Chips show this type's own four letters. The dark ones feed that dichotomy; red means it sits on the negative side. Count the red among the dark: an even count gives the blue pole, an odd count the red one. Dichotomies themselves are always named in the fixed E N T p basis — all four positive is ILE — so one axis keeps one name however you set the switches.
These are socionics codes, not MBTI codes. The final letter follows the leading element: INFj is EII, leading Relations; INFp is IEI, leading Telos. It is written lower case for exactly this reason. MBTI's J and P are fixed by the extroverted function instead, so for introverts the letter can land the other way — whether MBTI INFJ answers to IEI is a claim about correspondence between two different models, and a disputed one. Nothing in this app depends on it.
Four independent dichotomies. Take any two traits and they combine into a third: the combined trait holds when both agree and fails when they disagree. Logical equality, which is why multiplying signs works.
static = sign(E) × sign(P)
Combination is commutative and associative, so what matters is only which of the four a dichotomy depends on — a subset of {E, N, T, P}. Sixteen subsets. The empty one is the identity trait, true of all sixteen types, so it is no dichotomy at all. Fifteen remain, and the four Jungian ones are among them: C(4,2) + C(4,3) + C(4,4) = 6 + 4 + 1 = 11 beyond the original four.
The fifteen close under combination: choose two and their product is another of the fifteen. Hold those two constant across a group of types and the third is constant too — an interdependent triad, and where small groups come from.
Each small group is defined by three dichotomies whose products close on each other — which is why only two of the three are ever free.
The derivation is forced by the structure and is not in dispute. What each derived trait actually looks like in behaviour is contested among socionists, and the glosses on the cards are the classical readings rather than settled findings. Derivation follows Reinin's product list as set out at wikisocion.github.io/content/reinin_dich.html. WSS pole names and their function-level mechanisms are taken from Jack Oliver Aaron's Types Part I and II, and every one has been checked against the socion table.