Zhao's conjecture on the midpoint bound for exact-length zero-sum constants

Let $G$ be a finite abelian group, let $\exp(G)$ denote its exponent, and let $\mathsf{D}(G)$ denote its Davenport constant. Let $\mathsf{s}_{k\exp(G)}(G)$ be the smallest length forcing a zero-sum subsequence of length $k\exp(G)$. Zhao's conjecture. If $k\exp(G)\in[(\mathsf{D}(G)+1)/2,\mathsf{D}(G)]$, then

$$\mathsf{s}_{k\exp(G)}(G)\leq 2\mathsf{D}(G)-1.$$

If $k\exp(G)<(\mathsf{D}(G)+1)/2$, then

$$\mathsf{s}_{k\exp(G)}(G)>2\mathsf{D}(G)-1.$$

This conjecture proposes a sharp midpoint transition for the exact-length zero-sum invariant, building on the preceding bounded-length conjectures and known lower bounds.