Gödel Memory

This paper introduces a theory of memory and identity in which persistence is defined not by stored content but by the lasting structural changes imposed on future cognitive dynamics through permitted and coherent learning. The framework replaces storage-based models with a minimal internal memory trace that regulates plasticity and identity safety, ensuring that only stable and verified experiences are consolidated while unresolved or unstable states are prevented from shaping long-term structure. Short-term, working, and long-term memory emerge as regimes of a single dynamical process, and forgetting occurs through lack of reinforcement rather than deletion. As the final paper in the trilogy, it provides a unified account of memory, consolidation, and identity under uncertainty and incompleteness.