Reverse Engineering an ASIC

What happened

Jane Street recently released a puzzle where the goal is to reverse engineer an ASIC chip, figure out what it does, and submit a solution. I urged my friend Leander to join me and see if we could figure it out. Along the way, it dawned on me that the road to the solution could be illustrated in particularly pretty terms, so here is my attempt at that.

Summary assembled by rule from the sources below

Sources