"That means that the algorithm for obtaining those expectations can not be a function of that mapping procedure described in the fabrication of the model. If it is a function of that procedure, it is most certainly the wrong answer as the expectations become a function of that procedure and not a function of the elements of C:"
My experience is that the elements of C is a function of the mapping procedure the mapping procedure. I can imagine a model which as a special case includes evey possibe mapping procedure. But I cannot conceive of a model that is independent of the mapping procedure. Please give me an example of one.
Here is another interesting statement:
"any relationships you want to include in the modeled explanation must arise from C. "
Let's say C is the pattern of photons impinging on a detector. You seem to be saying that from just a few photon measurements you can tell all the pertinent relationships like if the photons went through a double slit or if the photon source was coherent, etc. Presumably A is the pattern that results in the infinite limit of detections. If not, please correct my thinking. It seems you have to nurse me from my present world model to yours.
Now, without the benefit of knowing whether the photon path contained a double slit or not, it seems unlikely to me that C alone could be
"the very best one can do (by definition)"
Do you claim that C contains enough information to say with certainty that the path contained a double, because we are 100% sure from an external relationship that it does. You have already said that all results are probablistic. So I know the answer.