Move on to the definition of the decoherence functional in this context. Fine-grained histories of spin networks are the individual spin foams, weighted by the “fundamental” spin foam amplitudes that the theory associated to them. Coarse graining is imposed on “bulk configurations”, that is on the spin foams being summed over. More precisely, one coarse grains all histories/spin foams that correspond to the same diff-invariant properties [identified in terms of suitable observables].