Disentangling beyond-cohomology symmetry protected topological phases

We construct a three-dimensional locality preserving unitary operator which disentangles the ground state of the Walker-Wang three fermion model. We show that this locality preserving unitary operator cannot be a quantum circuit, or otherwise one could construct a commuting projector model which realizes a phase with nonzero chiral central charge, which is widely believed to be impossible. We comment on the relation to Many-body localized Floquet topological phases.