Entropy-Gated Wave Control for Identity Preservation in Adaptive Systems Master Manuscript (Full Proof + Figures + Handwritten Origin Appendix) Kemar Armando Morrison Independent Researcher kemar.morrison@ou.ac.uk December 2025

We present an entropy-gated wave control framework for adaptive dynamical systems in which dissipation is activated only when an information-theoretic identity invariant is violated. The model couples a second-order wave equation to a binary gate defined by the Shannon entropy of a normalized field. When entropy remains within an admissible tolerance band, the system evolves freely; once the tolerance is exceeded, dissipation is triggered until admissibility is restored. We establish a Lyapunov-type energy identity with conditional dissipation, prove global energy boundedness, and show recoverable identity preservation under mild regularity assumptions linking entropy to the state norm. A numerical illustration is provided, and we append a provenance section linking the formal model to the author’s handwritten exploratory notes.