R-layer Mode Theory(RLMT) XV: develops the fully dynamical extension of the R-layer framework, transforming the static formulations of Volumes XII–XIV into a complete time‑dependent theory of tension, gravity, information, and central structure. The volume derives the nonlinear Schrödinger–Poisson system governing tension‑field evolution, analyzes symmetry‑breaking phase transitions, constructs the fluctuation cascade that generates hierarchical cosmic structure, and identifies R-waves as information‑carrying excitations capable of synchronizing distant regions. A major contribution of this volume is the integration of observational anchors that directly probe the predictions of the dynamic R-layer: Early‑universe localized condensation in the globular cluster M4, enabling the formation of the ~12.7 Gyr Methuselah planet Central reorganization in compact galaxies such as NGC 4486B and UCD736, including double‑nucleus structures, off‑centered supermassive black holes, and extreme BH mass fractions revealed by JWST These phenomena are interpreted as scale‑separated manifestations of the same R-layer reprojection dynamics, linking early cosmic maturation with late‑time central restructuring. Appendices provide a unified geometric interpretation across scales and outline observational strategies for testing the dynamic R-layer theory using JWST, ELT, SKA, and deep lensing surveys. This volume positions the R-layer Mode Theory for direct empirical validation and establishes the dynamical foundation for future developments in the RLMT series.

This Version 2 update adds the AI‑usage declaration and applies minor corrections. All equations, figures, and scientific results remain unchanged.