One explanation of existence is the Tegmark level 4 multiverse, the idea that all coherent mathematical structures exist, and our universe is one of them.

I object to using word 'exist' here. I can't see it refering to any sensible concept when you're talking about such a meta-level to our universe.

I posted some thoughts about this earlier. http://lesswrong.com/lw/1dt/open_thread_november_2009/1kj6