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

Description This publication develops the geometric interpretation layer of the Resonance-Based Subspace Dynamics (RBS-D) framework, extending the conceptual foundation introduced in Publication 01. It introduces a structural description in which physical reality is modeled as a continuous subspace, where observable phenomena arise from stable resonance configurations and relational mode structures. Unlike classical particle-based interpretations, this work assumes that physical observables emerge from geometric coupling relations within a higher-dimensional subspace. A key conceptual shift introduced in this publication is the transition from object-based physics to relational geometry: physical entities are no longer treated as independent units, but as emergent configurations defined by coupling relations between modes. This establishes geometry—not objects or trajectories—as the primary descriptive layer of physical structure. Core Contributions • Introduction of a geometric framework for resonance-based physical description• Definition of physical entities as phase-coherent relational structures• Transition from particle ontology to relational geometry• Interpretation of observables as projection-based manifestations of structure• Hypothesis: physical descriptions arise from deeper relational geometry RBS-D Content Map (P02 Positioning) • Core Focus:Geometric structure of resonance-based subspace relations • Key Contribution:Transition from conceptual model (P01) to geometric representation layer • Extends:→ Publication 01 (Foundational Concept and Structural Framework) • Leads to:→ Publication 03 (Mathematical Operator Formalization)→ Publication 04 (Stability Theory of Resonance Structures) • Structural Role in Series:Defines the geometric representation layer of RBS-D • Navigation Path:P01 → P02 → P03 → P04 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),through geometric structure (P02),toward mathematical formalization and stability analysis (P03–P07),and later 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 geometry and relational structure.