The diffeomorphism conjecture for the moment-angle manifold associated to $K$

Let $K$ be the simplicial sphere considered above, and let $\mathcal{Z}_{K}$ be its moment-angle manifold. Proposition 1 gives a connected sum of products of spheres with a cohomology ring isomorphic to that of $\mathcal{Z}_{K}$.

Diffeomorphism conjecture. $\mathcal{Z}_{K}$ is diffeomorphic to the connected sum of sphere products in Proposition 1.

For moment-angle manifolds corresponding to simplicial $2$-spheres, an isomorphism of the cohomology ring with that of a connected sum of sphere products implies diffeomorphism to that connected sum. The conjecture asks whether the same conclusion holds for this particular moment-angle manifold; no resolution is given here.