$t$-Fourier uniformity conjecture for the Liouville function

Let $t\in\mathbb{N}$, let $G$ be a nilpotent Lie group of step $t$, let $\Gamma$ be a cocompact lattice in $G$, and let $F\colon G/\Gamma\rightarrow\mathbb{C}$ be continuous. Let $\lambda$ denote the Liouville function. $t$-Fourier uniformity conjecture. One has

$$\lim_{H\rightarrow\infty}\lim_{N\rightarrow\infty}\mathbb{E}^{\log}_{n\leq N}\sup_{g\in G}\left|\mathbb{E}_{h\leq H}\lambda(n+h)F(g^h\Gamma)\right|=0.$$

The source states that this conjecture is equivalent to the logarithmically averaged Sarnak conjecture for every natural number $t$, and also to the logarithmic Chowla conjecture. Its general status is open.