Möbius support conjecture for base polymatroids

Given a polymatroid $\mathscr{P}\subset\mathbb{N}^p$, let $\mathscr{P}_{\leq}$ and the poset $\Gamma=\Gamma(\mathscr{P})$ be defined as in the source, with largest element $\hat{1}$ and smallest element $\hat{0}$. Define the Möbius support by

$$\mu\text{-supp}(\mathscr{P})=\left\{\mathbf{u}\in\mathscr{P}_{\leq}\mid \mu_{\Gamma}(\mathbf{u},\hat{1})\neq0\right\}.$$

Möbius support conjecture. For any base polymatroid $\mathscr{P}$, the Möbius support $\mu\text{-supp}(\mathscr{P})$ is a generalized polymatroid. The theorem preceding this conjecture proves the assertion for linear polymatroids; the conjecture proposes the extension to all polymatroids.