We develop a mathematical theory of the Economic Singularity—the finite-time threshold transition at which AI-driven growth destabilizes classical economic structures. Extending the hyperbolic-growth framework of Yaremenko (2026), we introduce a four-variable dynamical system: AI capability A(t), governed by ; AI capital K_ai(t); financial capital K_f(t) governed by a stochastic differential equation with AI-enhanced returns; and productive labor L_p(t), subject to hyperbolic displacement. We derive a dimensionless threshold parameter Λ(t) = ϕλA(t)/ξ, defined as the ratio of disruption to stabilization forces, together with the crossing time tΛ at which Λ reaches unity. Under baseline parameters the threshold is crossed at t_Λ ≈ 10.45 years (2036), with a labor half-life of 3.87 years and 99% displacement at 14.82 years. Because A(t) → ∞ as t → t_s, no finite friction can prevent the eventual transition; the policy problem is therefore to delay it and manage its distributional consequences. The elasticity of t_Λ with respect to ξ is approximately +0.82, confirming ξ as the dominant single policy lever within the model. We emphasize that all quantitative dates are scenario outcomes conditional on rough parameter estimates, not predictions, and we report global sensitivity analysis and stochastic first-passage distributions to quantify this uncertainty.