Subdivision conjecture for moment polyhedra of Kac–Moody flag varieties

Let $G$ be a Kac–Moody group of finite rank, and let $c$ be a Coxeter element. Write $\Phi_T(G/B)$ for the moment polyhedron of the Kac–Moody flag ind-scheme $G/B$, and let $X_w^{wc}$ denote the corresponding Richardson variety whenever $wc$ is length-additive.

Subdivision conjecture. The moment polyhedron $\Phi_T(G/B)$ has a locally finite subdivision into Bruhat interval polytopes

$$\{\Phi_T(X_w^{wc}): wc\text{ length-additive}\}.$$

This proposes a Kac–Moody analogue of the finite-type subdivision results for permutahedra and Lusztig varieties. Since the source presents it as a conjectural statement and supplies no resolution evidence, its status is open.