Classical Electromagnetic Confinement with Topological Closure: Numerical Derivation of Atomic Constants from Maxwell's Equations

Abstract: We investigate the numerical consequences of solving Maxwell's equations in a spherical cavity subject to a spin-1/2 topological closure constraint. The confinement radius is fixed by the geometric condition rp=4ℏ/(mpc)=0.84124 fm. Classical electromagnetic analysis at this radius yields angular momentum envelopes consistent with Quantum Mechanics. The non-relativistic envelope of this confined field satisfies equations identical in form to the free Schrödinger equation. A bidirectional feedback loop between Maxwell's equations and QED vacuum response produces values for electron mass (me), Bohr radius (a0), and proton magnetic moment (μp) that agree with measured values to sub-ppm precision.

Supplementary Code (CHAFM-FE_Code_Pack.zip): This repository includes the Python source code used to verify the paper's derivations. The codebase contains the following validation scripts:

• CHAFM_Electron_Mass.py: Derives the electron mass, Bohr radius, and Rydberg constant from the topological axiom.

• CHAFM_Angular_Momentum.py: Verifies the spin-1/2 topological correction factor (8/ξ1).

• CHAFM_Neutron_Mass.py: Derives the neutron-proton mass difference via geometric stress.

• CHAFM_Schrodinger_Bridge.py: Demonstrates the emergence of the Schrödinger equation from the cavity field envelope.

• CHAFM_Emission_Physics.py: Simulates photon emission as a geometric beat frequency.

• CHAFM_Self_Consistency.py: Verifies the complete bidirectional feedback loop.