The asymptotic count of maximal sum-free subsets in elementary abelian 5-groups

Let $k\bin\mathbb N$ and set $n:=5^k$. Write $f_{\max}(G)$ for the number of maximal sum-free subsets of a finite abelian group $G$. The elementary abelian 5-group conjecture.

$$f_{\max}(\mathbb Z^k_5)=3^{n/10+o(n)}.$$

This conjecture concerns the sharp asymptotic number of maximal sum-free subsets in $\mathbb Z^k_5$. Structural results on large sum-free subsets are known, but asymptotically exact bounds were not obtained in the source.