This work introduces the Homogeneous Compression Theory, a theoretical framework in which matter is described as localized structures of an underlying compression field with infinite internal hierarchy. Observable interactions arise from leakage of compression modes from this internal structure into the external three-dimensional sector. Within this framework, electromagnetism emerges as the dynamical response of the external sector to a leakage current of compression. The fine-structure constant is interpreted as a geometric efficiency governing the coupling between internal compression modes and external space. The theory provides a unified geometric interpretation of several fundamental physical properties. Electric charge arises as a topological winding number of the internal compression phase. Spin-1/2 emerges from a double-cover topology of the internal orientation space. The electron gyromagnetic factor g≈2 is obtained from the ratio between external circulation and internal phase closure, while the anomalous magnetic moment naturally appears from leakage-induced mixing of internal modes. A geometric route to the fine-structure constant is proposed through boundary eigenmode selection at the interface between internal hierarchical structure and external space, yielding the approximation __₁___ α≈ 4π (1+π2) which provides a close first-order estimate of the observed value. The framework also produces several testable predictions, including possible correlations between variations of the fine-structure constant and magnetic anomalies, as well as the existence of metastable fractional effective charge states in strongly constrained topological media.
Pablo Garcia (Thu,) studied this question.