Yup, I kinda wish someone would come up with a mathematical proof for geocentrism just to have something to have an FYI for the laity, so people don't go off the deep end over stuff like this.
Well, the frame of reference of the Earth is an inertial reference frame, and, in that frame, the Earth doesn't move, everything else moves, so, in that sense, a geocentric solar system, a heliocentric solar system, and a "center of mass of the solar system"-centric solar system are all just a mathematical transformation away from each other, so, if "the Earth doesn't move" counts as "geocentrism", that should take care of it.
"The Earth doesn't move, and everything orbits around it in simple circles or ellipses", however, is another matter. That's not going to happen with Newtonian mechanics or Einsteinian mechanics; Earth just doesn't have enough mass to put the center of mass of the sola system anywhere near its center.