A Bounded Elastic O(1) Safety Governor for Event-Gated Resource Control (B-ER-E-ATG-CGRC)

This work presents a novel, minimal-complexity safety governor designed for systems operating under strict computational ($\mathbf{O(1)}$ per timestep) and resource constraints. The architecture is built on five orthogonal statistical primitives ($\kappa_x, v_x, \alpha_x, P, \delta_{\text{plaus}}$) and is governed by a dual-timescale adaptive control law.

The system is explicitly designed to solve the critical trade-off between efficiency and resilience in adversarial environments.

Key Features and Results:

• Verifiable Resilience: Achieved zero observed catastrophic failures (False Negatives) against stochastic noise, correlated drift, and structured adversarial temporal probing (the $P_{\text{limit}}-1$ spoof).

• Bounded Adaptation: Implements a scale-invariant safety clamp on the adaptive margin ($\delta_{\text{plaus}}$) to prevent decision-boundary collapse, guaranteeing the structural preservation of the detection region for slow-onset, legitimate threats.

• Computational Efficiency: All decision primitives and adaptive updates are strictly $\mathbf{O(1)}$, making the governor suitable for deployment on low-power, embedded hardware (e.g., satellites, medical implants, or LLM runtime gates).

• Resource Economy: Demonstrated near-minimal resource expenditure, achieving a high ratio of budget saved by rejecting noise versus energy wasted on false alarms.

The B-ER-E-ATG-CGRC provides a mathematically defensible, practical primitive for safety-critical governance across aerospace, industrial control, and autonomous systems.