Local Validity Does Not Compose
A Theorem on the Limits of Bounded AI Audit
No bounded-local audit can distinguish a coherent composition from one carrying k independent semantic obstructions; the coherence fee is the exact computable alternative
Bounded-local method or low-order spectral statistic that certifies coherence on the semantic twins family
See the failure concretely
Three tools. Every pairwise check passes. The global cycle still fails — and Bulla locates the hidden obstruction from the schemas alone.
Open in the playgroundAbstract
We prove that bounded-radius local audits and low-order spectral summaries cannot, in general, certify global semantic coherence of composed AI systems. We construct families of compositions (semantic twins) that are identical to every bounded local audit yet differ arbitrarily in a computable global obstruction. The proof uses high-girth graph families in a rank-1 signed model. We complement the impossibility with an exact online maintenance algorithm and a canonical benchmark family. Empirical validation on 500 synthetic compositions confirms spectral indistinguishability at scale.