Why would you start a new CTE thread when there's so many other threads on it, one of which has over 500 posts with every possible question, link, explanation, and diagram?
CTE is "meant" to be understood by sifting through hours of and hours of drek, or at least that's how hal wants it to be for a certain group of people. I guess he wants them to "pay their dues" or whatever. So you're not going to get straight and valid answers. Only two guys are definitely qualified to answer (learned directly from hal) and another couple are big maybes (like maybe they figured it out and maybe they're just winging it).
Dig through spidey's posts, read his blog, read the CTE mathematics post, and you'll see a bunch of stuff about the pivot.
Note, I'm not really knocking you for asking. I asked the same thing many times. Lots of people have. I could not get a straight answer about whether the pivot happens from a fixed point or not. There probably are no straight answers regarding pivot because it's a feel thing that may be different from player to player. It may even matter if you're left handed or right handed. You might need to figure out a pivot that works and practice it for a thousand hours.
Spidey recommends pivoting from the hips. He stresses the pivot is not around the bridge, and pivoting around the bridge WILL cause failure. He's also mentioned that the central point of the pivot may be around the joint of the cue.