If you look at all three posts (including "Inter-dimensional DNA (1) and (2) and (3); you will find what can be formatted as a series of tables containing many symmetries.
I have only listed some of the possibilities of this speculation on the pre-mathematics of pre-space.
But already patterns are present that relate spectacularly to the superstring ideas discussed in "Superstrings and The Theory Of Everything" by F. David Peat.
At the moment I don't have the math to translate the pre-math into math; but if you read that book the meaning of these tables may become more clear.
I realise I have taken what I suppose is an Einstein-type approach (thinking deeply and philosophically about questions and obtaining an intuitive result). But it looks like this result correlates in too many ways with high-dimensional physics to be just a coincidence.
There are some philosophical mistakes being made by physicists in their approach, I think. The 6-dimensions supposed to co-exist with our familiar 4 might be curled up in US; rather than in nature (thus explaining why we don't see them).
So-called 'real numbers' are actually rather un-real; i-numbers are more realistic!
If you take the simplest representation of a quantum exchange, of relativity, of i-type orthogonal jumps; you have the interaction/ exchange of relativistic viewpoints between ABC and YPR.
Pattern-matching is pre-math; its pre-space is 'match-space'.
Physics starts with a definition. An agreement, a superposition, an exchange of viewpoint. And it finishes with that. Physics uses definition and agreement to discover definition and agreement.
Einstein held that pure thought can grasp reality, as the ancients dreamed.
If what I posted had been formated in the matrix-like tables I wrote it as; I think you might see that what I found is very curious. Hope you can re-format it and see.
This matrix-type representation I only just discovered; too early to have reaction to it. I'm an amateur you know!
The full 10 D system is: (note: each relativistic quantized 'object' (ABC) is like three compensating accelerations that can exchange one acceleration-viewpoint with another such object (YPR). In the following analysis of exchanges between ABC and YPR; the first two states occur only once- mirror reflections are excluded. Example: you see C with states A and B; but don't see C with states B, A).
Originally I had a series of symmetry group tables, then I added the remaining items to fill each 10 group.
10C: state A of C, state B of C; state Y of C, state P of C; (abreviating now:) A, P, of C; A, R of C; B, P, of C; B, R, of C; A, Y, of C;
Y, R, of C; P, R, of C; B, Y, of C.
10A: state B of A, state C of A; P, R, of A;
B, R, of A; B, P, of A; B, Y, of A; Y, R, of A; C, Y, of A; C, P, of A; C, R, of A.
10B: state A of B, state C of B; Y, R, of B; A, R, of B; A, P, of B; A, R, of B; Y, P, of B; P, R, of B; A, Y, of B; C, Y, of B; C, R, of B.
10Y: state P of Y, state R of Y; B, C, of Y; P, C of Y; P, B, of Y; A, P, of Y; A, B, of Y; A, R, of Y; B, R, of Y; C, R, of Y; A, C, of Y.
10P: state Y, R, of P; A, C, of P; Y, C, of P; Y, B, of P; Y,C, of P; A, B, of P; B, C, of P; A, Y, of P; A, R, of P; B, R, of P.
10R: state Y, P of R; A, B, of R; Y, B, of R; Y, C, of R; B, C, of R; A, C, of R; A, Y, of R; A, P, of R; B, P, of R; C, P, of R.
The other post shows 11 tables that relate to each other through various reflections and rotations. Each of those 11 symmetry tables uses 10A, 10B, 10C, 10Y, 10P, 10R; so the two arrangements of symmetries are interwoven.
Also my earlier post shows a large table of combinations that can be grouped in various ways.
You're the expert- can you see there's something in this? There are other groups I haven't listed.