Noncommutative Kato distinguished-triangle conjecture

Let $A^{\bullet}$ be a DG algebra over $\mathbb{Z}$. Let $CP^{\mathcal{D}}_{\bullet}(A^{\bullet}\otimes\mathbb{C})^\iota$ be its Deligne-type periodic cyclic complex with involution, and define

$$K'_{\bullet}(A^{\bullet})_{\mathbb{R}}=\left(K_{\bullet}(C^{\mathrm{pspf}}(A^{\bullet}))\otimes\mathbb{R}\right)^*.$$

The regulator and dual regulator are maps from algebraic $K$-theory through this complex.

Noncommutative distinguished-triangle conjecture. There is a natural distinguished triangle

$$K^{\bullet}(A^{\bullet})\otimes\mathbb{R}\xrightarrow{r}CP^{\mathcal{D}}_{\bullet}(A^{\bullet}\otimes\mathbb{C})^\iota\xrightarrow{r^*}K'_{\bullet}(A^{\bullet})_{\mathbb{R}}[1]\longrightarrow$$

where $r$ and $r^*$ are the regulator and dual regulator maps.

This is the proposed noncommutative analogue of the distinguished triangle for varieties, using periodic cyclic homology and the dual of algebraic $K$-theory. The source gives no resolution of the assertion.