Thanks for your comment.

To clarify: K is a fixed hyperparameter in this implementation, strictly independent of N. Whether we process 9k points or 90k points, we keep K at ~100. We found that increasing K yields diminishing returns very quickly. Since the landmarks are generated along a fixed synthetic topology, increasing K essentially just increases resolution along that specific curve, but once you have enough landmarks to define the curve's structure, adding more doesn't reveal new topology… it just adds computational cost to the distance matrix calculation. Re: sqrt(N): That is purely a coincidence!