The minimal mutation-infinite quiver conjecture for bounded exchange-graph components

Let $Q$ be a minimal mutation-infinite quiver. Let $\widehat{\Psi}(Q)$ denote the subgraph associated with quivers admitting maximal green sequences, as in Theorem~. Minimal mutation-infinite quiver conjecture. The results of Theorem~ hold for all minimal mutation-infinite quivers. The rank-four result is expected to extend to higher-rank minimal mutation-infinite quivers, but checking the quivers bounding the relevant component becomes substantially more difficult; the paper notes that even a rank-seven example requires checking at least 1200 quivers.