The finite-root-system conjecture for Nichols algebras of diagonal type

Let $V$ be a braided vector space of diagonal type, and let $\mathscr{B}(V)$ be its Nichols algebra. The root system of $\mathscr{B}(V)$ is the root system arising from its restricted PBW basis and associated Weyl groupoid. Finite-root-system conjecture. If $\mathscr{B}(V)$ has finite Gelfand--Kirillov dimension, then its root system is finite.

This conjecture relates the growth of Nichols algebras of diagonal type to the finiteness of their Weyl-groupoid root systems. The converse implication follows from a routine argument involving a PBW basis, but the stated implication remains open.