Stanley's classification conjecture for indecomposable upho modular lattices

Let $P$ be an upho modular lattice, meaning that $P$ is of finite type and its principal order filter at every element is isomorphic to $P$. Suppose that $P$ is indecomposable and contains a complemented interval of rank $3$. Stanley's classification conjecture. Then $P$ is isomorphic to the poset of submodules of $R^d$ of finite colength, ordered by reverse inclusion, for some local principal ideal domain $R$ with a finite residue field. This conjecture proposes that, apart from decomposable cases, these module posets account for upho modular lattices containing a complemented rank-$3$ interval; the paper records the conjecture but does not discuss its proof or status.