Vanishing of negative semi-topological K-groups for smooth proper dg-categories

Let $T$ be a smooth proper dg-category over $\mathbb{C}$, and let $\mathbf{K}^{\mathrm{st}}_i(T)$ denote its semi-topological K-groups. Vanishing conjecture.

$$\mathbf{K}^{\mathrm{st}}_i(T)=0\qquad\text{for all }i<0.$$

This is presented as a generalization of a known vanishing theorem for smooth proper dg-categories. The source gives no resolution status, so the conjecture remains open.