Purify based. State of current pair is on molecule with content on right of purifier and count next to critelli, and gold is represented as reactive silver.

One atom takes 42 cycles to process. Arm 1 pulls quicksilver from the projection overflow station if new atom is gold, or not gold and equals to previous pair. The quicksilver wands previous gold to purification output, so arm 2 grabs if new atom is equal to previous pair. These two molecules (current pair +1 - quicksilver, or silver - quicksilver - quicksilver) shed a quicksilver on critelli station which projects the current count atom. Arm 2 then pivots to isolate the gold-gold case's waste silver and then arm 3 swings the non-gold-equal case's purified metal to overflow station. At this point, a pair needs to be outputted if a metal is still on purification station. Arm 2 brings it to the count atom and do a postprocessing debond-project to turn silver-quicksilver back to gold.

This quicksilver detour takes a while, but being able to unify the gold-gold case and non-gold-equal case is very useful to reduce the travel of count atom (before I found this detour it needs to be projected in different places and then converge to suppress the lead input).