Costa–Mella–Pasotti–Pellegrini conjecture on zero-sum simple orderings

Let $(G,+)$ be an abelian group, and let $T$ be a finite subset of $G\setminus\{0\}$ such that no $2$-subset $\{x,-x\}$ is contained in $T$ and

$$\sum_{t\in T}t=0.$$

An ordering of the elements of $T$ is simple when its partial sums are all distinct and non-zero. Costa–Mella–Pasotti–Pellegrini conjecture. The set $T$ admits a simple ordering. This conjecture concerns zero-sum subsets in abelian groups and is motivated by the study of Heffter arrays. The source gives no resolution of the general case.