Enclosed mass does not determine a disc rotation curve

The spherical shell theorem yields $v_c^2=GM(<r)/r$ only in spherical geometry. A razor-thin axisymmetric disc instead requires $v_c^2=R{\partial }_R\Phi (R,0)$, including forces from exterior annuli. The interior gravitational force of an exterior thin ring gives a concrete counterexample with identical enclosed mass but different circular speeds.