The Standard Model of modern physics contains dozens of free parameters that cannot be derivedfrom theory (such as the fine structure constant ), and faces severe theoretical gaps when bridgingmicroscopic quantum scales and macroscopic cosmic scales. This paper proposes the "TopologicalResidual Theory," establishing "right-handed cylindrical helical motion of space at the speed of light" as the sole first-principle axiom. Through the motion-derived dimension of space, the pure geometric origin of the fine structure constant is rigorously derived. Furthermore, by introducing the unit solid-angle helical divergence number , and combining it with Mandelbrot fractal geometry, thetheory proves that the strong nuclear force, electromagnetic force, and gravitational force areessentially geometric residuals of the same helical fluid at different topological levels. Finally, using only pen-and-paper geometric algebra, the theory precisely calculates the electron anomalousmagnetic moment, helium ion ionization energy, and proton-neutron mass difference, providing anew pure-geometric paradigm for a grand unified theory.