Brieskorn spheres bound orbit spaces of torus manifolds

We construct a smooth, equivariantly formal, simply connected torus $8$-manifold over a contractible $4$-manifold with the boundary a Brieskorn homology $3$-sphere having a nontrivial fundamental group. We prove extension to a torus graph for GKM graphs of GKM${}_4$ manifolds in complexity $2$, and $3$ under a finite fundamental group assumption (that is not satisfied, in general).