There is no evidence!
There is no fossil record!
It's all been debunked!
The only reason you even need the wildly outlandish "Punctuated Equilibrium" myth in the first place is because of the striking absence of evidence in the fossil record for a slow progression of evolution over millions of years. (*cue the usual flurry of weak evidence for such from the evo crowd*)
With this theory, you've crossed the line from science to pseudoscience...from physics to metaphysics...from the natural to the supernatural.
The leap of faith; the suspension of disbelief; required to believe in PE is truly mindboggling.