Central pivot is just part of "first step" model allowing people to identify and retrain their bodies. I expand on that with exercises to free up the waist from the hips. These are part of a series of martial movement rewiring drills that we do along side of IP training. As the mind / body connection grows, it leads to more advanced training later on. When the internal and external match and move together it becomes a very potent mix.
As far as pivoting goes; producing dual supported spiral paths through your center makes any idea of pivoting axiomatic. They exist everywhere, instantly and reverse at will.
I had thought that's what would happen, i am at the moment trying to "free up the waist from the hips" but thus far having some difficulties, though it is a work in progress. My problem is that my bloody hips keep wanting to move with the waist. Should the hips remain stationary? Or should they have some movement?
I had a thought which may or may not be relate to this topic, in regard to the hara/dan tian (please forgive any wrong use of Japanese terms as i am not 100% how they correspond to the Chinese). I had started a thread at another forum in regard to generating power from this area, in trying to create a loop going down from the front of the chest to the dantian then up the spine and out through the hands.