The AMDCF Gravitational Memory Field: A Comprehensive Data Analysis of Singularity Avoidance and the Newtonian Limit

Classical General Relativity predicts the formation of spacetime singularities where curvature diverges to infinity, while Newtonian gravity fails to account for non-local historical effects. In this study, we propose the Adaptive Memory-Driven Coupling Framework (AMDCF), a generalization of Einstein's field equations incorporating a non-Markovian Memory Tensor (M_μν). The Memory Tensor is derived via a History Operator with an exponentially decaying kernel, ensuring the preservation of the Bianchi Identity and the conservation of energy. We demonstrate two fundamental properties using numerical simulations. First, at small scales (r < R_E), a sigmoid-based memory plateau prevents the central singularity, yielding a Regular Black Hole core. Second, at large scales (r >> R_E), the damped oscillatory tail of the memory field averages out, perfectly recovering Newton's inverse-square law. This Correspondence Principle proves that Newtonian gravity is a macroscopic approximation of a deeper, history-dependent spacetime geometry. By generalizing the formulation to arbitrary mass and length scales, this framework provides a robust, geometrically consistent foundation for resolving singularities and offers a novel interpretation of Dark Matter as residual gravitational memory. Gravity is not weak because of a cosmic coincidence or an infinite Multiverse. Gravity is weak because it is the memory of the past, not an impulse of the present. It requires cosmic scales of time and distance to accumulate enough memory density to dominate the universe. By introducing the Memory Tensor (M_{\mu\nu}) into General Relativity, the AMDCF framework solves the Hierarchy Problem without violating the Bianchi identities, offering a mathematically rigorous alternative to the Multiverse hypothesis.