try working on combining shift register, we morally are on the right track but need to finetune the indexing and make sure the boundary cases don't break stuff)

seems to work, i think we should write the shift register so we can do the proof against the golden model (which uses a nonsynthesizable RAM)

we can make this read-only because the only write that happens is for the parse tree and there's no read/write, it can be done with a straightforward gearbox, i believe.