Basically Peter Jackson and Decaln Traill have have shown - that the indistinguishable i - can be thought of as the two indistinguishable constants of closure on the geometry (of a sphere). Or the "Fundamental Theory Of Algebra" needs two constants to close a general "energy count of a measurable outcome". Clearly we need two halves at work from their work, that seem to imply we close Peter's equations on his sphere using (up,down) & (left, right) etc two ways.
From wiki - That is, i is a unique (i.e. distinguishable) number defined as the square root of minus one, i.e.,i тЙб +тИЪ-1. Since there are two possible square roots for any number +тИЪ and -тИЪ, clearly the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point +i and -i can then be distinguished. Since either choice is possible, there is no ambiguity in defining i as "the" square root of minus one.
Clearly looking at Traill's computer programme and Jackson's physical experiment - what is being mapped out is how +i and -i are indistinguishable, all his programme does is to use random numbers to show that quantum vectors can distributed over a whole sphere, as a classical system. All we do is assign +1 or -1 (via Bell/EPR duality), and then as compared to pure randomness, when we do the actual measurements as a series, we get quantum correlations. One half of the sphere we get +/- 1 and the other half we get +/- 1.
Well the indistinguishable +i and -i each has it's own +/- signs. That is, what Traill and Jackson have done is do the experiment to show that the "complex imaginary unit" (where +i and -i are indistinguishable hence we do the extraordinary as they have shown) in our current theories has been using only one-half of the indistinguishable "complex imaginary unit". See attachment didn't know how to attach diagrams in this message box.
I really enjoyed reading your essays over the last few years so full of details and always with an experiment as well. I think you have done some good work here, and I have mark you highly
see my essay "What is Fundamental is the area of the imaginary unit" for more details,and Peter please read the attachment in the first post as well. It is a FAQ post.
https://fqxi.org/data/essay-contest-files/Tiainen_Essay_2018_Final_2.pdf
Also Peter I have attached a PDF of more comments about +i and -i using your red/sock trick, it features heavily in my essay. Enjoy Harri