 It is fair to say that we are still quite far from a proof of the strong conjecture.But there has been outstanding progress in simpler models.In particular, Berger, Garfinkle, Moncrief, Isenberg, Weaver, and others showed that, in a class of models, as the singularity is approached the solutions to the full Einstein field equations approach the "velocity term dominated" (truncated) ones obtained by neglecting spatial derivatives.