Artificial intelligence (AI) is emerging as a foundational general-purpose technology, raising new dilemmas of sovereignty in an interconnected world. While governments seek greater control over it, the very foundations of AI--global data pipelines, semiconductor supply chains, open-source ecosystems, and international standards--resist enclosure. This paper develops a conceptual and formal framework for understanding sovereign AI as a continuum rather than a binary condition, balancing autonomy with interdependence. Drawing on classical theories, historical analogies, and contemporary debates on networked autonomy, we present a planner's model that identifies two policy heuristics: equalizing marginal returns across the four sovereignty pillars and setting openness where global benefits equal exposure risks. We apply the model to India, highlighting sovereign footholds in data, compute, and norms but weaker model autonomy. The near-term challenge is integration via coupled Data x Compute investment, lifecycle governance (ModelOps), and safeguarded procurement. We then apply the model to the Middle East (Saudi Arabia and the UAE), where large public investment in Arabic-first models and sovereign cloud implies high sovereignty weights, lower effective fiscal constraints, and strong Data x Compute complementarities. An interior openness setting with guardrails emerges as optimal. Across contexts, the lesson is that sovereignty in AI needs managed interdependence, not isolation.