Why AI Governance Fails: A Dominance-Geometry-Dynamics Diagnosis

Current AI governance frameworks—the EU AI Act, the NIST AI Risk Management Framework, and China's regulatory regime—share a structural blind spot: they conflate Pareto-dominance relations with metric-dependent scoring. Using the Dominance-Geometry-Dynamics (DGD) framework, this paper derives six governance principles from order-theoretic axioms and tests them against all three regulatory regimes. None implements any principle fully (0/18). The EU AI Act's Article 3(2) definition of risk as a scalar (probability × severity) is shown to be a geometric conflation made law. A three-phase DGD-native governance protocol is proposed: dominance mapping, attractor diagnosis, and geometric calibration with regime monitoring.