Identity is triadic considering the middle term is empty on its own terms and is defined through that which repeats under a circularlity. This can be seen under the example of P=P where "=" is empty of meaning except through the repetition of P. "=" is purely assumed and this assumption of "=" is defined through a repetition of P by a progression which is circular. The Munchauseen Trillema is reflected in this.
P=P, or more accurately P(p)P where "p" represents "-->", "<-->", "<--", etc., reflects a triadic nature in both structure and how it reflects through other assertions as p(P)p and (P(p)).
P(p)P, p(P)p, (P(p)) are all variations of the other as a cycling between assertions.
P(p)P where p is defined through P.
p(P)p where P is defined through p.
(P(p)) where P and p are defined through eachother.
One variable is expressed through a new one in a new variation. Under an expression of P(p)P where p can be defined as a variety of things as "therefore", "equals", "because", etc. the middle term is intrinsically empty and defined through the terms which repeat.
p(P)p observes this repetition inversely where P is defined through p.
The dualism between P(p)P and p(P)p observes P(p)P and p(P)p define eachother so that P and p are defined as existing strictly "as is" under (P(p)) where one context is defined as a tautology of the other as a variation of the original context.
"Equals" exists as a variation of "P" where a statement of "Cat equals Cat" reflects "Cat equals" in which "equals" is an action of "cat" as an extension of it. The dynamic state "equals" is the static state "Cat" expressed under a new variation where "Cat equals" observes "equals" as an action which is an extension of "Cat".