PL-manifold conjecture for the nerve of the meta-tree poset

For $n\ge 2$, let $MT(n)$ be the set of isomorphism classes of meta-trees with $n$ tails, and define a partial order $<$ on $MT(n)$ by declaring ${\bf T}<{\bf T}^{\prime}$ when there is a sequence from ${\bf T}$ to ${\bf T}^{\prime}$ in which each preceding meta-tree appears as a summand in the differential decomposition of the next with respect to the standard basis of $P_n$. Let $N(MT(n),<)$ denote the nerve of this partially ordered set. PL-manifold conjecture. The nerve $N(MT(n),<)$ is a PL-manifold with boundary, and the previously described homeomorphism between it and $FM_2(n)$ is a homeomorphism of PL-manifolds with boundary. The source presents this as a consequence of the preceding cell-decomposition conjecture and gives no resolution status.