Physics from SU(2) Phase Geometry on the 3-Sphere: Foundations

I develop a unified physical framework in which matter, fields, and interactions arise from the geometry and topology of a continuous SU(2) phase field defined over the compact 3-sphere S3. Physical space is modeled as a hypersphere, and local states are described by SU(2) orientations. Particles correspond to stable topological phase vortices, while forces emerge from the curvature and global coherence of the phase field. Within this model, I derive the key features of quantum behavior — including spin quantization, wave-particle duality, and the Pauli exclusion principle — from the underlying SU(2) structure. Gravitational and electromagnetic interactions are interpreted as manifestations of long-range phase curvature, and the equivalence of inertial and gravitational mass follows naturally from the energy content of localized vortices. This foundational work establishes the geometric principles and dynamic equations governing SU(2) phase configurations, providing a common ground for subsequent developments in thermodynamics, optics, nuclear structure, and condensed matter. The framework offers a topological alternative to conventional field theory, with quantization and interaction embedded in the global phase geometry of space.