Cohomological Limits of Local Verification in Agentic AI Reasoning

A new paper on arXiv (2608.11252) presents a mathematical proof that local verification methods in agentic AI systems are structurally incomplete. The authors model context spaces using nerve coverings and evidence as real-valued cochains, showing that an agent's reasoning path is path-independent only if the cochain is exact. Disagreements between valid reasoning paths correspond to the holonomy of a first Čech cohomology class. Hodge decomposition reveals three components of evidence conflict: gradient (calibration), curl (local inconsistency), and harmonic. The central theorem states that no family of simplex-supported consistency checks can distinguish all such classes, implying that local checks cannot ensure non-transportability of conclusions across biological, clinical, and financial contexts. The paper was announced as a new arXiv submission and is available at the provided URL.