The python code results on simple clustering example show things have serious bug or do work at all!

[mosfet123]

Give you a simple example: [1,2, 10,11,12, 54]. Your python code generates a completely wrong clustering tree.
I figured out the starting insert a new data point from 10 becomes completely misleading. It breaks 1 and 2 pairs which should be not!
In fact to get valid nearest neighbor you need search up the whole tree without breaking tighter sibling pairs.
Your introduction example using high dimension random numbers fool yourself and others who try to validate the algorithm.
Without correction I think that your work is not serious at all!