Cohomology proof shows local AI checks miss context non-transportability

Suyash Mishra's new arXiv paper, "Local verification cannot detect non-transportability: a cohomological theory of context preservation in agentic reasoning," delivers a rigorous mathematical blow to a common AI safety practice. As agentic AI systems increasingly transport conclusions across domains—say, a clinically validated hypothesis applied to a financial model—the default safeguard is local verification: confirming at each step that entities, parameters, and outputs are representable and coherent. Mishra proves this class of safeguard is structurally incomplete under a cohomological framework that models context space as a nerve and evidence as a real-valued 1-cochain.

The paper shows that an agent chaining evidence performs path integration, and its conclusion is path-independent only if the cochain is exact. Disagreements between valid reasoning paths correspond exactly to the holonomy of a first Čech cohomology class. Using Hodge decomposition, evidence conflict splits into gradient (calibration), curl (local inconsistency), and harmonic parts. The central result: no family of simplex-supported consistency checks can distinguish a cochain from one shifted by a harmonic component, which still generates nonzero disagreement between valid paths. Detection requires a statistic on a cycle basis. Mishra introduces Ksetra, which estimates via coboundary projection and gates abstention on the harmonic component—driven by effect modification and population composition.

Ksetra also yields an exact F-test for the existence of a global claim, partitioning evidence network degrees of freedom into calibration, coherence, and transport. The paper quantifies distortion under unequal precision and provides a precision-whitened form that restores exactness. A foreign exchange case serves as a calibration bench: the arbitrage-free null makes the cochain exactly a coboundary, and the test is correctly sized, firing on loop arbitrage while ignoring triangular arbitrage. At 17 pages with 10 figures, this is a dense but practical contribution for teams building verification layers for agents in high-stakes domains.