Gorensteinness conjecture for Rees algebras of ideals

Let $A$ be a Cohen–Macaulay local ring that is a homomorphic image of a Gorenstein local ring. Let $I\subsetneq A$ be an ideal with $\operatorname{ht}_A I\ge 2$, and let $\mathcal{R}(I)$ denote the Rees algebra of $I$.

Gorensteinness conjecture. If $\mathcal{R}(I)$ is an almost Gorenstein graded ring, then $A$ is a Gorenstein ring.

This conjecture asks whether the almost Gorenstein graded property of the Rees algebra forces the underlying Cohen–Macaulay local ring to be Gorenstein. The source states that it remains open; the theorem proved there establishes the corresponding result for Rees algebras of certain parameter ideals.