Boundary-map reformulation of the Kontsevich–Soibelman conjecture

Let ${\mathcal A}$ be a smooth and compact DG category, and let $HH_{\bullet}({\mathcal A})$ and $HC^-_{\bullet}({\mathcal A})$ denote its Hochschild and negative cyclic homology. Let $\delta$ be the boundary map from the Hochschild-to-negative-cyclic long exact sequence. Boundary-map reformulation. The boundary map

$$\delta:HH_{\bullet}({\mathcal A})\to HC^-_{\bullet+1}({\mathcal A})$$

vanishes. This is explicitly presented as a reformulation of the Kontsevich–Soibelman conjecture, so it is not a separate mathematical conjecture; the original conjecture is open in the generality stated in the supplied text.