component of each) are the same. This implies that to better fit $Z$-$b_L$-$\bar{b}_L$, we expand $Q_3$ into a bi-doublet under ($SU(2)_L$, $SU(2)_R$). The unwanted additional fermions in the bi-doublet are removed from the zero mode spectrum by adjusting their boundary conditions. Having promoted $Q_3$ to a bi-doublet, we recover freedom to consider the $c$ parameter for $Q_3$ very different from $-1/2$.

In order to have a specific framework, we analyze the model of gauge-Higgs unification [@Carena:2007ua] (similar to an earlier model [@Agashe:2004rs]) in which the allowed parameter space is analyzed in great detail [@Carena:2006bn], reproducing light fermion masses and mixings, and demanding consistency with flavor-changing neutral currents induced by the KK modes of the gauge bosons. While some of the features are particular to the gauge-Higgs unified model and the mechanism by which it realizes fermion masses and mixings, some of the most important features are fairly generic to models in which an expanded custodial symmetry is protecting $Z$-$b_L$-$\bar{b}_L$.

The bulk gauge symmetry is $SO(5) \times U(1)_X$, broken by boundary conditions to $SU(2)_L \times SU(2)_R \times U(1)_X$ on the IR boundary, and to the Standard Model $SU(2)_L \times U(1)_{Y}$ gauge group on the UV brane [@Agashe:2004rs]. The $U(1)_{X}$ charges are 