  We answer a question left open in [Arch. Rat. Mech. Anal. 230 (1) (2018),
125-184] and [Arch. Rat. Mech. Anal. 230 (2) (2018), 783-784], by proving that
the blow-up limit of minimizers $u$ of the lower dimensional obstacle problem
is unique at generic point of the free-boundary.
