Informational Physics, Vallejos Unit, Bullet Cluster, Dark Matter Alternative, Non-linear Field Theory, Quantum Gravity, Vacuum Saturation.

Informational Saturation Action: A Covariant Framework for Galactic Dynamics and the Bullet Cluster Lag This paper presents the formal mathematical development of the Informational Saturation Action, a non-linear covariant field theory that accounts for large-scale gravitational anomalies without the necessity of non-baryonic dark matter. Building upon foundational principles of informational physics, this work introduces an exponential-type Action regulated by the Vallejos Unit (V), defined as the vacuum's saturation action density ($J \cdot s \cdot m^{-3}$). This unit establishes a fundamental hierarchy scale where $V \gg \hbar$, explaining why General Relativity remains remarkably accurate at Solar System scales while diverging at galactic and extragalactic accelerations. Key Technical Highlights: Action Formalism: Derivation of a self-limited Lagrangian that prevents mathematical singularities through an asymptotic saturation mechanism. Energy-Momentum Tensor: Explicit derivation of a symmetric and locally conserved tensor ($\nabla^\mu T_{\mu\nu} = 0$) that incorporates the informational inertia of the vacuum. Bullet Cluster Resolution: The observed 35 kpc offset between baryonic matter and the gravitational potential is mathematically derived as a finite relaxation time ($\tau$) of the saturated informational network. Observational Consistency: The model is shown to be consistent with gravitational wave speed measurements ($c_{GW} = c$) and preserves the Strong Equivalence Principle in the local regime. This framework represents a rigorous unification between vacuum information capacity and macroscopic dynamics, proposing that "dark gravity" is an emergent effect of hysteresis and saturation within the informational substrate of spacetime.