Quantization conjecture for the conformal energy of simplicial Willmore spheres

Let $W$ denote the conformal energy of a simplicial Willmore sphere. Quantization conjecture. The conformal energy is quantized:

$$W=2\pi N,\quad N\in {\mathbb N}.$$

This conjecture is motivated by numerical experiments and by the relationship between conformal energy minimization and inscribability of simplicial spheres. The supplied source does not state a resolution.