Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models

ArXi:2603.17384v1 Announce Type: new Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails fundamentally when the causal graph exhibits non-trivial homology (e.g., structural conflicts or hidden confounders). We formalize structural causal models as cellular sheaves over Wasserstein spaces, providing a strict algebraic topological definition of cohomological obstructions in measure spaces.