Mutation invariance of unrestricted red size

Let $Q$ be a quiver and let $\mu_k(Q)$ denote the quiver obtained by mutation at vertex $k$. The unrestricted red size $\operatorname{uRed}(Q)$ is the minimum red size over general reddening sequences of $Q$. Mutation-invariance conjecture. The unrestricted red size is mutation invariant:

$$\operatorname{uRed}(Q)=\operatorname{uRed}(\mu_k(Q))$$

for any $k$. This conjecture concerns the potential mutation invariance of the unrestricted red number; unlike the unrestricted red size, the existence of a maximal green sequence is not mutation invariant.