a big goal of our paper was to really highlight how useful these operators really are. making it fast was more of a side-goal, so there would be less to complain about, as there was already a lot of disbelief, and we got comments such as it being a “theoretical curiosity”. i spent over a year experimenting with different approaches (there’s an initial draft on arXiv from 2023 where lookarounds had much worse complexity), but finally we found a combination that works extremely well in practice, and it helped me find a deeper intuition for what works both in theory and in the real world.
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