Chowla's conjecture for Liouville correlations

Let $\lambda$ denote the Liouville function, and let $H=\{h_1,\ldots,h_d\}$ be a non-empty set of non-negative integers. Chowla's conjecture. The correlation of the Liouville function along the shifts in $H$ satisfies

$$\lim_{x\to\infty}\frac{1}{x}\sum_{n\leqslant x}\lambda(n+h_1)\cdots\lambda(n+h_d)=0.$$

This is a central problem concerning higher-order correlations of the Liouville function and remains open in general, although the paper studies recent partial results in this direction.