Unified Cosmic Mechanics Evolution Theory (XII) Dynamic Compatibility Verification of the Particle Encapsulation Velocity Increase Equation

The only dynamic physical reality of the cosmic system: the evolutionary carrier is the momentum unit m₀, the evolution rate is the speed of light c, and the total number of momentum units is conserved. From this emerges the unified dynamic relationship of motion potential = resistance potential = inertia potential = thrust potential, and energy = force = momentum = m·v (upper limit m·c). Thus, the velocity increase equation is directly established: Δv = (Δp / Pₑff) · c, and this paper conducts multi-scenario dynamic compatibility verification on it. The essence of classical mechanics: Traditional equations (e. g. , F = m·a, ½ m·v²) are integral statistical equations depending on specific interaction paths, not descriptions of the inertial state itself. The essence of relativity: Relativity statistically describes the dynamic integral process of matter in a changing environment. The square term in E = m·c² expresses space-time state shaping capability, not the dynamic eigenstate. The essence of the velocity increase equation: This equation restores the underlying dynamic logic of all mechanical statistics, emerging mass, momentum, energy, velocity, space-time, and resultant force. It is an inertial maintenance equation that can be directly associated with the dynamic resultant force equation: Fₜotal ∝ Pₜotal · vₜotal.