Finite Quillen-Lichtenbaum dimension for smooth complex-linear stable infinity-categories

Let $\mathcal{A}$ be a smooth $\mathbb{C}$-linear stable $\infty$-category. The finite Quillen-Lichtenbaum dimension conjecture. Then

$$\dim_{\mathrm{QL}}\mathcal{A}<\infty.$$

Here $\dim_{\mathrm{QL}}\mathcal{A}$ is the least integer $d\geq 0$ for which the algebraic-to-topological K-theory comparison with coefficients modulo every $m\geq 1$ is an isomorphism for $n\geq d-1$ and a monomorphism for $n=d-2$. The source poses finiteness as a conjecture for smooth categories, while finiteness for arbitrary complex-linear stable $\infty$-categories is posed as a question.