<<As below, so above: Behold, Ravari's Wheel!
Lead source,
Tin reactive-ator,
Iron comparator,
Copper counter,
Silver sink,
Gold result,
and the Mercurial mover on which it pivots!>>

[[... silly poems aside, would you care to explain this confounded contraption?]]

<<Oh, *fine* -- we start with taking the input metal and converting it into an intermediate I call its Projection Representation.>>

[[Ah, so called because the quicksilver needed to project to the original metal is conveniently attached to the lead.]]

<<Correct. After that, we conditionally attach an additional quicksilver, then project the lead back to the original metal.>>

[[... sounds like that's just attaching a quicksilver with extra steps.]]

<<But, BUT! The Projection Representation allows us to attach the quicksilver from different directions! The end result is the reactive form of the metal, but with the physical orientation indicating the type of metal!>>

[[Ahhh, and that's why you call this the Reactive Representation.]]

<<Precisely! After that, you can compare the representations in pairs to determine if there's a match. If it's a match, then you increment the counter here by projecting it by one tier. If it's not a match, then the counter is used to make a segment of the output, resetting the counter in the process.>>

[[Impressive! ... well, except that you could probably make a cheaper counter by just rotating the wheel rather than projecting. Also it seems a bit big.]]

<<... I'm going back to my office.>>

[[Plenty of other work to do, I'm sure.]]