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This is called Puncuated equilibria.

I KNOW that. I have not been misinformed. You are making assumptions. I am aware that they came up with this to support the TOE, specifically to address the issue of lack of change for long periods, and then suddenly a burst of change.

The basis of PE is the neontological theory of peripatric speciation.

This statement converges two separate concepts. Neontology just means "current organisms" (but just try to find that word in your standard online dictionary. Heh heh.) Regarding PE, neontology just means using our understanding of current living organisms to understand paleospecies. While parapatric speciation is supposed to provide support for PE, in fact the parapatric speciation simulations tend to be run to support microevolution.

If I don't make a botch of it, here is the simplified specification of PE.
1st, a mutation generates a split between a parent and a daughter population.
2nd, it so happens there is geographical isolation of the daughter population, thus that population becomes a separate species. (Note, however, it might be better termed a "breed" but current species definition no longer requires inability to interbreed for a species to be defined within the context of the TOE. I personally think that is begging the question, but hey, what the heck.)
3rd, since the daughter species is isolated, and interbreeds, the mutation rate is higher. (Think "Deliverance" and the banjo boy.) Yikes.
4th, an "environmental event" or other situation occurs such that the daughter species breaks out of their niche and spreads widely, while the parent species croaks. Or not.

Now how is this different from microevolution? Well, PE asserts that since the mutation would occur in a limited geographical range, the "transitional" forms are unlikely to be found. Ergo, when the daughter species "breaks out" they appear without transitional forms.

Great. However, while PE is interesting, it doesn't explain two things. One I have said before regarding dogs, which is that we have bred the heck out of them and we can still cross them with wolves. TOE assumes that given enough time that speciation without the ability to interbreed will occur. This has not been experimentally verified in animals (I think), although it can be done fairly easily in plants. Secondly, PE explains how a new species can pop up, but doesn't explain really the problem of long periods of no change in the fossil record and then (what I referred to before as "WHAMO") you get huge form differences. Like when trilobites and brachiopods appeared, there wasn't anything even close in form to them. That event was comparable to having a jump from lemurs to humans with nothing in between. I don't think PE really explains a gap that big.