  The main result in this paper is motivated by the M\'ezard-Parisi ansatz
which predicts a very special structure for the distribution of spins in
diluted mean field spin glass models, such as the random K-sat model. Using the
fact that one can safely assume the validity of the Ghirlanda-Guerra identities
in these models, we prove hierarchical exchangeability of pure states for the
asymptotic Gibbs measures, which allows us to apply a representation result for
hierarchically exchangeable arrays recently proved in arXiv:1301.1259.
Comparing this representation with the predictions of the M\'ezard-Parisi
ansatz, one can see that the key property still missing is that the
multi-overlaps between pure states depend only on their overlaps.
