Self-Reflective Geometric Engine: Lossless Continual Learning via Geometric Phase and Orthogonal Injection

We present the Self-Reflective Geometric Engine (SRGE), a novel continual learning architecture that eliminates catastrophic forgetting through geometric self-awareness. SRGE treats transformers as dynamic Riemannian manifolds, using curvature detection in a 16D measurement space to trigger learning only when geometric surprise signals genuine novelty. Memories are stored via orthogonal injection, ensuring new knowledge cannot interfere with existing representations. The architecture achieves lossless continual learning through five mechanisms: curvature-triggered gates, injective hidden states, orthogonal decomposition, a Z-axis witness frame, and self-referential verification. This work bridges differential geometry with practical transformer architectures, offering a mathematically grounded approach to continual learning without forgetting..