Well I thought that this time Chatgtp was going to not make it past the Law of conservation, but backing into the system purely from a Newtonian perspective without energy considerations got the force and distances and all the motions and interactions make sense to Chat.
The kinematics are there, this means that the geometry passes the math test, the forces are there because they are required,, it is a loop.
This file is one of the "presentation" files Chat has prepared for me but I ran out of higher level calculation time so what is promised tomorrow is a polished file that I can share with all the stuff explained.