The zero dual-entropy Möbius disjointness conjecture

Let $A\subseteq\mathbb{N}$, let $1_A$ be its indicator function, let $\AE^*(A)$ denote the dual entropy of $A$, and let $\mu$ be the Möbius function. Zero dual-entropy Möbius disjointness conjecture. If $\AE^*(A)=0$, then

$$\lim_{N\to\infty}\frac{1}{N}\sum_{n=1}^N1_A(n)\mu(n)=0.$$

This is proposed as a dual-entropy analogue of the zero-anqie-entropy reformulation of Sarnak's conjecture; the paper presents it as a belief rather than a proved result.