Atomic Structure from Geometric First Principles: The Aperture-Well Unification Theory

We present a complete derivation of atomic structure from the Aperture-Well Unification Theory (AWUT), a geometry-first framework requiring only five fundamental inputs: two bubble frequencies (fBlue = 12.37 GHz, fRed = 9.22 GHz), two Planck-scale constants (ℓPS, TPS), and an energy partition ratio (68%/27%/5%). From these inputs alone, we derive: • The proton-electron mass ratio mp/me = 1834.8 (0.07% error vs. CODATA 2022) • Lepton mass ratios as exact integers: mµ/me = 207, mτ /me = 3477 • Hydrogen ground state energy E1 = −13.6 eV (99.985% accuracy) • Nuclear magic numbers 2, 8, 20, 28, 50, 82, 126 from rail quantization • Nuclear binding energies with 0.252 MeV RMS error across 2931 nuclei (AME2020) The key mechanism is rail quantization: phase circulation satisfying H dχ = 2πn generates discrete structure at every scale. Electrons are spatial loops (winding number n = 1); protons are three Red bubbles in frequency lock-in; atomic shells are Coulomb-well quantization of electron rails. We introduce the wobble correction—a time-slip screening effect from Purple (dark matter) wells—which reduces binding energy RMS error by a factor of 11.7 compared to the standard semi-empirical mass formula, using zero fitted parameters. Unlike the Standard Model, which cannot predict particle mass ratios, AWUT derives them geometrically. We present explicit falsification criteria and encourage experimental tests. The theory is ready for peer review. Keywords: unified field theory, atomic structure, nuclear binding energy, mass ratio derivation, geometric physics, dark matter