This work presents a C3-extended formulation of Schrödinger dynamics based on a phase algebra generated by an element j satisfying j³ = -1. In contrast to the standard complex formulation, which is organized by a two-channel phase structure, the present framework introduces a three-channel decomposition of the wavefunction, Phi = a + bj + cj². Starting from the generalized evolution law jhbar d/dt Phi = Hhat Phi, the paper derives the associated first-order cyclic component system, the induced second-order hierarchy, and a closed third-order evolution equation for each component. In the free-particle sector, this structure leads to cubic time closure and sixth-order spatial closure at the component level. The purpose of the work is to establish the minimal mathematical core of the C3-extended Schrödinger framework, clarify its structural relation to the standard complex case, and identify the first consequences of three-channel phase dynamics. Questions of norm, probability, measurement, and observable projection are treated as open problems within a broader research program rather than as completed assumptions in the present paper.
BORA AKTAŞ (2026) studied this question.