The scaling procedure that identifies the topological phase transitions is based on the divergence of the curvature function. It is an iterative procedure that, for a given parameter set M that controls the topology, searches for a new parameter set M ′ ′ that satisfies F ( k 0 , M ′ ′ ) = F ( k 0 + δ δ k , M ) , where k 0 is a high-symmetry point and δ δ k is a small deviation away from it. This procedure searches for the path in the parameter space of M along which the divergence of the curvature function reduces, yielding a renormalization group flow that flows away from the topological phase transitions. The name "curvature renormalization group" is derived precisely from this procedure that renormalizes the profile of the curvature function. Writing d M i = M i ′ ′ − − M i and δ δ k j 2 ≡ ≡ d l , and expanding the scaling equation above to leading order yields the generic renormalization group equation