Kaledin-Efimov generalized degeneration conjecture for DG categories

Let $\mathcal B$ and $\mathcal C$ be small DG categories over a field $\mathrm k$ of characteristic zero. Let $\operatorname{ch}:K_0(\mathcal B\otimes\mathcal C)\to (HH_{\bullet}(\mathcal B)\otimes HH_{\bullet}(\mathcal C))_0$ be the Chern character, and let $\delta:HH_{\bullet}(\mathcal C)\to HC^-_{\bullet}(\mathcal C)[1]$ be the indicated map. Generalized degeneration conjecture. The composition map

$$\varphi_0:K_0(\mathcal B\otimes\mathcal C)\xrightarrow{\operatorname{ch}}(HH_{\bullet}(\mathcal B)\otimes HH_{\bullet}(\mathcal C))_0\xrightarrow{\operatorname{id}\otimes\delta}(HH_{\bullet}(\mathcal B)\otimes HC^-_{\bullet}(\mathcal C))_1$$

is zero. This conjecture was proposed for arbitrary small DG categories and is stronger than the smooth and proper cases; the paper's counterexample to generalized degeneration refutes it.