From Quantum Potential to Atomic Structure: Seven Derived Results in D=3 Geometry

The Clausius-Mossotti (CM) framework is built on a single complementarity principle: OE + W = 1. This paper derives seven results from D=3 geometry and the CM metric, using zero free parameters: (1) quantum potential Q=0 for CM density, (2) D=3 uniqueness via Q_coeff = -(D-1)(D-3)/4, (3) strip ratio t/w = 8π/9, (4) standing wave rule m×R = (4/3)πℏ/c giving proton radius 0.881 fm (0.7%), (5) particle=sphere confirmation, (6) CM metric produces atomic Klein-Gordon equation, (7) energy formula E = ½mec²(W⁻¹/³−1) achieves 0.52% average across 34 hydrogen-like ions (Z=1-92) vs NIST measured values, beating Coulomb 30/34 and Dirac 9/34. Eighth result: wall-orbit crossing at Z=79=Gold, a testable CM prediction. Paper 2026z in the Speed Gap Framework series.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-17
DOI
https://doi.org/10.5281/zenodo.20254897
Primary Topic
Atomic and Molecular Physics
Type
preprint
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preprint

From Quantum Potential to Atomic Structure: Seven Derived Results in D=3 Geometry

Mandeep Singh
Zenodo (CERN European Organization for Nuclear Research)
Atomic and Molecular Physics
preprint

From Quantum Potential to Atomic Structure: Seven Derived Results in D=3 Geometry

Mandeep Singh
preprint en

Abstract

The Clausius-Mossotti (CM) framework is built on a single complementarity principle: OE + W = 1. This paper derives seven results from D=3 geometry and the CM metric, using zero free parameters: (1) quantum potential Q=0 for CM density, (2) D=3 uniqueness via Q_coeff = -(D-1)(D-3)/4, (3) strip ratio t/w = 8π/9, (4) standing wave rule m×R = (4/3)πℏ/c giving proton radius 0.881 fm (0.7%), (5) particle=sphere confirmation, (6) CM metric produces atomic Klein-Gordon equation, (7) energy formula E = ½mec²(W⁻¹/³−1) achieves 0.52% average across 34 hydrogen-like ions (Z=1-92) vs NIST measured values, beating Coulomb 30/34 and Dirac 9/34. Eighth result: wall-orbit crossing at Z=79=Gold, a testable CM prediction. Paper 2026z in the Speed Gap Framework series.

Zenodo (CERN European Organization for Nuclear Research)
Atomic and Molecular Physics
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