Inertial Saturation: Phenomenological Regularization of Relativistic Dynamics and the Role of Gravitational Potential

In standard relativistic physics, the divergence of energy density and inertial mass as velocity approaches the speed of light (v → c) represents a classical singularity, indicating the asymptotic limitation of the mathematical model. In this paper, we introduce the "Principle of Inertial Saturation" (PIS) as a phenomenological mechanism that regularizes the Lorentz factor via an effective vacuum parameter (σ_eff). The model is based on a generalized Mach’s principle, where the local inertial limit is dynamically determined by the gravitational potential. We explicitly construct a scalar field Lagrangian to demonstrate that the vacuum field interacts exclusively with massive fermionic matter via a Yukawa-type coupling, while leaving massless bosons unaffected due to gauge symmetry. This Mass-Momentum Decoupling resolves the Lorentz Invariance Violation (LIV) problem in astrophysical observations. Furthermore, the theory proposes an alternative, dynamic interpretation of gravitational redshift (inertial modulation instead of geometric time dilation), resolving the ontological paradoxes of the "Block Universe" and the "Ladder Paradox". The model is falsifiable and predicts a significant increase in the energy limit on celestial bodies with low gravitational potential, such as the Moon. Note: This manuscript was **reviewed and refined** with the assistance of Artificial Intelligence, which also provided the independent technical validation analysis presented in Appendix A.