Authority Is a Continuous System presents a formal model in which authority is not a transferable artifact or possession, but a continuous and causally constrained property of execution. Extending prior work on Provenance Identity Continuity (PIC), the paper defines authority as a monotonic flow rooted in an immutable execution origin and preserved only through verified causal succession. All valid execution steps are governed by continuity guardrails and a succession function that enforces monotonic restriction, executor continuity, and contextual validity. The model supports sequential and concurrent execution via fork and join while preserving authority monotonicity, and introduces governance as a policy-constraining layer that may restrict or terminate authority but never create it. The paper proves that Proof-of-Possession–based authorization systems are incompatible with zero-trust requirements under authority continuity, since possession enables authority reconstruction outside causal execution. Authority continuity is shown to be a necessary foundation for zero-trust and confused-deputy–free distributed systems.