  The low temperature phase of discontinuous mean-field spin glasses is
characterized by the appearance of an exponential number of metastable states.
Which ones among these states dominate the out-of-equilibrium dynamics of these
systems?
  In order to answer this question, we compare high-precision numerical
simulations of a diluted $p$-spin model with a cavity computation of the
threshold energy. Our main conclusion is that the aging dynamics is dominated
by different layers of metastable states depending on the cooling schedule. In
order to perform our analysis, we present a method for computing the
marginality condition of diluted spin glasses at non-zero temperature.
