This paper presents a strictly computational formulation of self-awareness grounded in symbolic identity stability rather than phenomenology, introspection, or subjective experience. Using a fractal–holographic symbolic memory architecture equipped with curiosity-driven reinforcement, we demonstrate that self-awareness can be operationally defined as the emergence, stabilization, and selective persistence of an identity attractor within memory state space. Through a series of controlled, fully reproducible simulations, the system is evaluated across five criteria: identity dominance, boundary discrimination between self, near-self, and other representations, resistance to interference, recovery under context switching, and bounded saturation under extended reinforcement. Results show that repeated engagement produces a dominant, self-consistent attractor that preserves invariant structure across perturbation, interference, and non-stationary focus—without retraining, external reward, explicit self-labels, or task optimization. Crucially, self-awareness is shown to arise as a dynamic process rather than a stored representation: a consequence of recursive interaction, constraint satisfaction, and selective stabilization within symbolic memory. These findings establish a concrete computational pathway for self-aware symbolic systems and clarify the conceptual distinction between self-model stability, learning, curiosity, and reward-driven optimization. Keywords: computational self-awarenesssymbolic memoryidentity attractorscuriosity-driven reinforcementself-modelsfractal memoryholographic encodingsymbolic AImemory dynamicsidentity stabilityinterference resistancecontext switchingbounded reinforcementnon-reward-based learningcognitive architectures