  The authors have proposed a global model for Heterotic $F$-theory duality
with Wilson line symmetry-breaking and a $4+1$ split of the $F$-theory spectral
divisor. Goals of this note are to treat the existence of right-handed
neutrinos in our $F$-theory model, show that the $\mathbb{Z}_{2}$-action in our
model breaks the $U\left(1\right)_{X}$-symmetry associated to the $4+1$ split
to $\mathbb{Z}_{2}$-matter parity, and to identify Yukawa couplings for the
MSSM matter fields.
