  The compactification from the 11-dimensional Horava-Witten orbifold to
5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed,
as is the specific $SU(4)$ vector bundle leading to the "heterotic standard
model" in the observable sector. A generic formalism for a consistent hidden
sector gauge bundle, within the context of strongly coupled heterotic M-theory,
is presented. Anomaly cancellation and the associated bulk space 5-branes are
discussed in this context. The further compactification to a 4-dimensional
effective field theory on a linearized BPS double domain wall is then presented
to order $\kappa_{11}^{4/3}$. Specifically, the generic constraints required
for anomaly cancellation and by the linearized domain wall solution, the
constraints imposed by the necessity for positive, perturbative squared gauge
couplings to this order and the restrictions on the $D$-terms for preserving or
spontaneously breaking $N=1$ supersymmetry are presented.
