Homogeneous Compression Theory: A Geometric Framework for the Emergence of Fundamental Constants, Gravity, and Quantum Structure

We present the Homogeneous Compression Theory (HCT), a geometric framework in which fundamental physical phenomena emerge from a common structural origin defined by a minimal projected cell and its associated phase dynamics. In this approach, the fine-structure constant arises as a closure count of the underlying geometry, linking microscopic atomic structure to macroscopic behavior without the introduction of free parameters. Gravity is interpreted as a manifestation of structural phase mismatch, recovering the Newtonian limit while naturally extending to galactic scales through coherence effects without requiring dark matter. Electromagnetic interactions are described by a propagating phase field coupled to internal structure, from which the leading-order anomalous magnetic moment of the electron emerges as a geometric consequence, yielding (g-2)/2 approximately alpha/(2pi). The theory further predicts detector-dependent modifications in interference experiments and small deviations in weak gravitational lensing. These features provide clear avenues for experimental falsification. HCT offers a unified structural perspective connecting constants, interactions, and large-scale phenomena within a single geometric framework.