Red-size conjectures for connected quivers without reddening sequences

Let $Q$ be a connected quiver, let $V(Q)$ be its vertex set, and suppose that $Q$ does not admit a reddening sequence. A general maximal green sequence is a mutation sequence resulting in one remaining green vertex, while a general reddening sequence is the corresponding unrestricted notion. Red-size conjecture. The source proposes the following versions, from weakest to strongest:

1. $\operatorname{Red}(Q)=|V(Q)|-1$.
2. $\operatorname{Red}(Q)=|V(Q)|-1$, and every vertex of $Q$ is the last remaining green vertex after some general maximal green sequence.
3. $\operatorname{uRed}(Q)=|V(Q)|-1$.
4. $\operatorname{uRed}(Q)=|V(Q)|-1$, and every vertex of $Q$ is the last remaining green vertex after some general reddening sequence.

These conjectures assert that connected quivers without reddening sequences can nevertheless be mutated to sequences with only one remaining green vertex. The paper states that even the weakest version implies mutation invariance of unrestricted red size and focuses on establishing special cases; the conjectures are not resolved in the supplied text.