Resonance-Based Subspace Dynamics (RBS‑D) – Framework 2 Publication Nr. 27: The Tetravalent Structural Theory

The publication introduces the Tetravalent Structural Theory within Framework 2 of Resonance-Based Subspace Dynamics (RBS‑D). While Framework 1 established the mathematical and computational foundations for analyzing nonlinear dynamical systems, Framework 2 investigates whether complex systems can be described through a small set of universal structural roles that remain independent of their physical realization. The theory defines four fundamental roles — U1 (Structural Stability), U2 (Structural Dynamics), r (Structural Topology), and φ (Structural Phase Organization) — together with the temporal ordering parameter τ. Based on these roles, the publication introduces a hierarchical family of structural models: ATM‑15, ATM‑31, and ATM‑63, representing progressively richer levels of organizational complexity. The work positions Framework 2 as an open, expandable scientific program aimed at developing a universal structural language for comparing, classifying, and interpreting complex systems across disciplines. It complements the dynamical and resonance‑oriented investigations of Framework 1 and establishes one of the central theoretical components of the broader RBS‑D research architecture.