a future study – we will here choose one particular example as a case study. The $\mathbb{Z}_3 \times
\mathbb{Z}_3$ orbifold construction of Font et al. [@Font:1989aj] begins with a non-standard embedding that utilizes two shift vectors and one Wilson line in the first complex plane. This Wilson line breaks the observable sector gauge group from $SO(10)$ to $SU(3) \times SU(2)_A \times SU(2)_B$. The massless spectrum of this model contains 75 species of fields. Those from the untwisted sectors have a multiplicity of one, while twisted sectors have a multiplicity of three or nine, depending on the representation. It is natural to consider this multiplicity factor as a generation index.

There are three species of fields which are bifundamental under the observable sector $SU(2)_A \times SU(2)_B$ (one in the untwisted sector and two in various twisted sectors), five doublets under $SU(2)_A$ and eight doublets under $SU(2)_B$. There were also 17 species that were singlets under all non-Abelian groups. So the minimal set of fields needed to generate the superpotential of (\[Wfull\]) are present, as well as an additional bifundamental representation that may be used to break the product group to the diagonal subgroup and/or generate the needed higher-order corrections in (\[psi\]). 