Within the framework of Topological Residual Theory (TRT), this study explores the unification ofgravitational and electromagnetic interactions at the level of spacetime geometry. Utilizing the cylindrical helical motion of spatial points (geometrization of Zitterbewegung) as the dynamical foundation, we derive the wave equationvia the variational principle of the displacement field . Using the geometric structure of thelocal cylindrical orthonormal frame induced by local helical symmetry, the electric, magnetic, and gravitational fields are defined as projections of the time derivatives of onto this orthonormal frame. Consequently, the mutual orthogonality of the three fields emerges as a geometric necessity of the frame decomposition rather than an independent postulate. The gravitational field is derived via two independent pathways: (i) the framekinematics and time evolution pathway ( ), and (ii) the second-order derivative pathway of the wave equation ( ). The mathematical consistency betweenthese two pathways indicates that gravity can be interpreted as a second-order residual effectof electromagnetic oscillations propagating at the speed of light. Furthermore, charge is defined as the topological charge (winding number / Hopf invariant) of the helical displacement field on a closed sphere (Euler characteristic ), which manifests as the effective rate of mass change only during the transient state of topological structure formation. Under the compatibility condition of theflux change rate (local topological flux continuity), we naturally derive the vacuum relations and . Based on this unified topological mechanism, the model provides a self-consistent geometric explanation for both charge quantization and particle spin.