Numerical Evidence for Informational Vacuum Saturation as the Origin of Gravitational Lag in Galaxy Cluster Collisions.

This document provides a detailed numerical investigation that validates the Informational Saturation Action formalism by simulating galaxy cluster collisions. The objective is to demonstrate the underlying dynamical mechanism for the observed gravitational lag between baryonic matter and the effective gravitational potential. By solving non-linear field equations in a dynamical environment, this work contributes quantitative evidence that the vacuum—acting as an informational network with finite processing capacity regulated by the Vallejos Unit (V)—induces a finite relaxation time during potential reconfiguration. Key Research Highlights: Model Implementation: Solving reduced dynamical equations using an adaptive leapfrog integration scheme to ensure numerical stability in high-saturation regimes ($\Omega \geq 1$). Emergence of the 35 kpc Lag: Results show that the ~35 kpc offset observed in the Bullet Cluster arises naturally from the inertia of the coherence field, without the need for ad hoc tuning parameters. Sensitivity Analysis: The simulation demonstrates that the lag scales proportionally to the surface mass density ($\Delta x \propto \Sigma$), confirming the informational nature of the phenomenon. Post-Collision Stability: The simulation confirms that the system is causally stable, exhibiting a smooth decay of the lag without generating mathematical instabilities or shocks. This work constitutes the definitive numerical evidence supporting the elimination of dark matter as a necessary explanation for gravitational lensing offsets, proposing instead a vacuum informational saturation dynamic.