Connectivity conjecture for zero-sumfree complexes

Let $\Delta_{n,\ell}$ be the simplicial complex of $\ell$-zero-sumfree subsets. Regard it as connected when for any two vertices there is a sequence of vertices joining them through edges of the complex. Connectivity conjecture. For every $n>2\ell$, the complex $\Delta_{n,\ell}$ is connected. This conjecture predicts connectivity for a broad parameter range and was motivated by computational evidence; the source gives no resolution status.