Emergent Regime Geometry in Dynamical Systems: A Curvature-Based Informational Perspective

This preprint investigates curvature-like observables extracted from embedded dynamical trajectories as descriptors of metastable regime structure in complex systems. The work combines empirical analysis with a conceptual information-theoretic framework, suggesting a hierarchical interpretation in which regime organization constitutes the dominant structural level, while curvature acts as a secondary observable induced by underlying correlation constraints. The manuscript should be interpreted as a research preprint and not as a fully validated microscopic theory.