  Much of the recent work on random constraint satisfaction problems has been
inspired by ingenious but non-rigorous approaches from physics. The physics
predictions typically come in the form of distributional fixed point problems
that are intended to mimic Belief Propagation, a message passing algorithm,
applied to the random CSP. In this paper we propose a novel method for
harnessing Belief Propagation directly to obtain a rigorous proof of such a
prediction, namely the existence and location of a condensation phase
transition in the random regular $k$-SAT model.
