Nice!
Indeed, the Lix algo tries to have savestates of useful phyus (= physics updates = moments in gametime).
In particular, there is always a savestate younger than a second, and another younger than two seconds, for quick take-backs of the most recent error.
Memory for savestates is not as cheap as the article might make it sound, but still cheap enough to carry several savestates of larger maps. The trick is to throw away most older savestates: The older the savestates are, the larger is the required phyu interval to keep them, and all others are discarded.
2015 Lix offered no takeback at all in singleplayer, which is perplexing because the infrastructure already existed from multiplayer, to recompute whenever laggy game packets arrived.
2015 NL had no savestates at all and recomputed from the beginning for every takeback.
2019 NL is grained looser than Lix, but keeps more overall savestates. 2019 NL is slightly less performant for undoing recent mistakes.
-- Simon