We note that there are additional species that have non-trivial representations under the non-Abelian groups of [*both*]{} the observable and hidden sectors. In order to avoid potential complications should any of these hidden sector groups undergo confinement we have not considered these in what follows.

From the selection rules given in [@Font:1989aj] it is possible to construct all possible dimension three (renormalizable) and dimension four (non-renormalizable) superpotential couplings consistent with gauge invariance. Considering only the 33 relevant fields mentioned in the previous paragraph, the selection rules and gauge invariance under the observable and hidden sector non-Abelian groups allow 32 and 135 terms at dimension three and four, respectively. Requiring in addition gauge invariance under the six $U(1)$ factors (one of which being anomalous) reduces these numbers to a tractable 15 and 8, respectively.

To ascertain which of the terms in (\[Wfull\]) can be identified from the above it is necessary to choose a linear combination of the five non-anomalous $U(1)$ factors to be identified as hypercharge, and then determine the resulting hypercharges of the bifundamentals, doublets and singlets under this assignment. Our algorithm was to begin with the two bifundamentals of the twisted sector, as the untwisted bifundamental had no 