  We address novel features of deep inelastic lepton scattering on nuclei at
small Bjorken variable $x_{Bj}$. In this regime the lepton-nuclear cross
section involves the interference between the standard lepton-quark scattering
amplitude for the deep inelastic scattering (DIS) process on a single nucleon
and a two-step process where diffractive scattering on a first nucleon combines
with the amplitude for DIS on a second nucleon. The phases associated with the
$t$-channel exchanges to the diffractive amplitude can produce either a
destructive or constructive quantum-mechanical interference of the one-step and
two-step amplitudes. This provides a mechanism regulating the respective
amounts of shadowing suppression and anti-shadowing enhancement at low
$x_{Bj}$. Furthermore, the standard leading-twist operator product and handbag
diagram analyses of the forward virtual Compton amplitude on the nucleus are
inapplicable, barring a conventional probabilistic interpretation. A main
observable consequence is the impossibility of extracting momentum and spin sum
rules from nuclear structure functions. We present numerical predictions
supporting this picture and test them against DIS neutrino-nucleus and
charged-lepton-nucleus scattering data.
