Resonance-Based Subspace Dynamics (RBS-D): Stability Theory of Coupled Resonance Structures

esonance-Based Subspace Dynamics (RBS-D) is a 24-part scientific framework that introduces a structural interpretation of physical systems based on coupled subspaces, resonance phenomena, and nonlinear dynamics. This publication (No. 04 / 24) develops the stability theory of the RBS-D framework by analyzing how coupled resonance structures behave under perturbations and how stable, metastable, and unstable configurations emerge. The focus lies on the mathematical and structural characterization of stability in coupled subspace systems, where resonance states are interpreted as attractor-like configurations within a dynamic operator framework. Within the RBS-D framework, stability is described in terms of: resonance attractor structures perturbation response of coupled subspaces phase coherence stability conditions eigenmode-based structural stability analysis This publication extends the mathematical formulation (P03) by introducing a stability framework that allows classification of resonance states into stable, metastable, and unstable regimes.