The dual cross-number conjecture for long zero-sumfree sequences

Let $G$ be a finite Abelian group with longest possible decomposition

$$G\simeq C_{\nu_1}\oplus\dots\oplus C_{\nu_s},$$

where $\nu_i>1$ for every $i\in\llbracket1,s\rrbracket$. Given a zero-sumfree sequence $S$ in $G$ with cross number at least $\mathsf{k}^*(G)$, one has

$$\lvert S\rvert\leq\sum_{i=1}^s(\nu_i-1).$$

Dual cross-number conjecture. A zero-sumfree sequence whose cross number is at least the lower bound $\mathsf{k}^*(G)$ has length at most the corresponding maximal lower-bound length.

This is proposed as a dual version of the cross-number conjecture, concerning the maximal length of a zero-sumfree sequence with large cross number. The source gives no resolution status.