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

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-22
DOI
https://doi.org/10.5281/zenodo.19687460
Primary Topic
Hydrogen Storage and Materials
Type
article
Field-Weighted Citation Impact
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Phase-2 Geometric Closure of the Hydrogen Atom from Constrained Null Geometry

Luka Gluvić
Zenodo (CERN European Organization for Nuclear Research)
Hydrogen Storage and Materials
article

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

Luka Gluvić
article en

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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