A thread on Home of Poi asking for a definition of CAPs has turned up not just an interesting history of the concept, but the most comprehensive mathematical description I've yet seen of the move. I don't pretend to understand much (or, really most) of the mathematics in this post, but I'm considering it a moral imperative to educate myself and figure out the mathematics of poi (mainly because I suspect it has major implications for concepts like Alien Code and antispin flowers).

Here is Zaltymbunk's description: