Tao's logarithmic Chowla conjecture

Let $\bm\mu$ denote the Möbius function. For integers $r\geq 0$, shifts $1\leq a_1<\dots<a_r$, and exponents $i_s\in\{1,2\}$ that are not all equal to $2$, consider the logarithmically weighted shifted correlations. Tao's logarithmic Chowla conjecture. For any such $r$, $a_1,\dots,a_r$, and exponents, we have

$$\sum_{1\leq n\leq N}\frac{\bm\mu^{i_0}(n)\bm\mu^{i_1}(n+a_1)\cdot\ldots\cdot\bm\mu^{i_r}(n+a_r)}{n}=o(\log(N)).$$

This is the logarithmic version of Chowla's conjecture and is used in the paper in connection with Tao's logarithmic results. The general assertion remains open in the source's presentation.