Electron as a Dynamically Maintained SU(2)-Locked Delay Closure\\ on a Growing Hyperspherical Time Front

We present a geometric model of the electron within a hyperspherical time-front framework. In this approach, physical time is not treated as an independent coordinate with its own dynamics. Instead, time is identified with the uniform radial growth of a four-dimensional hyperspherical front, R(t)=ct. Matter is modeled as a localized delay of this front growth. Within this picture, the electron is interpreted as a compact, dynamically maintained, topologically closed delay-domain tangent to the growing front. The central idea is that a local fluctuation of the delay field may either disperse back into the front or become topologically trapped. If the ongoing growth of the front is continuously converted into sufficiently stable SU(2)-locked circulation around the local growth-leading axis, the fluctuation may become dynamically trapped into a self-maintained delay closure. The electron is then identified not as a static object, but as the minimal dynamically maintained closure of this type. A distinction is introduced between the compact closure core and its extended front imprint. The compact core remains localized and determines the rest mass, spin, and internal circulation scale. The front imprint is the distributed deformation of the time-front associated with an unpinned electron during free propagation. This separation allows the framework to describe both localized interactions and wave-like propagation without requiring the electron core itself to spread over macroscopic distances. Within the model, the characteristic closure scale is related to the electron Compton wavelength, while the internal SU(2)-locked circulation naturally leads to a spinorial 4π closure structure. The resulting geometric picture provides a unified interpretation of electron mass, spin-1/2 behavior, localization, and propagation in terms of a single dynamically maintained delay configuration. The work develops the mathematical foundations of this framework and derives the corresponding closure conditions, stability criteria, and mass-scale relations. The proposed model is intended as a geometric alternative framework for investigating the emergence of elementary particle properties from the dynamics of a growing hyperspherical time front.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-29
DOI
https://doi.org/10.5281/zenodo.20446431
Primary Topic
Quantum chaos and dynamical systems
Type
preprint
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preprint

Electron as a Dynamically Maintained SU(2)-Locked Delay Closure\\ on a Growing Hyperspherical Time Front

Vitalii Bakhariev
Zenodo (CERN European Organization for Nuclear Research)
Quantum chaos and dynamical systems
preprint

Electron as a Dynamically Maintained SU(2)-Locked Delay Closure\\ on a Growing Hyperspherical Time Front

Vitalii Bakhariev
preprint en

Abstract

We present a geometric model of the electron within a hyperspherical time-front framework. In this approach, physical time is not treated as an independent coordinate with its own dynamics. Instead, time is identified with the uniform radial growth of a four-dimensional hyperspherical front, R(t)=ct. Matter is modeled as a localized delay of this front growth. Within this picture, the electron is interpreted as a compact, dynamically maintained, topologically closed delay-domain tangent to the growing front. The central idea is that a local fluctuation of the delay field may either disperse back into the front or become topologically trapped. If the ongoing growth of the front is continuously converted into sufficiently stable SU(2)-locked circulation around the local growth-leading axis, the fluctuation may become dynamically trapped into a self-maintained delay closure. The electron is then identified not as a static object, but as the minimal dynamically maintained closure of this type. A distinction is introduced between the compact closure core and its extended front imprint. The compact core remains localized and determines the rest mass, spin, and internal circulation scale. The front imprint is the distributed deformation of the time-front associated with an unpinned electron during free propagation. This separation allows the framework to describe both localized interactions and wave-like propagation without requiring the electron core itself to spread over macroscopic distances. Within the model, the characteristic closure scale is related to the electron Compton wavelength, while the internal SU(2)-locked circulation naturally leads to a spinorial 4π closure structure. The resulting geometric picture provides a unified interpretation of electron mass, spin-1/2 behavior, localization, and propagation in terms of a single dynamically maintained delay configuration. The work develops the mathematical foundations of this framework and derives the corresponding closure conditions, stability criteria, and mass-scale relations. The proposed model is intended as a geometric alternative framework for investigating the emergence of elementary particle properties from the dynamics of a growing hyperspherical time front.

Zenodo (CERN European Organization for Nuclear Research)
Sustainable cities and communities
Quantum chaos and dynamical systems
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