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 Isn't String Theory itself a description of how manifolds emerge from other manifolds and then join, since they describe the interaction of world-sheets which are manifolds? Isn't M-theory a study of how lower dimensional submanifold (strings) emerge from higher dimensional manifolds (membranes)? Perhaps M-theory itself is the theorem I'm looking for. Or perhaps the theorem I'm looking for would be the non-perturbative form of M-theory we would all like to see. My earlier point was that if two different things are true in conjunction at the same place at the same time (as they would have to be at the singularity from which the big bang occured), then this implies that one proves the other so that there is an equality between them. So the question is whether the universe begins with both particle creation (emergence of submanifolds) and universal expansion simultaneously, or whether we could have expansion without particle creation.