note that the Standard Model fermion fields (including the right handed neutrinos) come from all three [ SO (10) F × U (1) B ]/ Z 4 representations. In particular, they happen to be the 10 1 of 16 1, the 5 ¯ ¯ − − 3 of 10 −2 and the 1 5 of 1 4 (apologies to the readers for mixing up SO (10) × U (1) notation with SU (5) × U (1) notation, but it would be really cumbersome if we have to spell out which group any given notation happens to refer to. It is left up to the reader to determine the group from the context. This is a standard practice in the GUT model building literature anyway).