  One of the robust features found in simulations of core-collapse supernovae
(SNe) is the prompt neutronization burst, i.e. the first $\sim 25$ milliseconds
after bounce when the SN emits with very high luminosity mainly $\nu_e$
neutrinos. We examine the dependence of this burst on variations in the input
of current SN models and find that recent improvements of the electron capture
rates as well as uncertainties in the nuclear equation of state or a variation
of the progenitor mass have only little effect on the signature of the
neutronization peak in a megaton water Cherenkov detector for different
neutrino mixing schemes. We show that exploiting the time-structure of the
neutronization peak allows one to identify the case of a normal mass hierarchy
and large 13-mixing angle $\theta_{13}$, where the peak is absent. The
robustness of the predicted total event number in the neutronization burst
makes a measurement of the distance to the SN feasible with a precision of
about 5%, even in the likely case that the SN is optically obscured.
