Analysis utilities

These functions support downstream diagnosis and interpretation, but are not required for the core pipeline.

circle_bundles.fiberwise_clustering	Cluster each fiber with DBSCAN and then merge clusters globally via an overlap graph.
circle_bundles.get_local_pca	Compute and plot local PCA embeddings for fibers of a cover.
circle_bundles.get_local_rips	Compute Ripser persistence separately on each fiber of a cover.
circle_bundles.plot_local_rips	Plot a grid of persistence diagrams for multiple fibers.
circle_bundles.get_cocycle_dict	Construct a Z2-valued Čech 1-cocycle dictionary from a fiberwise cluster graph G.
circle_bundles.lift_base_points	Assign consistent signs to representative vectors of points in a double cover (e.g. S^2 -> RP^2).