Kontsevich's smooth DG algebra degeneration conjecture

Let $A$ be a smooth DG algebra. Let $\operatorname{ch}:K_0(A\otimes A^{op})\to (HH_{\bullet}(A)\otimes HH_{\bullet}(A^{op}))_0$ be the Chern character, and let $\delta:HH_{\bullet}(A^{op})\to HC^-_{\bullet}(A^{op})[1]$ be the indicated map. Kontsevich's smooth degeneration conjecture. The composition

$$K_0(A\otimes A^{op})\xrightarrow{\operatorname{ch}}(HH_{\bullet}(A)\otimes HH_{\bullet}(A^{op}))_0\xrightarrow{\operatorname{id}\otimes\delta}(HH_{\bullet}(A)\otimes HC^-_{\bullet}(A^{op}))_1$$

vanishes on the class $[A]$ of the diagonal bimodule. This is the dual proposed generalization of categorical Hodge-to-de Rham degeneration for smooth DG algebras; the paper states that it is disproved together with the proper version.