  A Wannier-Stark optical lattice clock has demonstrated unprecedented
measurement precision for optical atomic clocks. We present a systematic
evaluation of the lattice light shift, a necessary next step for establishing
this system as an accurate atomic clock. With precise control of the atomic
motional states in the lattice, we report accurate measurements of the
multipolar and the hyperpolar contributions and the operational lattice light
shift with a fractional frequency uncertainty of 3.5$\times$10${}^{-19}$.
