Voevodsky's slice-filtration conjecture for infinite loop spaces

Let $k$ be a perfect field. Write $\mathcal{SH}(k)$ for the motivic stable homotopy category and $\mathcal{SH}^{S^1}(k)$ for the $S^1$-stable motivic homotopy category. Let $\omega^{\infty}$ denote the functor from motivic spectra to $S^1$-spectra, and let the slice filtrations on these categories be given by the stages $f_q$. Voevodsky's slice-filtration conjecture. The functor

$$\omega^{\infty}:\mathcal{SH}(k)\longrightarrow\mathcal{SH}^{S^1}(k)$$

respects the slice filtration. This conjecture concerns compatibility between the stable motivic slice filtration and its $S^1$-stable counterpart. The source states that it was proved by Levine.