Here you go again. Rude, rude, and more rude.
***And I find it rather laughable that you would go so far as to say that reality is not what you perceive it to be!***
What you do not seem to grasp is that 'reality' is a very vague term, and people have been confusing what they mean by this term for eons and eons. It can mean what you perceive, or it can mean the structures that scientific theory postulate, or it can mean all mathematical structures, or dozens if not hundreds of other possible interpretations. This is the whole reason for sticking with R1 which is just a mathematical structure that you define that has nothing to do with these myriad of other interpetations. You can't seem to comprehend this basic, basic principle.
***"But the objects of the world are not symmetrical, and our ignorance of them does not make them symmetrical." While you are making statements of unsupported belief, are those angels dancing on the head of a pin symmetric or not?***
You couldn't have said: "Well, Yaniru, you are addressing objects of the world as an objective thing, but we don't experience the world objectively, all of our experiences are subjective, and it is this subjective experience of the world where symmetry and symmetry-breaking arises. It is meaningless to talk about objective symmetries coming from our subjective experience of the world." Couldn't have been polite, could you?
***Spherical symmetry and mirror symmetry and exchange symmetry are all embedded in my presentation. Exchange symmetry is explicitly included when I say that every data element is equivalent to any other and you of all people should recognize the other symmetries in my fundamental equation.***
Symmetry arguments are mostly used in conjuction with theoretical predictions that should arise from them. You use symmetry arguments not in terms of theoretical predictions of what new observations in nature to expect, but in terms of our subjective inability to determine the difference between two different outcomes. I suspect that this is why you don't see this as an assumption, you imagine that you see it as the only possibilities that there are to interpret our ignorance. This is not how symmetry arguments are usually constructed in science. Symmetry arguments in physics are usually construed as 'what if' this symmetry holds in nature (e.g., Einstein's equivalence principle), then a whole list of equations can follow. You do not approach your paper's subject matter as a 'what if', but as 'how can I theoretically represent my subjective knowledge at this point'.
What you do not realize is that by including terms and concepts on 'how can I theoretically represent my subjective knowledge at this point' is that you are constructing your ignorance/knowledge in terms that automatically lead to the existing laws of physics. From your perspective this means that you've come upon significant, but in fact, there are other possibilities. The biggest possibility, I think, is that our laws of physics is based on the conceptual schemes we use to construct them. If you change the conceptual scheme, then the laws of physics would be different. We just happen to choose the conceptual scheme that most closely matches our observations, but these observations are always based on our ignorance of what has not been measured as well as our instrument sensitivity at the time. By expanding the number of conceivable observations and increasing our instrument sensitivity, we therefore must change or improve our conceptual schemes to keep up with the theoretical discrepancies that keep popping up. Since you have phrased your approach in your paper according to an older conceptual scheme (early 1960s as it was known at Vanderbuilt at the time), you only obtain results that this conceptual scheme was capable of deriving. This is why new physics is missing. You didn't use the conceptual schemes of group theory (etc), and hence you could not produce new physics. This is not to say that this view is correct, but I favor it over the notion that you somehow have produced the laws of physics from some fundamental approach.
The last 40 years you've been fooling yourself and having fun....