  In this paper we translate Talagrand's solution of the K-sat model at high
temperature into the language of asymptotic Gibbs measures. Using exact cavity
equations in the infinite volume limit allows us to remove many technicalities
of the inductions on the system size, which clarifies the main ideas of the
proof. This approach also yields a larger region of parameters where the system
is in a pure state and, in particular, for small connectivity parameter we
prove the replica symmetric formula for the free energy at any temperature.
