The finite GK-dimension conjecture for Nichols algebras of diagonal type

Let $(V,c)$ be a braided vector space of diagonal type over an algebraically closed field of characteristic zero, and let $\mathfrak{B}(V)$ denote its Nichols algebra. The finite GK-dimension conjecture. If

$$\operatorname{GKdim} \mathfrak{B}(V)<\infty,$$

then the generalized root system of $(V,c)$ is finite. This conjecture concerns the relationship between finite Gelfand–Kirillov dimension and finiteness of the root system; the source states that it was proved for $\dim V=2,3$, while the supplied status does not establish whether the general statement is resolved.