The Competence Shadow: Theory and Bounds of AI Assistance in Safety Engineering

As AI assistants become integrated into safety engineering workflows for Physical AI systems, a critical question emerges: does AI assistance improve safety analysis quality, or introduce systematic blind spots that surface only through post-deployment incidents? This paper develops a formal framework for AI assistance in safety analysis. We first establish why safety engineering resists benchmark-driven evaluation: safety competence is irreducibly multidimensional, constrained by context-dependent correctness, inherent incompleteness, and legitimate expert disagreement. We formalize this through a five-dimensional competence framework capturing domain knowledge, standards expertise, operational experience, contextual understanding, and judgment. We introduce the competence shadow: the systematic narrowing of human reasoning induced by AI-generated safety analysis. The shadow is not what the AI presents, but what it prevents from being considered. We formalize four canonical human-AI collaboration structures and derive closed-form performance bounds, demonstrating that the competence shadow compounds multiplicatively to produce degradation far exceeding naive additive estimates. The central finding is that AI assistance in safety engineering is a collaboration design problem, not a software procurement decision. The same tool degrades or improves analysis quality depending entirely on how it is used. We derive non-degradation conditions for shadow-resistant workflows and call for a shift from tool qualification toward workflow qualification for trustworthy Physical AI.