Could you add a footnote somewhere about the shortcuts that you took and the problems that may arise from the changes?

I didn’t implement the “fake infinite” points at the start and end of the series, and I'm not 100% sur that my feature-merging algorithm is correct.

Should the number of displayed labels be clamped to the number of computed features? It's a bit weird to see data points labeled outside of the simplified line.

It's just one of many possibilities. Another difference is that for the labels I force the sorting by "error" rather than "by persistence", because it looks better for this chart.

Being completely foreign to the topic, I found this article to be an excellent introduction: https://towardsdatascience.com/persistent-homology-with-examples-1974d4b9c3d0

Cool graphs :) To do TDA in 2 dimensions or more you can use the union-find data structure to merge features efficiently (https://observablehq.com/@fil/union-find?collection=@fil/tda); in 1 dimension like here, the algorithm is much simpler: look to the left for all the points of the old feature, and absorb them; then do the same to the right.