Cancellation conjecture for finitely generated prime algebras

Let $\Bbbk$ be a field of characteristic zero, and let $A$ be a noetherian finitely generated prime algebra. An algebra $A$ is cancellative if, for every algebra $B$, an isomorphism $A[t]\cong B[t]$ implies $A\cong B$.

Cancellation conjecture.

1. If $\operatorname{GKdim} Z(A)\leq 1$, then $A$ is cancellative.
2. If $\operatorname{GKdim} A=3$ and $A$ is not PI, then $A$ is cancellative.

These assertions generalize the preceding cancellation results for AS-regular algebras. Their status is not specified in the source.