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

Hierarchical exchangeability of pure states in mean field spin glass models