Tsuifukusosu: A Reassessment of the Limits of Complex Number Extensions

This paper introduces Tsuifukusosu, a new algebraic structure obtained by duplicating the internal structure of the complex numbers. In Chapter~4, the multiplication of Tsuifukusosu is defined explicitly, and in Chapter~5, commutativity is established as a minimal algebraic property inherited from the complex numbers. Unlike the external direct product C × C, the tsuifukusosu system arises from an internal duplication of the complex structure and therefore represents a distinct direction of extension beyond traditional multicomplex or hypercomplex approaches. This paper focuses only on the minimal structure, while further properties and potential applications are discussed in the foundational reference~{Morimoto2026}.