2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31371In 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.13 pages, 3 figuresComputational ComplexityDisordered Systems and Neural NetworksG.3, G.2.1text