Obviously one should not confuse the physical picture of Caroline Thompson's classical chaotic ball model with the physical picture of Joy Christian's S^3 (or even S^7) models.
Joy has proposed a computer simulation of his model (I do not understand the derivation, but it stands there on the table, plain for all to see.)
It's obvious how to do a computer simulation of Caroline's model.
My claim is that the two computer simulation models are mathematically isomorphic. Rename things in one of the simulation models, and it has magically become identical to the other one. And vice versa.
I make this claim modulo a minor extension to both simulation models, extensions which were already explicitly put on the table by both originators. In Caroline's ball model, we let the radius R of the sperical caps be random, not fixed. In Joy's S^3 inspired model, we let the probability distribution of theta_0 and the functional form of the function f(.) be arbitrary, so that S = sin(f(theta_0)) has an arbitrary probability distribution.
The two are related by R = arc cos(S), S = cos(R).
At this level of generality the Pearle (1970) model is a special case, and so is the Marshall, Santos, Selleri (1983) model.
The *unique* model which reproduces *exactly* the singlet correlations is the Pearle (1970) model.
By the way I am not talking about the original Christian-Roth simulation model in which A times B was simulated (Java, Javascript, Mathematica, R versions by Chantal Roth, Daniel Sabsay, John Reed, Richard Gill) but the newer Minkwe (Michel Fodje) "event-based" simulation model in which both outcomes A and B are separately simulated (Python and R versions by Michel Fodje, Richard Gill, Chantal Roth).
