Valence and Atomic Mass from Double-Vortex Confinement in TDRE-II (Harmonic Regime)

We present a unified TDRE–II derivation of chemical valence and atomic mass from a single geometric object: a quantized, closed double-vortex of eterons inside a pulsating spherical domain. In this framework, magnetic effects are emergent from the internal double- vortex motion; chemical valence measures the deficit of closure channels at the boundary layer, while atomic mass is defined as the total number of eterons stably confined by the saturated double vortex. A minimal topological argument yields a fundamental confinement quantum of four eterons per vortical level. We provide explicit, step-by-step examples (O, Cl, Ar/Ca, Fe) and state the domain of validity (harmonic regime) where a single double-vortex topology applies without torsional bifurcation.