Universal Scaling of the Gravitational Potential in Galaxy Systems: Empirical Verification

We present a direct empirical test of the fundamental law linking the observedbaryonic dynamics to the gravitational potential in bound systems. Based on an extended sample of 25 galaxy clusters and a consolidated sample of 10,000 low-mass galaxy groups (Yang Group Catalog, SDSS DR16), we demonstrate that the asymptotic relation δ = 4(σ/c)^2 holds across nearly two orders of magnitude in δ (from ∼ 8×10^−7 to ∼ 7×10^−5). The combined analysis yields a global agreement with the prediction at the level of ∼ 0.04% (⟨δobs/δpred⟩ = 1.00039 ± 0.00036). Data from weak gravitational lensing (KiDS-1000) and X-ray density profiles are in full agreement with this prediction. This result, which contains no free parameters, shows that the gravitational potential in collective systems is uniquely determined by the observed velocity dispersion. The exceptional precision of this law corresponds to a level of agreement that would require parameter tuning at ∼ 7σ in standard cosmological models, confirming its fundamental nature and the predictions of the AB-tomography formalism.[1, 2]