Description
This monograph introduces a unified framework for the analysis of complex systems based on the concept of mixed fields, replacing the traditional representation of systems as collections of variables with a structured, multi-component field: amplitude, phase, variation and tension are treated as fundamental and irreducible dimensions of system behavior. The theoretical construction integrates algebra, geometry, dynamics, and scale into a single formalism. A mixed algebra combining complex, dual, and hyperbolic numbers provides the minimal structure necessary to encode the four components. This algebra induces a composite geometry in which Euclidean, degenerate, and hyperbolic metrics coexist, enabling the definition of invariants and curvature associated with coherence, responsiveness, and instability.