Power Law Distribution of AI Incidents on an Epistemic Toroidal Manifold

We analyze 1,392 AI incidents from the AI Incident Database (aiid) and show that incident severity, measured by report count, is consistent with a power law distribution with exponent α = 5.06 ± 0.65 above a minimum threshold xmin = 25 (KS statistic = 0.093, bootstrap p = 0.575, power law not rejected). The empirical distribution exhibits heavy-tail behavior with a Gini coefficient of 0.977, where the top 10% of incidents concentrate 99.6% of the total severity weight. We embed these incidents into a 5-dimensional epistemic manifold—the Directional Relational Manifold (drm)—projected onto a flat torus T 2. On this surface, catastrophic incidents cluster in geometrically identifiable regions near the Ignorance and Ambiguity anchor points, while moderate incidents distribute more uniformly across the toroidal surface. Building on this empirical distribution, we calibrate a Pareto-weighted gravitational field on the manifold that amplifies monitoring intensity in catastrophic regions by up to 30.4× compared to a uniform baseline. The resulting field concentrates computational resources where the empirical tail predicts the highest risk, providing a data-driven foundation for epistemic safety architectures.