Injective-dimension conjecture for the Jacobson radical of an Artin algebra

Let $A$ be an Artin algebra, let $J$ denote its Jacobson radical, and write $\operatorname{gldim}(A)$ for its global dimension and $\operatorname{id}(J)$ for the injective dimension of $J$. Injective-dimension conjecture. One has

$$\operatorname{id}(J)=\operatorname{gldim}(A).$$

The paper proves this when $A$ has finite global dimension and in some other cases; the assertion is presented as open in general.