"[the two share deep mathematical structure, they are isomorphic as mathematical models. This doesn't mean they are isomorphic as physical models]."
However, you even denied the simulations were based on valid mathematics until you saw that Pearle's analytic structure is isomorphic to your own probabilistic model.
One need point out here that Joy is the physicist in this dialogue, and as a physicist he has crafted a non-probabilistic framework for quantum correlations. Therefore, if with probability 1.0, an analytic model (Pearle's) is isomorphic to at least one probabilistic model (yours), it follows with probability 1.0 that at least one other continuum model (Joy's) simulated on S^2 is isomorphic to a continuum model on a smooth simply connected manifold (S^3)with a bijective inverse (diffeomorphism) -- why? -- because the S^2 manifold contains at least one tangential point (Poincare-Hopf theorem)that maps smoothly to itself only if S^2 X S^2 is simply connected (it is) with a reversible function over the manifolds (S^2 X S^2 = S^3, a simply connected sphere), in a space of complete measurement results.
"If Mr Ray knows how to simulate the so-called Christian model then he could do it too. Idem Fred, Idem world. Study the conditions / regulations first. There is no 'small print' but every single word is there for a reason, and there are quite a few words to be processed ..."
Dr. Gill has verified that the Christian model has already been simulated on S^2 both analytically and probabilistically. Since that is the physical limit of all computer simulations, his faux challenge is another "heads I win, tails you lose" wager. A sucker bet.
What needs to be shown is that S^2 X S^2 is complete and continuous physically, that Perelman has already proved mathematically. So if an isomorphism exists for quantum correlations between analytical and probabilistic models on S^2, a diffeomorphism exists between S^2 and S^2 on the S^3 manifold, differentiable by the topological twist that Dr. Christian has expertly described.
