Curvature continuity conjecture for PN-modified Catmull-Clark subdivision

Let a PN-modified Catmull-Clark subdivision be applied to a control mesh with control normals that are neither a constant vector nor zero. The subdivision surfaces produced by this process have curvature-continuous surfaces, and their extraordinary points need not be flat.

Curvature continuity conjecture. The PN-modified Catmull-Clark subdivision can generate curvature-continuous subdivision surfaces, and the extraordinary points of the resulting surfaces can be no longer flat when the control normals are not a constant vector nor vanish.

The paper states that this assertion is motivated by observed $C^2$ continuity and nonvanishing curvature at extraordinary points, but that a theoretical proof of $C^2$ continuity is not currently available.