  We study microscopic operators describing the experience of an observer
falling into the horizon of a unitarily evaporating black hole. For a young
black hole, these operators can be taken to act only on the degrees of freedom
in the black hole region: the soft---or stretched horizon---modes as well as
the semiclassical modes in the zone region. On the other hand, for an old black
hole, the operators must also involve radiation emitted earlier; the difference
between the two cases comes from statistics associated with the coarse-graining
performed to obtain the effective theory of the interior. We find that the
operators relevant for the interior theory can be defined globally as standard
linear operators throughout the microstates, which obey the correct algebra up
to corrections exponentially suppressed in the ratio of excitation energy to
the Hawking temperature. We conjecture that the existence of such global
operators is required for the emergence of the semiclassical picture. We also
elucidate relation between the present construction and entanglement wedge
reconstruction of the interior.
