Model performance as a function of τ, evaluated using three target-score definitions: past-merger (left), future-merger (middle), and full-merger (right) scores. Orange and blue curves show the training and test R², respectively, and gray histograms indicate the sample count. These tests assess projection robustness. Top: Treating the three orthogonal projections of each halo as independent samples, using the leakage-minimized split (grouping by halo ID). Bottom: Following the setup in Section 3.1.1 (grouping by halo ID and snapshot number and using rotation-based filtering), the projection-rotation order is changed from [z, drop, x, drop, y, drop] to [x, drop, y, drop, z, drop]. The similar performance suggests that the model is not sensitive to the projection order, which is favorable for observational applications where only one projection is available.