Thanks for the reference! This looks like an implementation of a disjoint set/union-find data structure. I think it could be an interesting direction to explore

Thanks for the reference! This looks like an implementation of a disjoint set/union-find data structure. I think it could be an interesting direction to explore by adapting union-find to handle intervals efficiently, or maybe apply some of the union-find amortized operations tricks to another interval-based tree or similar.