This preprint introduces The Infrastructure Sovereignty Gap, a governance framework that distinguishes between legal authority over AI systems and material authority over their execution.

The paper formalizes the concept of the executability constraint—the dependence of AI-enabled public services on continuous access to external compute, models, and infrastructure—and presents the National AI Sovereignty Index (NASI) as a multidimensional, non-compensatory diagnostic tool for identifying sovereignty risks before they manifest as service failures. Rather than ranking states, NASI is designed for internal risk assessment across critical sectors such as health, welfare, identity, and security.

The paper is accompanied by a practical NASI Application Protocol (NAP) that enables governments to apply the framework immediately using existing procurement, regulatory, and operational evidence, even in contexts with zero domestic hardware production. Positioned as a v1.0 conceptual and diagnostic release, this work aims to place infrastructure dependency on record as a first-order AI governance problem and to support iterative empirical refinement through future versions.