Logarithmic Chowla conjecture

Let $\lambda$ be the Liouville function. For every $t\in\mathbb{N}$ and every collection of distinct natural numbers $h_1,\ldots,h_t$, logarithmic Chowla conjecture. One has

$$\lim_{N\rightarrow\infty}\mathbb{E}^{\log}_{n\leq N}\lambda(n+h_1)\cdots\lambda(n+h_t)=0.$$

This is the logarithmically averaged Chowla correlation statement and is asserted in the source to be equivalent to the $t$-Fourier uniformity conjecture for every $t$. The general statement remains open.