I don't know how to lay things out properly, but luckily using way too much track saves the day.
The revari's wheel makes a copy of the input atom so that it can be sent to the output. I was originally going to make three copies to compare using purification, but then you can't detect gold, so I had to use sticks instead. There's a consistent anchor point for the stick with arm 13/14 to move it to the second station, where it moves in reverse - so it has an exact position if the current metal is equal to the last one. Then we just normalize the position and give arm 18 a lead if it wasn't equal. It's just straightforward conditionals from there and not really worth discussing.

The main repeating loop to test one quicksilver on the input has an extra 2 cycle delay I added early on just in case I ever needed it. I didn't need it, but I didn't want to figure out how safe it would be to remove it. I was also too lazy to figure out adding a disposal for one of the wastechains (the lead one, probably) despite how it would absolutely be worth it due to how much area those cost.

Another approach I considered was making three copies of metals anyway since you can compare (including gold) compactly with quicksilver, but I felt like that would make the solution actually pretty slow. It'd save all the gold I spent on tracks though.