BU77 AAI-09 | AI-Shadow Unavoidability Theorem under B_U Finite Envelope, Moving Reality, Source-Level Boundary, and Iterative Settlement

This paper develops BU77 AAI-09|AI-Shadow Unavoidability Theorem under B_U as the ninth file in the B_U-based Agentic AI series. Its central claim is that shadow-level bugs and failure modes in AI systems cannot be eliminated once and for all by additional code review, testing, red-teaming, or formal verification. In an evolving real-world environment, every finite AI system is built from finite models, finite data, finite validation sets, finite tool interfaces, finite runtime constraints, and finite resolution. Such a system can only envelope a limited time slice of reality. Once deployed, the world continues to move: user behavior changes, task distributions shift, institutional rules adjust, impedance…