Jackson
If you haven't already, I suggest you look at papers by Tamari, Schultz, and Dariano.
Dariano
Are models based on probabilities `physical theories'? I suggest `physical models' necessarily require a cause - effect model. I think probability models suggest a cause - effect model. The probability models are measurement models.
Would you classify the group models of particle classification the same as you classify statistical analysis? The periodic table was developed first by noting common characteristics of elements. A few holes were filled (predicted) by where the hole was in the classification scheme. Later, the causal underlying structure of atoms explained the periodic table. Indeed, the position of an element indicated something about the atomic structure. The same type of classification is true for the group models. Holes in the group model have been used to predict particles that were found. Can this be used to imply an underlying structure of particles? How would such a study proceed? Is anyone working on the structure of particles (papers I see seem to stop with the group description with no indication of an underlying structure)?
Tamari sugggested a how to build elementary particles' structure.
Schultz suggested the patterns of the 5 Platonic solids could be the pattern of the elementary particles' structure. The same patterns construct crystal structures.
I combine these to solve the problem of my models of how to construct elementary particles from photons. Thus, the SU() groups may be the result of structures of photons much like the periodic table suggested the structure of atoms (my fractal thinking). This would be a physical model rather than a probabilistic model.
Hodge