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

This work introduces a formal framework for the Universal Informational Net, a non-linear covariant field theory that accounts for galactic-scale gravitational anomalies without the necessity of non-baryonic dark matter. By implementing a logarithmic self-interaction potential, the theory establishes a dynamic vacuum saturation that eliminates central singularities (the core-cusp problem) and analytically derives the Baryonic Tully-Fisher Relation (BTFR). Key Technical Milestones: Vainshtein-like Screening Mechanism: A conformal coupling $A(\Phi) = \exp(\Phi/\Phi_{crit})$ is introduced to ensure the recovery of General Relativity in high-density environments, satisfying Solar System constraints with a precision of $10^{-12}$. Cluster Dynamics and Lensing: Utilizing a finite vacuum relaxation timescale $\tau \approx 3.4 \times 10^{14}$ s, the model explains observed spatial offsets in merging clusters (e.g., the Bullet Cluster). Quantitative Falsifiability: The framework provides a specific numerical "litmus test": in cluster mergers at $1000$ km/s, the spatial offset between the baryonic centroid and the gravitational lensing peak must be exactly $\approx 35$ kpc. Holographic Foundation: The saturation constant $\lambda$ is directly linked to Bekenstein-Hawking entropy bounds and zero-point vacuum energy, bridging the gap between galactic dynamics and fundamental quantum gravity principles. This Version represents the definitive state of the theoretical framework, offering a robust, testable, and mathematically consistent alternative to the $\Lambda$CDM paradigm.