Bucher–Machacek's mutation-invariance conjecture for unrestricted red size

Let $Q$ be a quiver, and let $\operatorname{uRed}(Q)$ denote its unrestricted red size, namely the maximal number of red vertices obtained after an arbitrary mutation sequence. Two quivers are mutation-equivalent if one can be obtained from the other by a sequence of quiver mutations. Bucher–Machacek's mutation-invariance conjecture. The unrestricted red size is invariant under mutation; equivalently, mutation-equivalent quivers have the same unrestricted red size.

This conjecture generalizes mutation-invariance of admitting a reddening sequence. The supplied status evidence resolves part (3) of the preceding connected-quiver conjecture, but does not state that this mutation-invariance claim itself has been proved, so it remains open.