Selection Load as a Computable Invariant for N-Body Outcome Prediction

The gravitational N-body problem is chaotic: individual trajectories are exponentially sensitive to initial conditions and no closed-form solution exists for N ≥ 3. I show that a scalar trajectory invariant—the selection load L = ∫ K dt—derived from the phase-space probability flux through absorbing boundaries, organizes the statistical outcomes of chaotic three-body scattering into monotonic ejection-probability classes. The operator K is obtained from the Liouville equation restricted to the survival manifold, not from a phenomenological ansatz. An associated admissibility field Xi on shape space, computed by averaging K over microcanonical velocity ensembles, recovers the Lagrange equilateral equilibrium as its global maximum without trajectory integration. I prove that the three-body selection kernel is non-factorizable under flat marginals, establishing that pairwise decompositions are structurally insufficient to predict ejection outcomes. Numerical experiments with a DOP853 integrator at energy conservation |ΔE/E| ~ 10^-8 confirm: (i) ejected systems carry 5. 4x higher median L than bound systems, (ii) ejection probability increases monotonically across L-quartiles from 8% to 43%, and (iii) pairwise-factorized predictions achieve only 56% accuracy against a 33% baseline. I demonstrate cross-domain universality by showing that the same K-geometry framework predicts epidemic extinction times on heterogeneous networks (r = 0. 90) and eigenvalue decay rates in non-Hermitian random matrices (r = 0. 96, universal across GUE, GOE, and Wishart ensembles).