Aiming at the inherent problems of existing fundamental interaction unified theories, including redundant dimensional assumptions, strong parameter fitting, and discontinuous physical mechanisms, this paper constructs a self-consistent Unified Evolution Theory based on the geometric framework of three-dimensional physical space coupled with intrinsic S^3 topological degrees of freedom. Abandoning extra-dimensional hypotheses and artificial fitting parameters, this paper takes a single topological functional minimization axiom as the core, whose underlying mechanism is the constraint imposed by functional minimization on the configurational potential energy: the configurational potential energy carried by the field configuration is the sole source of all energy (particle rest mass, interaction energy, and vacuum background energy), and the minimization condition deltaS=0 determines the realized stationary configurations and the direction of evolution. The paper accordingly gives the unified governing equation of four fundamental interactions, and realizes the topological unification of general relativity and quantum mechanics at the underlying structure level. This paper strictly classifies the physical mechanisms of fundamental interactions. Gravitation, electromagnetic interaction and strong interaction correspond to continuous topological evolution modes on the manifold, while weak interaction corresponds to the discrete topological transition process of topological knot breaking and reconnection. All theoretical parameters are endogenously derived only from the extremum condition of the topological functional (at the axiom-functional level; at the numerical calibration level, experimentally measured constants are used only for benchmark comparison, see Chapter 5). The complete six groups of pairwise relative intensity ratios of the four fundamental interactions are derived. The relative intensity of electromagnetic force to gravitational force is derived from first principles at the order of 10^39 in the first-order approximation without the fine-structure constant; incorporating the fine-structure constant alpha ~ 1/137, the theoretical output becomes the order of 10^37, qualitatively consistent with the experimental reference (10^36). The propagation speed of spacetime topological perturbation is solved endogenously, and its invariance is strictly deduced mathematically. Gravity originates from continuous topological manifold deformation, naturally free of singularities and ultraviolet divergences at short distances, which resolves the inherent contradiction between classical gravitation and quantum field theory.