Electron Orbitals — 4-D Curvature Domains, Where Matter Meets Vacuum

Electron orbitals are reinterpreted as finite-β curvature domains—four-dimensional (4-D) regions of self-correcting geometry embedded in the infinite-feedback vacuum. Each orbital is a standing curvature wave on S³ whose 3-D projection forms the familiar s, p, d, and f patterns of atomic structure.Quantization arises from 4-D phase closure (nΔφ₄ = 2π), while orbital stability results from continuous curvature feedback that prevents radiative collapse. The boundary between matter and vacuum is not spatial but dynamical: where β → β_vac, curvature self-correction becomes instantaneous and the 4-D motion flattens into the 3-D electromagnetic field. Bonding and molecular structure emerge as synchronized β-fields linking multiple curvature domains; delocalization and superconductivity represent extended 4-D coherence across atoms. Charge and field appear as feedback gradients at this interface, and quantized energies reflect discrete curvature harmonics on S³. Predicted experimental signatures include 4π rotational periodicity in photoelectron phase maps, isotopic β-shifts beyond mass scaling, attosecond re-coherence delays, and field-induced curvature tails. The electron’s orbital thus marks the true contact surface between matter and vacuum—the geometric frontier where the universe’s self-correction becomes visible and substance emerges from space itself.