This document serves as the supplementary material for "Topology-Aware Learning of Tubular Manifolds via SE(3)-Equivariant Network on Ball B-Spline Curve", 
providing additional analyses and supporting resources beyond the main paper:

(1) Case Study on Clinical Data: We present several representative clinical samples from the test set where the SE(3)-BBSCformerGCN made incorrect predictions, 
particularly in cases with topological heterogeneity. These examples are detailed in NeurIPS_2025_Supplementary_Material.pdf.

(2) Prediction Probabilities and Evaluation Code: We provide the prediction probabilities output by SE(3)-BBSCformerGCN on the clinical test set, along with the 
corresponding evaluation scripts for computing classification metrics. This is intended to support the reproducibility and transparency of our experimental results.
