Unitarity of supergravity and Z2 or Z2 x Z2 or Z2 x Z2 x Z2 gradings of gauge and ghost fields

Unitarity can be proven from the usual Z2 grading of gauge and ghost fields, or from a Z2 x Z2 grading, geometrically derived by Ne'eman and Thierry-Mieg, or from a Z2 x Z2 x Z2 grading derived here. The claim that only the Z2 x Z2 grading leads to unitarity is incorrect. The opposite is shown to hold: signs due to different gradings are physically unobservable. We show how the Z2 x Z2 grading follows from the Z2 grading by taking a product space