Andruskiewitsch–Angiono–Heckenberger finite-root-system conjecture for Nichols algebras

Let $\Gamma$ be an abelian finitely generated group, let $V$ be a Yetter–Drinfeld module of diagonal type over $\Gamma$, and let $\mathfrak{q}\in(\Bbbk^\times)^{\theta\times\theta}$ be the matrix describing its braiding. Write $\mathscr{B}_{\mathfrak{q}}$ for the Nichols algebra of $V$, and let $\varDelta^{\mathfrak{q}}$ be its root system. Finite-root-system conjecture. If

$$\operatorname{GKdim}\mathscr{B}_{\mathfrak{q}}<\infty,$$

then the root system $\varDelta^{\mathfrak{q}}$ is finite. This conjecture concerns the classification of diagonal-type Nichols algebras of finite Gelfand–Kirillov dimension and is attributed in the source to the authors cited there; the supplied text gives no evidence that it has been resolved.