Mathematical Lifting of Eigenvergence in Recursive Expansive Dynamics

This lift scaffolds the core geometric, algebraic, and physical components of the refined Recursive Expansive Dynamics (REDS) framework, integrating the hierarchical structure of dimensional modulators, recursive influence pathways, and eigenvergence principles governed by the golden ratio. It consolidates foundational equations, geometric constructions, coupling mechanisms, and empirical predictions, extending the original theory with detailed mathematical formalism and physical implications. This comprehensive analysis integrates two advanced mathematical prototypes for eigenvergence theory with the refined Recursive Expansive Dynamics (REDS) framework, creating a unified theoretical scaffolding that extends eigenvergence principles across topological, categorical, stochastic, and quantum domains