Red-path realization conjecture for maximal green sequences

Let $\mathcal{A}$ be an abelian length category of finite rank. A red path is a path in the wall and chamber structure of $\mathcal{A}$ satisfying the red-path conditions used to induce maximal green sequences. A maximal green sequence is a maximal sequence of torsion classes arising from the corresponding wall-crossing process.

Red-path realization conjecture. Every maximal green sequence in $\mathcal{A}$ is induced by a red path in the wall and chamber structure of $\mathcal{A}$.

The preceding results show that every red path inducing a maximal green sequence satisfies the first two conditions of a $\mathfrak{D}$-generic path, while an external result states that every maximal green sequence is induced by a $\mathfrak{D}$-generic path. The conjecture asks whether such a sequence can always be realized specifically by a red path.