We present a battery of 2880 three-dimensional N-body simulations testing which initial summaries of particle structure and phase-space information carry predictive power for future gravitational clustering. The battery spans N ∈ 256, 2048 particles, softening lengths ε ∈ 0.02, 0.10, 4 initial condition families, and 2 force-model classes, with 30 independent realisations per parameter cell. The result is not a universal ranking: which description best predicts later clustering depends on both the initial condition family and the observable class. Bimodal (two-cluster) initial conditions define a robust coarse-dominance regime in which the initial large-scale density variance predicts future clustering with r = −0.975 (95% CI −0.99, −0.95) at representative N = 1024, ε = 0.05; this bimodal verdict holds without exception across the full parameter sweep. None of the tested positional fine observables—local kNN density, small-scale Fourier power, close-pair fraction—outperforms the coarse predictor for this family. Concentrated profiles (Hernquist, Plummer) show a suggestive fine-leaning VelDisp signal at small softening; the 95% confidence intervals include zero at the current replicate count and the pattern is not robustly established. Tested positional fine observables do not outperform the coarse predictor for concentrated profiles either. The boundary between regimes appears to be governed in part by the softening-to-scale-radius ratio: the VelDisp signal weakens substantially by ε = 0.10. These results show that in 3D self-gravitating N-body systems, predictive advantage is family-dependent and observable-class-dependent: bimodal mergers robustly favor coarse density structure, whereas concentrated profiles show only a suggestive fine-kinematic signal at small softening, with no tested positional fine observable outperforming the coarse predictor.
Kunal Bhatia (Fri,) studied this question.