  We prove that for minimizers of the vectorial Alt-Caffarelli functional the
two-phase singular set of the free boundary is rectifiable and the blow-up is
unique almost everywhere on it. While the first conclusion is an application of
the recent techniques developed by Naber and Valtorta, the uniqueness part
follows from the rectifiability and a new application of the
Alt-Caffarelli-Friedman monotonicity formula.
