The number and nature of the Element Dichotomies

[The Ineffable]

According to Wikisocion, there are 7 Element Dichotomies. On short: wrong.

In its dedicated section, it's asserted that the IEs can be separated using:
- the 3 basic dichotomies of the IAs;
- the 4 derived dichotomies out of the basic ones.

Ok, the basic three dichotomies we all know, they're fundamental to Socionics. But how comes that using "the mathematics of Reinin" we can deduce exactly four derived ones?

Assuming that by "derived dichotomies" we refer to the second tier ones:
1: Bodies + Dynamic, Fields + Static = D1A (we find it as Rational/Judging)
-- Bodies + Static, Fields + Dynamic = D1B (Irrational/Perceiving)
2: Bodies + External, Fields + Internal = D2A (Decisive and Serious - listed there as Gamma values)
-- Bodies + Internal, Fields + External = D2B (Judicius and Merry - Alpha values)
3: Dynamic + External, Static + Internal = D3A (<not known1> - Delta values)
-- Dynamic + Internal, Static + External = D3B (<not known2> - Beta Values)

Related:

I previously explained what Decisive and Serious on one hand, and Judicious and Merry on the other have in common. Let's say on short - and probably not very accurate -, that the first type of information is "generality" vs the second, "speciality". Eg:
- generality: this guy is a winner, people are mortal, this machine is working;
- speciality: this guy keeps winning, people die, this machine worked every time/the last time.

The "not known" is a dichotomy I told you about and that, from my observations, may offer a difference of suggestibility to types (I once called it: Suggestible/Non-Suggestible). Some other findings of mine revealed a property - with maybe a better naming convention for this - that I can't remember right now, but I was associating it, when it's over the Base function, with people who for example:
- after a long period of having a different lifestyle, living abroad or experiencing important events etc, they feel everything changed, that they changed, that old things are not applicable anymore to them or the new contexts. They're stereotypically accused of becoming arrogant, of "forgetting their roots", forgetting their old friends, becoming startups (esp associating them with a better career or so), while they feel that they're simply "on something else". They can't resume familiarities so easily with old acquaintances because their attitude changes. Types: LII, ESE, all Beta, SEE, ILI.
- after living elsewhere, they remain "the same", their attitude on things, people and events doesn't change much; they may come back years later after living in totally different environments and resume relationships from where they left them like nothing happened, may even tend to use old nicknames. Types: ILE, SEI, LIE, ESI, all Delta.

Note that I'm not sure about it, I have to make further observation on a larger sample and observe consistency, maybe even focusing on the information itself.

There are only three of them. Only Rational/Irrational, Gamma/Alpha values and Delta/Beta values are correct derivations of the core dichotomies, so where come Abstract/Involved from? In my opinion, it is a false, speculative dichotomy; there's currently no reasonable evidence that it actually manifests in types that I know of. It is apparently added because it was the grouping of the 8 IEs that was missing, having all other Reinin dichotomies named, but it is based on nothing else (again, that I know of) - and at least not on the three fundamental ones.