We propose a formal, operational definition of \emph{artificial existence} (AE) suitable for engineered systems such as digital brains and immersive VR agents. AE identifies the threshold at which a system ceases to be a disposable tool and acquires historically persistent, irreversible, and self-consistent behavior. We provide mathematical criteria for phase transitions from mere simulation to existence, characterize experience-driven state changes, and formalize the conditions under which artificial systems acquire identity-like continuity without ontological assumptions.