The Radial Acceleration Relation as a Consequence of Sub-threshold Substrate Equilibrium

The empirical Radial Acceleration Relation (McGaugh et al. 2016, PRL 117, 201101) is derived as a direct consequence of the UCM isothermal halo profile. The acceleration scale g† = 1.20 × 10⁻¹⁰ m/s² emerges without parameter adjustment. A rigorous six-variant circularity test demonstrates that this result is independent of the choice of core radius — the RAR transition is controlled by v_flat and baryonic mass, not by the halo profile details. The RAR is not a new law of nature but a statistical imprint of isothermal sub-threshold equilibrium.