Empirical Test of Asymptotic Predictions of Projective Gravity Theory for Galaxies and Clusters

An empirical test of two key asymptotic predictions of the theory interpreting observed gravity as a projection of a fundamental geometry (AB-tomography) is presented. The theory predicts: 1) for spiral galaxies – a relation mpred to the plateau velocity Vflat, resulting in an observably flat rotation curve; 2) for galaxy clusters – a quantitative relation δpred to the velocity dispersion σg. Using a sample of 85 galaxies (SPARC), it is confirmed that all objects with a calculated mpred exhibit the predicted flat asymptotic. For 15 clusters, direct comparison of δpred with independent gravitational lensing data shows agreement within 1σ with a mean relative deviation of < 0.5%. The theory achieves agreement with observations without introducing hypothetical particles, using only observed kinematic quantities and fundamental constants.