Authors: Nicolas Poupart
We investigate the evaluation of effective gravitational binding energy in heterogeneous stellar systems and compare a permutation-invariant exact estimator with heuristic sequential formulations. The exact estimator provides a physically consistent reference based on additive contributions and volume-conserving mergers, whereas the heuristic formulation introduces a path dependence that can strongly modify the reconstructed dark-to-baryonic mass ratios.A systematic exploration of stellar-population permutations quantifies this sensitivity and shows that optimized orderings can substantially reduce the bias of the heuristic approximation. Using SPARC-based reconstructions together with GALEX and SDSS photometric tests, we show that the apparent numerical advantage of the heuristic method is partly artificial when it is evaluated against the exact energy. A simplified reconstruction program nevertheless demonstrates that similarly high dynamical success rates can be recovered when the exact estimator is used directly during optimization.These results establish the exact estimator as the physical baseline for effective gravitational binding energy, while showing that the success of the reconstruction is driven primarily by the underlying physical constraint rather than by algorithmic sophistication.
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