Semisimplicity conjecture for FJRW theory of two-variable invertible polynomials

Let $(W,G)$ be an admissible Landau–Ginzburg pair, where $W$ is an invertible polynomial with at most two variables and $G$ is an admissible group. Semisimplicity conjecture. The FJRW theory of $(W,G)$ is semisimple. The conjecture is the paper's main general claim for admissible pairs with at most two variables; the authors prove substantial cases, including simple singularities and almost all Fermat polynomials, while the full assertion remains open.