Universal Saturation of the Informational Net: A Non-Linear Covariant Field Theory of Vacuum Coherence and Galactic Kinematics

We present a covariant non-linear field theory where galactic-scale gravitational anomalies emerge from the saturation dynamics of an informational vacuum field. By postulating a logarithmic self-interaction potential, the theory removes central singularities (core-cusp solution) and predicts the Baryonic Tully-Fisher Relation (BTFR) as an asymptotic limit. The framework introduces a finite vacuum relaxation timescale ($\tau$) to account for gravitational lensing offsets in cluster collisions (Bullet Cluster) without dark matter particles. The saturation constant ($\lambda$) is interpreted through holographic entropy limits and linked to the cosmological constant ($\Lambda$), anchoring galactic dynamics to global vacuum topology.