Artin's conjecture on birational classes of noncommutative surfaces

Let $A$ be a connected graded domain with $\operatorname{GKdim}(A)=3$, and let

$$D=D_{\operatorname{gr}}(A)$$

be its graded quotient division ring. Artin's conjecture. One of the following holds:

1. $D$ is finite-dimensional over a central commutative subfield of transcendence degree $3$.
2. $D$ is a division ring of fractions of a skew polynomial extension of $\Bbbk(X)$, for a commutative curve $X$.
3. $D\cong D_{\operatorname{gr}}(S)$ for a three-dimensional Sklyanin algebra $S$.

The conjecture concerns the classification of birational classes of noncommutative integral projective surfaces. The supplied text gives no resolution, so it remains open here.