arXiv:2503.08725v3 Announce Type: replace-cross Abstract: As artificial intelligence transforms public sector operations, governments struggle to integrate technological innovations into coherent systems for effective service delivery. This paper introduces the Algorithmic State Architecture (ASA), a novel four-layer framework conceptualising how Digital Public Infrastructure, Data-for-Policy, Algorithmic Government/Governance, and GovTech interact as an integrated system in AI-enabled states. Unlike approaches that treat these as parallel developments, ASA positions them as interdependent layers with specific enabling relationships and feedback mechanisms. Through comparative analysis of implementations in Estonia, Singapore, India, and the UK, we demonstrate how foundational digital infrastructure enables systematic data collection, which powers algorithmic decision-making processes, ultimately manifesting in user-facing services. Our analysis reveals that successful implementations require balanced development across all layers, with particular attention to integration mechanisms between them. The framework contributes to both theory and practice by bridging previously disconnected domains of digital government research, identifying critical dependencies that influence implementation success, and providing a structured approach for analysing the maturity and development pathways of AI-enabled government systems.