Geometric Prediction of the Proton Radius Puzzle and a New Lattice Resonance Frequency from a Rhombic Dodecahedral Vacuum

This research provides a purely geometric resolution to the Proton Radius Puzzle by modeling the vacuum as a discrete rhombic dodecahedral substrate, the optimal Voronoi tessellation of volumetric space. By applying the universal bridge equation (n = _ r), we demonstrate that the 0. 036 fm discrepancy between muonic and electronic hydrogen measurements is a mechanical necessity of the lattice, resulting from particles anchoring at discrete generations (n=23 and n=13). Beyond resolving the radius anomaly, this paper introduces the 9 Ring Saturation Postulate, identifying the proton as a Saturation Node where the vacuum state space reaches its maximum geometric capacity of 360⁹ 10^23 states. This alignment provides a first-principles derivation of Avogadro’s Number (the Mole) as a physical limit of the spatial manifold. Furthermore, the model identifies Dark Matter as the mandatory Antiphase Rarefaction (0. 5 -) of the proton’s compressional standing wave, providing a no new particles explanation for gravitational doubling. The paper offers a high-precision, falsifiable prediction of a discrete resonance signature at 1. 78 10^19 Hz. This framework identifies the mechanical torsion limit (= 4/) as the primary driver of spatial quantization, bridging the gap between nuclear geometry and cosmological observations.