This work presents a rigorous derivation of the quaternary structure as the minimal carrier of non-trivial complexity. Starting from a finite system without privileged elements, we prove that the smallest structure capable of supporting independent distinguishability, closure, and non-trivial selection must consist of four states. The system is shown to be uniquely isomorphic to Z2 x Z2. Furthermore, we develop a structural framework including relations, paths, closure, boundary, object, and selection, establishing quaternary structure as a fundamental mathematical basis for complexity.
Yao Wu (Sun,) studied this question.
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