The type I conjecture for maximal distinct sum-free subsets

Let $G$ be a type $I$ abelian group of order $n$. Write $f^\star_{\max}(G)$ for the number of maximal distinct sum-free subsets of $G$, and let $\mu(G)$ denote the maximum density of a sum-free subset of $G$. The type I maximal distinct sum-free subset conjecture.

$$f^\star_{\max}(G)=2^{\mu(G)/2+o(n)}.$$

The conjecture predicts the asymptotic count for maximal distinct sum-free subsets in type $I$ abelian groups. General upper bounds are known, but the matching lower-order asymptotic remains open in the source.