  We establish a version of the Momentum/Complexity (PC) duality between the
rate of operator complexity growth and a radial component of bulk momentum for
a test system falling into a black hole. In systems of finite entropy, our map
remains valid for arbitrarily late times after scrambling. The asymptotic
regime of linear complexity growth is associated to a frozen momentum in the
interior of the black hole, measured with respect to a time foliation by
extremal codimension-one surfaces which saturate without reaching the
singularity. The detailed analysis in this paper uses the Volume-Complexity
(VC) prescription and an infalling system consisting of a thin shell of dust,
but the final PC duality formula should have a much wider degree of generality.
