Observable-Class Predictability in Stylised Three-Dimensional Self-Gravitating N-body Families: Coarse Dominance, Kinematic Advantage, and Softening Dependence

We perform a controlled battery study of predictive performance across coarse positional, fine positional, and fine kinematic observables in four stylised three-dimensional self-gravitating N-body families, using 140000 simulations with 500 realisations per cell, two force models, and a five-point softening sweep (ε ∈ 0.02, 0.10). The primary result is robust coarse dominance for merging binary clusters: grid-scale density variance predicts future clustering at r = 0.984 (ε = 0.05; winner-gap CI −0.42, −0.30) across all tested N, ε, and force models. A secondary result is a restricted fine-kinematic regime: local velocity dispersion outperforms the coarse predictor for concentrated cusp profiles at low softening (Hernquist ε ≤ 0.05, Plummer ε = 0.02; gap CIs exclude zero), though the effect is modest (R2 ≈ 0.18–0.28 at N = 1024). This advantage erodes with increasing ε and vanishes by ε = 0.10. The strongest negative result is that no positional fine-scale observable outperforms the coarse predictor in any tested cell. No universal ranking is supported: predictive advantage is structured by initial-condition family, observable class, and the softening-to-scale-radius ratio ε/a. The point is not that finer descriptions are generally worse, but that additional spatial detail alone is insufficient unless it carries the dynamically relevant information channel.