Unified Cosmic Mechanics Evolution Theory (X) Dynamic Reconstruction of Mercury's Perihelion Precession and Gravitational Waves Based on Relativistic Effects

Based on the comprehensive derivation of multiple preceding chapters within the framework of Information Dynamic Evolution Theory, focusing on the core conservation relations and dynamic principles of the underlying physical reality, this paper conducts a complete discrete derivation of the phenomena of Mercury's perihelion precession and gravitational wave radiation. Different from the continuous space-time curvature hypothesis of general relativity, the evolution of momentum units takes "discrete interaction" as the core physical image, holding that the gravitational effect in celestial motion originates from the successive interactions between momentum units and the gravitational field, and gravitational waves are discrete radiation events of momentum unit decoupling during the violent motion of massive celestial bodies. The derivation process strictly follows the two core conservation relations: the Conservation of Space-time State Shaping and the Conservation of Perceptual Resource Competition, combined with the velocity increment formula and the Path Curvature Perceptual Opportunity Multiplication Effect. Finally, the numerical result of Mercury's precession angle is consistent with the observed value and the result of general relativity; the discrete model of gravitational waves matches the dimension of the quadrupole radiation formula of general relativity in the continuous limit, and can explain the gravitational wave waveform characteristics in black hole mergers. This study verifies the self-consistency of the momentum unit evolution theory framework and provides a new discrete dynamic perspective for the essential explanation of gravitational phenomena. Physical Reality and Relativistic Relations: The evolutionary carrier is the momentum unit (m₀), the evolution rate of a single unit is the speed of light (c), the system has vector superposition capability, and the total number of momentum units is conserved. Therefore, energy = force = momentum = m·v (upper limit m·c). Both multiplicative force and additive force are incremental changes to the momentum unit m₀·c, and the mass-energy equation E = m·c² in relativity is precisely the space-time state shaping equation in the integral of path redundancy or perceptual capability. Thus, a Pythagorean theorem conservation relation in the integral is formed, which is not a dynamic mass-energy equation. Therefore, the relativistic integral effect is induced by interactive environments such as relative motion or massive celestial bodies. This paper conducts mathematical and logical verification based on this underlying foundation to be compatible with quantum mechanics and classical mechanics.