we discuss a natural form of ricci-flow conjugation between two distinct general relativistic data sets given on a compact $n$-dimensional manifold. the ricci flow generates a form of $l^2$ parabolic averaging, of one data set with respect to the other, with a number of desiderable properties: (i) preservation of the dominant energy condition; (ii) localization by a heat kernel, (associated with the linearized ricci flow), whose support sets the scale of averaging; (iii) entropic stability.