This paper proposes a geometric interpretation of atomic structure in which the electron is modeled as a minimum-energy logarithmic spiral mode confined between the reduced Compton scale and the Bohr scale. In this framework, the inverse fine-structure constant is interpreted through the geometry of the spiral mode, while the electron gyromagnetic factor g = 2 is interpreted through the 4pi closure topology of the internal oriented structure. The work connects the Bohr radius, the reduced Compton wavelength, the classical electron radius, and the fine-structure hierarchy within a unified geometric-topological picture. It is presented as a theoretical structural interpretation rather than a complete first-principles derivation of quantum electrodynamics.