Resonance-Based Subspace Dynamics (RBS-D): Geometric Formulation of Coupled Subspace Structures

This publication develops the geometric interpretation of the Resonance-Based Subspace Dynamics (RBS-D) framework, extending the conceptual foundation introduced in Publication 01. It establishes a structural description in which physical reality is modeled as a continuous subspace, where particles and observable properties emerge from stable resonance configurations and relational mode structures. This publication (No. 02 / 24) defines the geometric interpretation layer of the RBS-D framework and provides the transition from conceptual hypothesis to structurally interpretable subspace geometry. Core Contributions: • Introduction of a structural vision for a unified physical description based on resonance dynamics • Definition of physical entities as:Stable, phase-coherent mode configurations within a continuous subspace • Conceptual shift from particles to:Relational, geometry-dependent structures • Interpretation of physical properties as:– emergent from internal structure– dependent on phase relations and coupling geometry • Structural hypothesis:Mathematical state spaces represent projections of deeper relational subspace structures Motivation and Conceptual Position: Modern physics provides highly accurate predictions, yet often relies on abstract mathematical frameworks with limited direct structural interpretation. Phenomena such as:• high-dimensional quantum states• nonlocal correlations• wave-particle duality suggest that an underlying structural layer may exist. RBS-D introduces a framework that:• preserves empirical validity• while offering a more physically interpretable structural description Core Principles: • Physical reality is continuous at the foundational level • Stable physical entities correspond to resonance states with phase coherence • Observable properties emerge from internal geometric and relational structure • Mathematical representations correspond to projections of deeper subspace relations Within the RBS-D framework, physical systems are described in terms of: • continuous subspace structures• phase-coherent mode configurations• relational geometry between interacting components• resonance-based stability conditions RBS-D CONTENT MAP (Series Navigation) • Core Focus:Conceptual and geometric vision of subspace-based physical description • Key Contribution:Transition from conceptual hypothesis (P01) to geometric interpretation • Extends:→ Publication 01 (Foundational Concept and Structural Framework) • Leads to:→ Publication 03 (Mathematical Operator Formalization)→ Publication 04 (Stability Theory of Resonance Structures) • Application Context:Conceptual physics, geometric modeling, interpretation of quantum and field structures Recommended Entry Path: → Publication 01 (Conceptual Foundation)→ Publication 03 (Mathematical Formalization)→ Publication 04 (Stability Theory) Series Context: This publication is part of the 24-part framework"Resonance-Based Subspace Dynamics (RBS-D)". The series develops a unified structural approach across: • theoretical physics• applied mathematics• nonlinear dynamics• plasma and fluid systems• astrophysical structures The framework progresses from conceptual foundations (P01–P03)to geometric and stability analysis (P04–P07),and further toward applied resonance engineering (P15–P24). Scientific Position: RBS-D does not replace established physical theories, but provides a structural interpretation that connects them through resonance-based dynamics and relational geometry. Abstract (English) This publication develops the geometric interpretation of the Resonance-Based Subspace Dynamics (RBS-D) framework, in which physical reality is described as a continuous subspace structured by resonance and phase relations. Physical entities are interpreted as stable, phase-coherent mode configurations, while observable properties emerge from internal geometric and relational structure. Mathematical state spaces are understood as projections of deeper subspace dynamics. This work establishes the transition from conceptual foundation to geometric interpretation and provides the basis for subsequent mathematical formalization and stability analysis within the RBS-D series.