Dirichlet boundary values of the SLE angle process ($h_t=\pi {\omega }_{D_t}(\cdot ,S_t^{-})$)

For the SLE angle process, the bounded Dirichlet problem on the unbounded surviving domain has data $\pi$ on the intrinsic boundary mapped to the left of the Loewner driving function and zero on the boundary mapped to its right. For a simple Loewner trace these are its left and right banks, with the negative and positive real rays respectively. The tip is a discontinuity point of the boundary data.