Trinity Topology: An Ultra-High-Throughput CUDA Framework for Chaotic Three-Body Decays, Phase-Space Invariants, and Universal Scaling Across 26 Orders of Magnitude

The gravitational three-body problem has stood for over 130 years as the archetype of deterministic chaos, traditionally treated as an ergodically scrambled, memoryless Markov process. Here, we present an ultra-high-throughput computational framework powered by a register-tuned CUDA C++ symplectic leapfrog engine executing on consumer GPU hardware (NVIDIA GeForce RTX 4070), achieving sustained throughputs of 4,236,081 gravitational systems per second and 8,676,681 atomic Coulomb systems per second. Using this engine, we perform two 1,000,000,000-system numerical experiments:1. Among 519,810,403 verified chaotic ejections in the gravitational regime, we identify a fundamental Two-Phase Transition: orbits N <= 4 preserve initial binary pairings in over 70% of configurations and remain governed by deterministic geometric invariants evaluated strictly at t = 0. By orbit N = 5, mutual partner exchanges reach 88.9% (averaging 2.57 swaps per system), erasing initial condition memory and initiating an ergodic Poisson decay process with an invariant escape rate of lambda_grav = 0.0567 per orbit (R^2 = 0.9973, half-life approx. 12.2 revolutions).2. We formulate two novel geometric observables evaluated at t = 0: the Gravitational Time-Shear Delta_Phi_rel and the Doppler Gate cos(alpha). At t = 0, Trinity predicts the escaping candidate with 74.43% accuracy, outperforming Heggie's classical law in 69.89% of direct head-to-head trials. We validate the formulation against observational data from Gaia DR3, Kepler, and the NASA Exoplanet Archive (reproducing the UIUC APEX 2024 ExoStab 2.0 boundary for Kepler-16b to within 0.25% in microseconds), and successfully identify physical false alarms in the NASA TESS candidate catalog (TOI-712.03).3. To test scale universality, we simulate 1,000,000,000 semiclassical Helium atoms (Z = +2, 2 electrons) under Coulomb repulsion (+1/r_12). The resulting 500x500 phase-space density matrix reveals isomorphic topological structures—specifically the Wannier Saddle Ridge (cos(alpha) -> -1.0) and the Frozen Planet Oasis (cos(alpha) -> +1.0)—with an identical decay rate per orbit of lambda_Coulomb = 0.0617 (R^2 = 0.9656). Spanning 26 orders of magnitude in space (10^11 m to 10^-10 m) and 30 orders of magnitude in time, chaotic decay in inverse-square (1/r^2) force fields demonstrates 91.9% topological universality. Source Code & Open Datasets: https://github.com/Bamboulete/three-body-problem-gpu