The semisimplicity conjecture for three-variable invertible Calabi–Yau LG pairs

Let $W$ be an invertible Calabi–Yau polynomial in three variables, and let $(W,G)$ be an admissible Landau–Ginzburg pair. Semisimplicity conjecture for three-variable Calabi–Yau LG pairs. The LG A-model theory of $(W,G)$ is either generically semisimple or equivalent to the LG A-model theory of a Fermat Calabi–Yau pair

$$\left(W=x_1^{a_1}+x_2^{a_2}+x_3^{a_3},\langle J_W\rangle\right).$$

This conjecture would reduce the Virasoro problem for these Calabi–Yau pairs to generically semisimple theories and specified Fermat cases. It is stated as a reduction principle in the source and remains open in the generality given.