  In this note we study the existence of a solution to the survey-propagation
equations for the random K-satisfiability problem for a given instance. We
conjecture that when the number of variables goes to infinity, the solution of
these equations for a given instance can be approximated by the solution of the
corresponding equations on an infinite tree. We conjecture (and we bring
numerical evidence) that the survey-propagation equations on the infinite tree
have an unique solution in the suitable range of parameters.
