2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/26130Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.4 pages, 1 figureDisordered Systems and Neural NetworksComputational Complexitytext