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April 24, 20260 citationsOpen Access

Phase-2 Geometric Closure of the Hydrogen Atom from Constrained Null Geometry

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LGLuka Gluvić

Key Points

  • The aim is to derive a closed geometrical model of the hydrogen atom using constrained null geometry.
  • Developed a geometric model starting from a closed microphysical layer.
  • Derived properties such as radius, velocity, and energy directly from the geometry.
  • Validated numerically with the n = 2 block and higher orbital branches.
  • Established a unified hydrogen spectrum law and general nS contact law.
  • Identified structural properties including orbital fine-structure and transport averages.
  • Demonstrated the closure conditions applicable to hydrogen's principal tower.

Abstract

This release contains the paper Phase-2 Geometric Closure of the Hydrogen Atom from Constrained Null Geometry. The paper derives the hydrogen atom as a closed one-center sector of constrained null geometry, starting from the already closed microphysical layer of reduced phase geometry, closure spinor structure, protected transport, and the globally anchored fine-structure axis. The paper derives the principal hydrogen tower from one-center closure conditions and reduced mass, obtaining the radius, velocity, energy, and transition laws directly from the geometry. It then derives the orbital fine-structure sector as a transported-spinor sector of the same central geometry, including an exact radial transport average and a residual defect law. The remaining s-sector is treated as the contact complement of transport, yielding a general nS contact law and a unified hydrogen spectrum law. The numerical validation includes the n = 2 block and the higher orbital branches 3P, 3D, 4P, 4D, and 4F. The scope of the paper is intentionally narrow: it closes hydrogen as the first atomic realization of the theory, but does not yet treat shell capacities, Aufbau structure, many-electron atoms, chemistry, or condensed matter sectors. This release is intended as the Phase-2 hydrogen paper following the closed Phase-1 microphysical sector.

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Cite This Study

Luka Gluvić (2026) studied this question.

synapsesocial.com/papers/69eb0a94553a5433e34b4a80https://doi.org/10.5281/zenodo.19687460
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