Machine-Learning Classification of N = 4 Orbital Families via Kelvin-Simplex Face-Activity Descriptors: Accuracy, Cross-Pipeline Robustness, and Regime Sensitivity

The Kelvin-simplex framework represents N-body gravitational dynamics as trajectories on the (N−1)-simplex of normalised kinetic energy fractions. Paper V of this series extended the framework to the four-body problem and introduced two vector-valued descriptors: face-exclusion (FE), measuring the fraction of time each body is kinetically marginalised, and pair-dominance (PD), measuring the fraction of time each pair co-dominates the energy budget. Together these form a ten-dimensional face-activity descriptor vector. Here we ask whether this vector encodes orbital architecture with sufficient fidelity to classify orbital families under supervised machine learning. Using 400 trajectories drawn from five N = 4 families (Square, Hierarchical, Lagrange+1, Chaotic, and Near-Ejection) and four classifiers implemented from first principles, we find that the face-activity vector achieves 88.0 % ten-fold cross-validated accuracy (k-NN, k = 7), compared with 74.3 % for the four-dimensional classical scalar set {H_mean, D_mean, C_prox, Path}. The Hierarchical and Lagrange+1 families are classified with perfect recall. Feature discriminability analysis identifies FE_3 as the dominant single feature (ANOVA F = 133), reflecting the consistent kinetic marginalisation of the fourth body in these families. The face-activity vector thus provides an architectural fingerprint of the four-body problem that can strongly outperform classical simplex scalars as a classification instrument when orbital families express clear energy-partitioning structure, closing the analogue of Paper III for N = 4.