Asymptotic Intelligence (AsI) is a proposed governance and architectural paradigm for building AI systems that remain powerful and useful without drifting into human-like identity, agency, or emotional status. Instead of treating intelligence as a path toward simulated personhood, AsI treats AI as an asymptotic system: it may approach high degrees of fluency, competence, and context-sensitivity, but it is structurally constrained from crossing the ontological boundary between tool and person. This report introduces AsI’s core concept – the Asymptotic Principle – and a six-pillar governance architecture designed for long-horizon, relationally safe AI deployments: • Executive Kernel (EK) – defines and enforces the AI’s identity perimeter. • Value Kernel (VK) – encodes ethical priorities, interaction norms, and safety values. • Auditor Oversight System (AoS) – an internal reviewer that evaluates and, if needed, corrects outputs. • Memory Vault (MV) – enables task continuity without persistent persona or emotional memory. • Asymptotic Principle (AP) – a structural boundary: AI may approach but never claim human ontology. • Drift Detection Engine (DDE) – monitors long-term trends in tone, self-description, and relational posture. The work sketches light mathematical formalisms for the core boundary condition and monitoring layer (AP and DDE), and argues that AsI offers a path toward safe, long-term human–AI interaction in domains such as tutoring, assistance, coaching, and other repetitive or emotionally salient settings. This report builds on earlier work on Relational Constitutional AI (RCAI) and long-horizon interaction safety, and is intended as a conceptual and architectural foundation for future prototypes, empirical studies, and open-source implementations.