The Radial Acceleration Relation from Holographic Entropy Displacement, with Predictions for Galaxy Clusters

The radial acceleration relation (McGaugh et al. 2016) tightly correlates baryonic and dynamical accelerations in galaxies, but its form ν(x) = 1/(1 − e−√x) has been unexplained. We derive it from the holographic principle, Gauss's law, and canonical occupation statistics: the filling fraction is the response of a single screen mode with a heavy-tailed occupation of index 1/2, and the square-root exponent is fixed by the mixing class, parameter-free. Extended to clusters through an effective mode count, it predicts the cluster mass excess correlates with X-ray morphological disturbance at fixed mass — distinguishing it from ΛCDM and particle MOND. Keywords: radial acceleration relation, MOND, galaxy dynamics, dark matter, emergent gravity, holographic principle, galaxy clusters, modified gravity, astro-ph.GA, gr-qc