Minuscule distributive-lattice mCDE conjecture

Let $P$ be a minuscule poset, and let $J(P)$ denote its distributive lattice of order ideals.

Minuscule mCDE conjecture. The distributive lattice $J(P)$ is mCDE.

The preceding theorem establishes the weaker CDE property for $J(P)$, and the paper reports that all classified minuscule cases checked are in fact mCDE. The conjecture asks for this stronger property for every minuscule poset.