  There are two evidences for information loss during black hole evaporation:
(i) a pure state evolves to a mixed state and (ii) the map from the initial
state to final state is non-invertible. Any proposed resolution of the
information paradox must address both these issues. The firewall argument
focuses only on the first and this leads to order one deviations from the Unruh
vacuum for maximally entangled black holes. The nature of the argument does not
extend to black holes in pure states. It was shown by Avery, Puhm and the
author that requiring the initial state to final state map to be invertible
mandates structure at the horizon even for pure states. The proof works if
black holes can be formed in generic states and in this paper we show that this
is indeed the case. We also demonstrate how models proposed by Susskind,
Papadodimas et al. and Maldacena et al. end up making the initial to final
state map non-invertible and thus make the horizon "cool" at the cost of
unitarity.
