The Stack Sovereignty Theorem: A Mathematical Framework for Strategic Economic Power in the Age of Artificial Intelligence, Energy Scarcity, Quantum Risk, and Space Industrialization
Abstract
For decades, standard economic models have compressed technological progress into a weightless, frictionless scalar of total factor productivity (A). This paper develops the Stack Sovereignty Theorem as a theoretical and policy framework for strategic economic power under geopolitical fragmentation. It makes three primary contributions. First, it provides a formal model integrating O-Ring bottlenecks, supermodular complementarities, and convex state-contingent dependence to derive the net condition under which a coherent capability stack dominates isolated technological specialization. Second, it operationalizes the model through a pre-registered Sovereign Stack Index Core (SSI-Core) linking artificial intelligence, compute, energy, and critical-mineral processing. Third, it specifies a pre-registered empirical and public-policy protocol, illustrated through the 2022 European energy crisis, that shows how to diagnose bottlenecks, estimate stress-dependent fragility, and translate the theorem into industrial-policy, strategic-capital-allocation, and alliance-design rules. The paper does not claim completed causal validation; it offers a falsifiable architecture for testing when technological leadership remains robust and when it is undermined by physical constraints, external dependence, or coordination costs. Contemporary strategic power is therefore defined not by isolated technological peaks, but by coherent capability net of supply fragility and integration cost.
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