Imaginary Axes Deprivation in Euclidean Space

Version 3: This version refines the exposition, restores and standardizes the structural notation, and clarifies the status of coherent dimension, the dual readability of the complex field, and the D3 model as a structural counterfactual rather than as a replacement for quaternion algebra. The article’s central thesis and role within the MGQC research program remain unchanged. Abstract The Cartesian formalization of Euclidean space stabilized a three-dimensional structure composed of mutually orthogonal real axes before imaginary quantities acquired a coherent geometric interpretation. When the complex field was later consolidated, internal orientation became mathematically expressible through the imaginary…