Stanley's toric g-vector conjecture for Gorenstein* meet-semilattices

Let $P$ be a Gorenstein meet-semilattice*, meaning a meet-semilattice with minimum element whose order complex after removing the minimum is Gorenstein*. Denote its toric $g$-vector by $g(P)$. Stanley's toric g-vector conjecture. The vector $g(P)$ is an $M$-sequence. In particular, $g(P)$ is nonnegative. The conjecture concerns the extension of the nonnegativity phenomenon for toric $g$-vectors from polytopes to Gorenstein* meet-semilattices; the paper constructs many nonpolytopal nonsimplicial examples with nonnegative toric $g$-vector, supporting the conjecture.