Gravitation as a Vacuum Energy Deficit within General Relativity (v12)

This is a refined version of the framework, capable of addressing both dynamical and lensing phenomena. Note that full-system evaluations may be computationally demanding for large datasets. The current implementation can model, without invoking dark matter: ✔ velocity dispersion ✔ rotation curves ✔ dwarf galaxies ✔ ultra-diffuse galaxies (UDGs) ✔ Einstein rings ✔ galaxy-scale gravitational lensing Saturation Gravity is a field-based framework in which gravity is interpreted as arising from a vacuum energy deficit associated with matter. Gravitational effects are described through a formally imaginary, electric-field–like bookkeeping quantity whose cumulative behavior reproduces gravitational time dilation. This formulation introduces a universal saturation scale, 𝐸ₘax, emerging from time-dilation consistency arguments. The resulting scale is of the same order of magnitude as the Schwinger critical field, though no physical equivalence is implied. General Relativity remains the correct macroscopic description of gravity. Saturation Gravity does not modify Einstein’s equations; rather, it provides an interpretative explanation for why gravitational fields remain finite in extreme regimes. The framework introduces a single universal acceleration scale, aₒffset = 1×10^−10 m/s². from which a critical surface density follows naturally. Gravitational dynamics arise from a continuous coupling between baryonic surface density and an offset acceleration term. The model recovers Newtonian and relativistic behavior in the weak-field limit without introducing dark matter particles, additional forces, or new degrees of freedom.