The additive reachability conjecture

Let $\mathcal{C}$ be the stable category of the Frobenius category $\mathcal{F}$, let $T$ be a cluster-tilting object, let $\Sigma$ denote the suspension, and let $\mathcal{E}(\mathcal{C})$ be the exchange graph of cluster-tilting objects. Additive reachability conjecture. If there is a path in $\mathcal{E}(\mathcal{C})$ connecting $T$ and $\Sigma T$, then $\mathcal{E}(\mathcal{C})$ has exactly one connected component. This is the additive form of reachability: the stated hypothesis is equivalent to injective reachability, while the conjectured connectedness of the exchange graph remains unresolved in general.