Frantzikinakis's logarithmic Chowla conjecture along Beatty sequences

Let $k\geqslant 1$ be an integer, and let $\alpha_1,\ldots, \alpha_k>0$ be such that $1,\alpha_1,\ldots, \alpha_k$ are linearly independent over $\mathbb{Q}$. For multiplicative functions $f_1,\ldots, f_k:\mathbb{N}\to [-1,1]$, write

$$\mathbb{E}_{n\leqslant X}^{\log} g(n):=\frac{1}{\sum_{n\leqslant X}1/n}\sum_{n\leqslant X}\frac{g(n)}{n}.$$

Frantzikinakis's conjecture. For any such multiplicative functions, one has

$$\lim_{X\to \infty}\mathbb{E}_{n\leqslant X}^{\log}\prod_{i=1}^k f_i(\lfloor \alpha_i n\rfloor)=\prod_{i=1}^k \lim_{X\to \infty}\mathbb{E}_{n\leqslant X}^{\log}f_i(n).$$

In particular,

$$\lim_{X\to \infty}\mathbb{E}_{n\leqslant X}^{\log}\lambda(\lfloor \alpha_1 n\rfloor)\cdots \lambda(\lfloor \alpha_k n\rfloor)=0.$$

This is a logarithmic correlation analogue of Chowla's conjecture for the Liouville function along Beatty sequences, extending the known length-one cancellation result. The source describes it as an open problem posed by Frantzikinakis; the displayed claim concerns arbitrary multiplicative functions and the Liouville special case.