semi-microscopic viewpoint, the other invoking phenomenological parameters. Thus, the equivalence of the two schemes provides the values of the phenomenological parameters as functions of the semi-microscopic parameters. ]{}]{}

Before concluding this introduction, let us emphasize that this work is a first attempt to [*derive*]{} the elastic heterogeneities of vulcanized matters. To date, the prevalent strategy in studies of disordered systems is to assume a particular structure for the quenched disorder on phenomenological grounds (such as Gaussian, short ranged, etc.) and explore the consequences. Assumptions about disorder structure are usually based on symmetry arguments and also the preference for simplicity, but otherwise lack theoretical substantiation. It is one of the main advantage of vulcanization theory that it can [*predict*]{} some generic properties of the disordered structure in vulcanized matter, as is shown in the present work, which can be used to support and sharpen the assumptions underlying more phenomenological theories.

The classical theory of rubber elasticity, which was shown to be derivable from the saddle-point approximation of vulcanization theory, is known to fail to describe rubber elasticity in the intermediate and large deformation regimes [@Treloar1975]. While a recent study [@Xing2007] shows that long wave-length thermal elastic fluctuations account qualitatively for this 