locked-in at the instant of cross-linking. In order to account for this quenched randomness, as well as the thermal fluctuations in particle positions which are the origin of the entropic elasticity, we adopt the framework of vulcanization theory [@Goldbart1996]. This framework includes the use of the replica method to eliminate the quenched randomness, followed by a Hubbard-Stratonovich transformation to construct a field-theoretic representation in terms of an order parameter field—in this case, the random solidification order parameter. We analyze this representation at the stationary-point level of approximation, and then focus on the gapless excitations around the stationary point—the Goldstone fluctuations—observing that these excitations can be parameterized in terms of a set of replicated shear deformation fields [@Mao2007; @Ulrich2006; @Goldbart2004]. The second prong of our approach is less conventional. It begins with our introduction of a phenomenological model free energy of an elastic continuum, characterized by a nonlocal kernel of quenched random attractions between mass-points. To obtain statistical information about this quenched random kernel, we use the replica method to eliminate the randomness, and obtain a pure model of replicas of the deformation field with couplings controlled by the disorder-moments of the kernel; these disorder-moments are then treated as unknown quantities 