The A2 obstruction conjecture for reddening sequences

Let $Q$ be a quiver of rank at least $4$, and let $[A_2]$ denote the finite-type $A_2$ quiver. Say that $[A_2]$ embeds into the mutation class of $Q$ when it occurs there under the paper's embedding notion. A reddening sequence is a mutation sequence with the usual reddening condition, and the coframed quiver is the framed quiver obtained by reversing the framing arrows. A2 obstruction conjecture. If $[A_2]$ does not embed into the mutation class of $Q$, then every reddening sequence for $Q$ produces the coframed quiver. This is supported in the paper by the stated results for abundant acyclic quivers and keys. The conjecture addresses whether the absence of an $A_2$ configuration forces every reddening sequence to have trivial associated permutation; no resolution is supplied.