Significant Others (SOs) stabilize identity, regulate emotion, and support narrative meaning-making, yet many people today lack access to such relational anchors. Recent advances in large language models and memory-augmented AI raise the question of whether artificial systems could support some of these functions. Existing empathic AIs, however, remain reactive and short-term, lacking autobiographical memory, identity modeling, predictive emotional regulation, and narrative coherence. This manuscript introduces Significant Other Artificial Intelligence (SO-AI) as a new domain of relational AI. It synthesizes psychological and sociological theory to define SO functions and derives requirements for SO-AI, including identity awareness, long-term memory, proactive support, narrative co-construction, and ethical boundary enforcement. A conceptual architecture is proposed, comprising an anthropomorphic interface, a relational cognition layer, and a governance layer. A research agenda outlines methods for evaluating identity stability, longitudinal interaction patterns, narrative development, and sociocultural impact. SO-AI reframes AI-human relationships as long-term, identity-bearing partnerships and provides a foundational blueprint for investigating whether AI can responsibly augment the relational stability many individuals lack today.