^*$ is shown to be a stationary point of the heat kernel functional: the proper-time-weighted integral of the linear spectral susceptibility vanishes, and the leading screening beyond the one-body projection is quadratic in the bosonic fluctuations, proportional to the meson propagator $G_\\pi$; the Class B and C deficits are thereby shown to be structurally irreducible at the fixed point within the mean-field framework. Sixth, the quantitative reconstruction of the bosonic fluctuations via the normal-mode expansion of the quadratic susceptibility (20 quenched modes) yields corrections that worsen the agreement with experiment ($\\Delta g_A \\approx -12\\%$), establishing by exclusion that the Class B and C deficits arise from inter-sector meson exchange currents, not from mean-field profile fluctuations. Seventh, the Soler 1D benchmark confirms chaotic dynamics in non-integrable soliton collisions ($\\lambda_{\\max} > 0$, 14/14 cases) and establishes a three-scale spectral hierarchy $\\gamma_{\\mathrm{PR}} \\lesssim \\lambda_{\\max} \\lesssim \\alpha_{\\mathrm{dyn}} \\ll \\omega^2$ whose monotone ordering parallels the deficit hierarchy (Classes A--D), with the spectral modification rate governed by the mass gap; this provides a dynamical mechanism for the correlation between infrared spectral weight and deficit magnitude observed in the 3+1D soliton. The Goldberger--Treiman spectral analysis closes the Class B deficit: center-of-mass and meson exchange current corrections, mapped to zero and non-zero modes of the Koopman operator, yield $g_A \\approx 1.28$ --- within $1\\%$ of experiment ($1.267$) --- and cascade to $\\tau_\\beta \\approx 864$ s ($-1.6\\%$), promoting both observables to Class A; combined with the $(N_c+2)/N_c$ recovery for $\\mu_p$, eleven of the fourteen observables in Table S9.1 are within $5\\%$ of experiment with zero adjustable parameters. Together, these results establish a triple screening structure---isospin $\\times$ operator $\\times$ spectral depth---that the deficit hierarchy encodes as a diagnostic of the one-body projection of $K(\\tau)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Fabien Déchery"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fn7zb0yy1pbar.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "fn7zb0yy1pbar",
  "issns": [],
  "landing_url": "https://hal.science/hal-05841411v1",
  "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.hthe"
    ],
    [
      "hal",
      "1.phys.nucl"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05841411/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fn7zb0yy1pbar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05841411",
      "source": "hal",
      "url": "https://hal.science/hal-05841411v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "hal:1.phys.hphe",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.nucl",
      "subfield": "nuclear"
    }
  ],
  "title": "Screening Anatomy of the Heat Kernel: From One-Body Projections to Multi-Body Spectral Content",
  "title_text": "Screening Anatomy of the Heat Kernel: From One-Body Projections to Multi-Body Spectral Content",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/fn7zb0yy1pbar",
  "venue": "HAL",
  "versions": []
}