Agentic AI systems transport conclusions across different contexts, and local verification is the emerging safeguard. However, we prove that this class of safeguard is structurally incomplete. Modeling context space by its nerve and evidence by a real-valued 1-cochain, an agent chaining evidence performs path integration: its conclusion is path-independent if and only if the cochain is exact. Disagreement between valid reasoning paths is exactly the holonomy of a first Cech cohomology class. Hodge decomposition partitions evidence conflict into a gradient part, a curl part, and a harmonic part. Our central result is that no family of simplex-supported consistency checks can distinguish ω from ω+h for harmonic h, which nonetheless generates non-zero disagreement between valid paths; detection requires a statistic on a cycle basis. The resulting procedure, Ksetra, estimates by coboundary projection and gates abstention on the harmonic component, which we give a mechanism: it arises from effect modification combined with overlap-specific population composition, and vanishes to machine precision when effect modification is absent. The degrees of freedom of an evidence network partition into calibration, coherence, and transport, yielding an exact F-test for the existence of a global claim; we quantify its distortion under unequal precision and supply the precision-whitened form that restores exactness. Foreign exchange, where the arbitrage-free null makes the cochain exactly a coboundary, serves as a calibration bench: the test is correctly sized, fires on loop arbitrage, and ignores triangular arbitrage. Blogger's Review: This paper provides a significant theoretical framework for context preservation in agentic reasoning, revealing the limitations of local verification and the mechanism of harmonic conflict, which is crucial for understanding and handling transportability issues in agent systems.