Postnikov–Reiner–Williams subdivision conjecture for gamma-vectors

Let $\Delta$ and $\Delta'$ be flag homology spheres, and suppose that $\Delta'$ geometrically subdivides $\Delta$. Let $\gamma(\Delta)$ and $\gamma(\Delta')$ denote their gamma-vectors. Postnikov–Reiner–Williams conjecture. The gamma-vector of $\Delta'$ is entry-wise greater than or equal to the gamma-vector of $\Delta$. This is proposed as a natural extension of Gal's conjecture and is open in the source.