  We discuss unpolarized neutrino- and anti-neutrino-nucleon deep inelastic
scattering (DIS) using a chiral doublet of baryonic sources with explicit
symmetry breaking, in a slice of AdS$_5$ with both a hard and soft wall. We
explicitly derive the direct and transition form factors for the vector and
axial-vector currents for the holographic dual of a proton and neutron. We use
them to derive the s-channel structure functions for neutrino and anti-neutrino
scattering on a proton and neutron in bulk. The t-channel contributions
stemming from the Pomeron and Reggeon exchanges are also evaluated explicitly.
The pertinent even and odd structure functions in the limit of large and small
parton momentum fraction $x$ are given. The results allow for the extraction of
the nonperterbative parton distribution functions carried by the sea and
valence quarks both at large-x and small-x regimes. Our holographic PDF sets
compare well with LHAPDF and CTEQ PDF sets in the large-x and small-x regimes
in the intermediate range of $Q^2<10~\rm{GeV^2}$.
