Local Verification Fails to Detect AI Context Transport Issues

This paper presents a theoretical proof demonstrating a fundamental limitation in current safeguard practices for agentic AI systems. It argues that "local verification," which involves checking consistency at each step of an agent's reasoning, is structurally incomplete and cannot reliably detect "non-transportability." Non-transportability occurs when conclusions are inappropriately carried over between different contexts, such as biological, clinical, or financial domains, leading to incorrect outcomes. The research introduces a cohomological theory to model context space and evidence, showing that disagreement between valid reasoning paths is precisely the "holonomy" of a first Cech cohomology class. This theory partitions evidence conflict into calibration, local inconsistency, and a harmonic part. Crucially, the paper proves that local checks cannot distinguish the harmonic component, which generates non-zero disagreement. A new procedure, Ksetra, is proposed to estimate this harmonic component and gate abstention, offering a mechanism to detect context preservation failures that local methods miss.