  We define the "kink transform" as a one-sided boost of bulk initial data
about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, we
conjecture that the resulting Wheeler-DeWitt patch is the bulk dual to the
boundary state obtained by Connes cocycle (CC) flow across the cut. The bulk
patch is glued to a precursor slice related to the original boundary slice by a
one-sided boost. This evades ultraviolet divergences and distinguishes our
construction from one-sided modular flow. We verify that the kink transform is
consistent with known properties of operator expectation values and subregion
entropies under CC flow. CC flow generates a stress tensor shock at the cut,
controlled by a shape derivative of the entropy; the kink transform reproduces
this shock holographically by creating a bulk Weyl tensor shock. We also go
beyond known properties of CC flow by deriving novel shock components from the
kink transform.
