Conjecture on Weyl groupoids for cyclic-group Nichols algebras

Let $C_n$ be the cyclic group of order $n$, and let $\mathcal{B}_{C_n}$ denote the Nichols algebra with the braiding considered in the paper. Weyl-groupoid conjecture. The Weyl groupoid associated with the braiding of $\mathcal{B}_{C_n}$ is defined only when $n$ is prime or $n=4$. Computations for $n\leq 1000$ support this assertion, while the general statement remains unproved in the source.