From Particle Dimensions to Electron Motion and Hydrogen Spectral Structure

We present the successful mathematical and numerical results of a trajectory-led investi-gation of hydrogen within Infinite Dimensional Wave Theory. Starting with the particle-depthpicture, a four-real-coordinate electron orbit yields exact rotation/precession components |δ − β|and δ + β. The component ratios, whole-frequency patterns, and energy sequences follow fromthe stated equations. An absolute calculation using electron mass and specified hydrogen energyand radius scales gives an ultraviolet component at 101.91 nm without tuning a wavelength, ap-proximately 0.65% from Lyman-β. The complete pattern (1, 2, 3, 4) has seven exact placementsin the gross hydrogen spectrum through upper level 100 and an octave chain through level200. The supplied orbit-action family contains the square energy sequence (1, 4, 9, 16), with 43exact placements through level 100 and 147 through level 200. We give the derivations, alllevel-100 assignments, exact octave identities, and reproducible checks. A separate anisotropicnuclear-potential calculation generates precession dynamically. The account follows the success-ful progression and identifies what the results calculate: trajectory geometry, energy relations,gross spectral correspondences, and conditional precession dynamics. These do not yet consti-tute a complete derivation of hydrogen’s selected states or optical strengths.