We show that the autopoietic hierarchy is a formal consequence of three foundational premises within any stable, spatially extended environment. These premises are change (the cosmic ought), finite information capacity (the Bekenstein bound), and stable low-level conditions. From these we derive the three orders of persistence (static, dynamic, and novelty-generating) as a chain of formal consequences. A formal Stack Theoretic interpretation of the Law of Increasing Functional Information shows that persistence under novelty favours weakness maximisation, because this keeps the most compatible futures open. We show that weakness maximisation diverges from simplicity maximisation in stable environments. This bridges a void of unviable intermediate forms and entails self-producing, boundary-maintaining systems. We then invoke the Law of the Stack to show that dynamic persistence at lower levels unlocks higher-level adaptability, creating selection pressure for novelty generation and the preconditions for open-ended evolution. The three orders are thus derivable from axioms rather than identified as empirical regularities. We ground each stage in established models of self-replicating cellular automata, autopoietic protocells, and homeodynamic selves. The result subsumes Assembly Theory's proposed orders of selection while deriving them from weaker assumptions, and reframes the origin of life as a question about mechanism rather than about possibility.