Re: Yoshinkan and "aiki"
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.