In response to this paragraph:

"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."

1. You say that all data sets are unique. That excludes exchange symmetry.

2. You explicitly say that all the data has scale and shift symmetry. No way can all the same data have spherical and mirror symmetry.

You did introduce a new virtual dimension for representing unknowable data and claimed that the properties of the data were independent of direction on that 2-D plane. But that was cylindrical symmetry, not spherical.

Well, I suppose you could as well have created a third dimension an then claimed spherical symmetry, which then has mirror symmetry across a plane in any direction, as long as the plane goes through the origin. But the origin can be anywhere by the shift symmetry.

So bottomline, the only set of data that can possess both shift symmetry and spherical symmetry, is a set of uniform data points. Spherical symmetry requires an origin for anything more complicated.

Think I am just talking to myself. No need to continue.