Generic non-degeneracy conjecture for spectral gap edges

Consider an elliptic periodic operator and vary its parameters, for example its periodic potential. Generic gap-edge non-degeneracy conjecture. For almost all such parameters, the edges of the spectral gaps are isolated in $k$-space and non-degenerate; equivalently, the dispersion relation has a parabolic shape at each gap edge. The claim concerns genericity rather than every operator; exceptional periodic operators can have non-isolated or degenerate gap edges.