In this paper, we continue the study of blade arrangements and their induced positroidal subdivision in $\Delta_{k,n}$. A blade is a tropical hypersurface generated by a system of $n$ affine simple roots of $SL_n$ type with cyclic symmetry. Placing a blade in the center of the simplex induces its decomposition into $n$ largest cells, known as the Pitman-Stanley polytope.
We introduce the weighted blade arrangement complex $(B_{k,n},\partial)$ and prove that positive tropical Grassmann surjects to the upper component of the complex. Delta_{2,n-(k-2)}$ in $\Delta_{k,n}$ are (1) non-negative and (2) their support is weakly decoupled.
Finally, we introduce a hierarchy of basic weighted blade placements for all hypersimplices that are minimally closed under the boundary map $\partial$ and apply the result to the positive tropical Grassmann $\ Classify all rays in text{Trop}_ up to isomorphism. + G(3,n)$ $n\le 9$.
