Density and openness of conical degeneracies for periodic Schrödinger operators

Let $V\in C^\infty(\mathbb{R}^3/\mathbb{Z}^3)$ be a smooth periodic potential, and consider the periodic Schrödinger operator $-\Delta_{\mathbb{R}^3}+V$. A degeneracy of its Bloch eigenvalues is called conical when the corresponding eigenvalue branches meet conically in quasi-momentum space. Conjecture. The set

$$\big\{ V \in C^\infty(\mathbb{R}^3/\mathbb{Z}^3): \ \text{all degeneracies of Bloch eigenvalues of } -\Delta_{\mathbb{R}^3}+V \text{ are conical }\big\}$$

is dense and open in $C^\infty(\mathbb{R}^3/\mathbb{Z}^3)$. This proposes that conical band crossings are the generic degeneracies for three-dimensional periodic Schrödinger operators, extending the paper's topology-driven genericity perspective to differential operators.