This paper presents a revolutionary geometric framework that unifies all fundamental interactions through multidimensional curvature of spacetime. Gravity emerges as 3D curvature, electromagnetism splits into 2D surface stretching (electric field) and 0D point twisting (magnetic field), while acceleration corresponds to 1D worldline curvature. The theory introduces a radical new interpretation of elementary particles as stable topological defects: electrons as spherical hedgehogs, protons as double hedgehogs, and muons as toroidal configurations. All fundamental constants - including the fine structure constant and particle masses - arise naturally from geometric constraints. The model provides exact quantitative predictions for magnetic moments, radii, and decay rates without free parameters. Experimental verification through precision measurements and particle scattering experiments is proposed. This work represents a paradigm shift from quantum field theory to a purely geometric description of physical reality.