OK, I have now studied Philip

Pearle's 1970 paper thoroughly and analyzed his analytical solution extensively.

His solution

does not produce perfect cosine correlation in Richard Gill's simulation.

I replaced my initial function f(theta_o) with

Pearle's analytical solution in Richard Gill's simulation as follows:

theta <- runif(M, 0, pi) ##

Pearle's alpha from his 1970 paper

g <- (2/3)*((((theta)-sin(theta))/((sin(theta/2))^2))+(((pi-theta)-sin(theta))/((cos(theta/2))^2))) ##

Pearle's solution g(alpha), see his eq. (23)

s <- g*((sin(theta/2)^2)/2)

This produces cosine correlation, but not as perfectly as with the initial function f(theta_o) of my model:

http://rpubs.com/chenopodium/joychristian.

This proves that my model is

fundamentally different and it has nothing whatsoever to do with data rejection or detection loophole.

But some of us already knew that.