Nonexistence of finite-dimensional DG algebra phantoms

Let $\mathscr R$ be a smooth finite-dimensional DG algebra, and let $\mathscr{P}\!\mathit{erf}\!\operatorname{--}\mathscr R$ denote its DG category of perfect modules. A phantom is a smooth and proper DG category with trivial Hochschild homology and vanishing $K_0$. Nonexistence conjecture for DG algebra phantoms. There are no phantoms of the form

$$\mathscr{P}\!\mathit{erf}\!\operatorname{--}\mathscr R.$$

The source discusses the existence of geometric phantoms but suggests that quasi-phantoms and phantoms arising from smooth finite-dimensional DG algebras should not exist; no resolution is given.