This paper develops a dynamical theory of long-term memory and identity stability within the Reasoning Turing Machine (RTM) framework. Memory is formalized not as stored symbolic content, but as persistent deformation of the system’s energy landscape under behaviorally gated learning. The model integrates computability constraints derived from Gödel incompleteness and Turing limits, treating undecidable regions as structural boundaries in the epistemic manifold. Consolidation, suppression, and forgetting emerge as stability phenomena governed by a minimal memory trace and continuous-time dynamics. This work constitutes the third component of a trilogy, following Empathy Energy Minimization and Intelligent Action, and completes a unified dynamical framework for reasoning, action, and memory in bounded intelligent systems.