This document defines three irreducible governance primitives, Authority ≠ Outcome, Permission ≠ Decision, and Declared Authority, to establish a formal framework for structural legitimacy in automated systems. Through a clean-room logic sequence, it demonstrates that while escalation detection is a computable and deterministic function, the mapping from escalation to action selection is inherently non-unique, mathematically requiring an explicit human authority function. The sequence provides a total control flow for escalated events, introducing constraint-scoped action sets, explicit permission declaration, authority liveness requirements, and immutable execution records. These elements jointly ensure that authority cannot be automated, inferred, or silently delegated, even in systems with perfectly aligned objectives or complete signal observability. Outcome quality is shown to be irrelevant to legitimacy; legitimacy depends solely on the explicit placement and declaration of authority within the system. This work formalises the minimum structural conditions under which automated systems may act without exercising implicit or unauditable authority, providing a foundational logic for governance, safety, and accountability in AI-mediated decision processes.
Passell et al. (Wed,) studied this question.