Conjecture on an infinite family with few maximal sum-free subsets

Let $\mu(G)$ denote the relevant group parameter used in the paper, and let $f_{\max}(G)$ denote the number of maximal sum-free subsets of a finite abelian group $G$. Few maximal sum-free subsets conjecture. There is a sequence of finite abelian groups $\{G_i\}$ of increasing order such that, for every $i$,

$$f_{\max}(G_i) \leq 2^{\mu(G_i)/2.01}.$$

This conjecture proposes an infinite family for which the upper bounds in the preceding conjecture and in the paper’s related question are far from tight. The supplied context does not define $\mu(G)$ or give evidence of resolution.