From Quantum Potential to Atomic Structure: Seven Derived Results in D=3 Geometry
Year: 2026
Type: preprint
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.
Author: Singh, Mandeep
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161482494
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