  We compute the Bray and Moore (BM) TAP Complexity for the
Sherrington-Kirkpatrick model through the cavity method, showing that some
essential modifications are needed with respect to the standard formulation of
the method. This allows to understand various features recently discovered and
to unveil at last the physical meaning of the parameters of the BM theory. We
also reconsider the supersymmetric (SUSY) formulation of the problem finding
that the BM solution satisfies some proper SUSY Ward identities that are
different from the standard ones. The SUSY relationships encode the physical
meaning of the parameters obtained through the cavity method. The problem of
the vanishing prefactor is addressed showing how it can be avoided.
