Generalized Sarnak conjecture for non-pretentious multiplicative functions

Let $\mathbb{D}$ be the closed unit disc, and call a sequence $a:\mathbb{N}\to\mathbb{D}$ deterministic if it is generated by a continuous observable on a zero-entropy topological dynamical system. Let $f:\mathbb{N}\to\mathbb{D}$ be a non-pretentious multiplicative function. Generalized Sarnak conjecture. There exists a set $\mathcal{X}\subset\mathbb{N}$ with upper logarithmic density $\delta^+_{\log}(\mathcal{X})=1$ such that for every deterministic sequence $a$,

$$\lim_{\substack{x\to\infty\x\in\mathcal{X}}}\frac1x\sum_{n\le x}f(n)a(n)=0.$$

This is a sparse-scale orthogonality statement; the supplied text gives no resolution status.