The Tri-Polar Compute Manifold. Regime Structure, Relative Compute, and Escape Velocity

How do domestic political structures constrain a state’s capacity to build and deploy frontier compute? Aggregate measures of industrial scale and defense spending do not answer the question. This article models technological state capacity as relative compute against a moving frontier. Regime coercion enters as a tax on true feedback fidelity; reported capacity is an observation, not the state. Three basins follow from the sign of a single growth gap β. Russia occupies an analogue attractor: relative compute is globally asymptotically stable at zero. China occupies a dual-pole band: market scale supplies a logistic restoration that yields a unique finite lag if and only if scale exceeds a coercion-and-sanctions threshold. The United States occupies an escape-velocity face if and only if its net growth outranks both rivals; that face is positively invariant and is destroyed if American administrative friction or talent restriction flips the ranking. 2025–26 evidence is consistent with the Russian and Chinese sign patterns. American industrial policy has already moved U.S. friction off the theoretical zero bound. Lyapunov proofs are given in the appendix.