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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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On the Non-Perturbative Nature of the 0-Sphere Model and Magnetic Monopole Absence: A Supplement on Structural Analysis and Physical Interpretation

Authors: Hanamura, Satoshi;

On the Non-Perturbative Nature of the 0-Sphere Model and Magnetic Monopole Absence: A Supplement on Structural Analysis and Physical Interpretation

Abstract

[42 Supplement] This supplementary comment discusses why the absence of magnetic monopoles can be naturally understood within the structural framework of the 0-Sphere Model, while explicitly acknowledging that a complete geometric formulation remains under development. The emphasis is placed on clarifying the current scope of the model and connecting the structural features of the energy conservation identity to the physical mechanisms of the two-kernel structure, phase-dependent energy localization, and the distinction between open-path and closed-loop line integrals. The present note serves as a conceptual clarification complementary to earlier supplements on Zitterbewegung (zenodo.18356895), the anomalous magnetic moment (zenodo.18511664), and observer-dependent torsion (in preparation). Core Structural Argument The energy conservation identity of the 0-Sphere Model is given by \[ E_0 = E_0 \left[ \cos^4\!\left(\frac{\omega t}{2}\right) + \sin^4\!\left(\frac{\omega t}{2}\right) + \tfrac{1}{2}\sin^2(\omega t) \right]. \] This expression exhibits a natural structural asymmetry between its three terms. This asymmetry provides the basis for distinguishing electric charge from magnetization: Single-term contribution \( \tfrac{1}{2}\sin^2(\omega t) \): kinetic energy of the photon sphere — globally coherent, undivided, and identified with electric charge as a monopole quantity. Paired-term contribution \( \cos^4\!\left(\frac{\omega t}{2}\right) + \sin^4\!\left(\frac{\omega t}{2}\right) \): potential energies localized at spatially separated kernels \( A \) and \( B \) — inseparably coupled, giving rise to magnetization as an intrinsically dipolar quantity. Because magnetization emerges from the gradient of the paired potential structure, no standalone magnetic monopole degree of freedom appears within the present formulation. The two kernels are dynamically inseparable through the photon sphere, and no mechanism exists to isolate a single kernel and assign it an independent magnetic charge. Connection to the Line-Integral Framework The structural prohibition of magnetic monopoles is further understood through the distinction developed in the line-integral trilogy (zenodo.18067760, zenodo.18135855, zenodo.18203433): the primacy of open-path line integrals is incompatible with a closed-surface Gauss's law for magnetism, while the globally coherent photon sphere admits standard enclosure and yields well-defined monopole charge for electricity. Methodological Stance This document follows the methodological framework established in the companion supplement on non-perturbative character and methodological scope (zenodo.18603340): conclusions are presented as a working structural hypothesis, not as a completed theoretical derivation. A rigorous geometric framework connecting the energy identity structure to Maxwell-type equations, fiber bundles, Chern classes, and topological invariants (Nakahara 2003) remains under development. Key Results Structural identification of the single-term photon-sphere contribution with electric charge (monopole quantity via Gauss's law) Structural identification of the paired-term kernel contribution with magnetization (dipole quantity via Ampère's law) Working hypothesis for magnetic dipole inseparability derived from the architecture of the energy identity Conceptual alignment with the reinterpretation of the Dirac equation as absorption/emission radiative phases (zenodo.17760132) Connection to the predicted Zitterbewegung velocity \( v_{ZB} \approx 0.04047\,c \) via \( \gamma = 1 + a \) (zenodo.17765409, zenodo.18356895) Comparison with Dirac (1931) and ’t Hooft–Polyakov monopole frameworks (tabular summary) Open Directions Future work should address: (i) geometric interpretation of term pairing via fiber bundles and connection structures; (ii) systematic relation to topological charge quantization (Chern classes, winding numbers); (iii) derivation of Maxwell's equations from the energy identity; (iv) experimental verification of the predicted Zitterbewegung velocity as indirect support for the internal circulation picture. Related Publications Foundational framework: zenodo.16759284 (A Model of an Electron Including Two Perfect Black Bodies, 2018) Methodological companion: zenodo.18603340 (Non-Perturbative Nature and Fine-Structure Constant, 2026) Zitterbewegung supplement: zenodo.18356895 (Geometrical Confinement: Rest Mass and ZB, 2026) Gravitational-like phenomena: zenodo.18511664 (Detailed Exposition, 2026) Line-integral trilogy: zenodo.18067760, zenodo.18135855, zenodo.18203433 Vacuum energy / integral ontology: zenodo.18275142 Dirac equation reinterpretation: zenodo.17760132 Spin from Berry phase / \( v_{ZB} \) prediction: zenodo.17765409

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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