Abstract Enterprise organisations are causal systems of extraordinary complexity. The artificial intelligence frameworks deployed to manage them have universally failed to model this causal complexity — operating instead on statistical correlations in observed data, without access to the generative structure that produces those observations. This paper introduces Causal Topology Detection — a systematic framework of nine algorithms for identifying the fundamental patterns of causal dependence that govern enterprise systems. Grounded in the Meta-Generative Principle and implemented through VectorPeak's Generative Hierarchy Algorithm (GHA) and Sustainability Optimizer (SO), the framework identifies eight fundamental causal topologies — Linear, Divergent, Convergent, Cyclical, Hierarchical, Mesh, Latent, and Interventional — and a meta-algorithm, the Hybrid Topology Classifier, that identifies the unique causal topology signature of an enterprise. Each topology is defined precisely, its detection algorithm specified formally, and its enterprise applications developed in detail. Together, the nine algorithms constitute the first systematic framework for causal topology detection in enterprise systems — enabling AI that understands the generative architecture of organisations rather than merely approximating their statistical surface.