Han's conjecture on Hochschild homology and smoothness

Let $B$ be a finite-dimensional algebra over an algebraically closed field $k$. Write $\operatorname{HH}_n(B)$ for the Hochschild homology groups of $B$. The algebra $B$ is (homologically) smooth over $k$ when it is perfect as a bimodule over its enveloping algebra. Han's conjecture. If $\operatorname{HH}_n(B)$ is nonzero for only finitely many $n\in\mathbb{Z}$, then $B$ is (homologically) smooth over $k$. The conjecture is a classical statement for finite-dimensional algebras; this paper's abstract distinguishes it from the DG generalization, which the paper disproves. The supplied text does not state whether Han's original conjecture has been resolved.