Goodearl's conjecture on Jacobson radicals of affine algebras of GK-dimension 2

Let $R$ be an associative algebra over a field ${\mathbb K}$ generated by a finite-dimensional subspace, so that $R$ is an affine algebra. Its Gelfand–Kirillov dimension measures the growth of the dimensions of powers of a finite-dimensional generating subspace. The Jacobson radical $J(R)$ is the largest ideal of $R$ all of whose elements are quasi-regular, where an element $x$ is quasi-regular if there exists $y\in R$ such that $x+y+xy=0$. An ideal is nil if each of its elements is nilpotent.

Goodearl's conjecture. If $R$ is an affine algebra of GK-dimension $2$, then its Jacobson radical $J(R)$ is nil.

This conjecture concerns the expected structural restrictions on affine algebras of low finite Gelfand–Kirillov dimension, relating growth to the behavior of the Jacobson radical. The supplied source does not state whether the conjecture has been resolved.