I have some long note for this:

To ship the products, you need 24 silver

Input generate quick silver at every 2, and prolif could consumes a qs and generate a gold, which becomes the slow silver at every 3

The first prolif metal can be grabbed at cycle 6, by first input goes to reject

you lose 2 metal this way, one by reject, and one by purif

if prolif keeps running, at cycle 33 you get 17 quick silver and 10 slow silver, yielding min=36 with 1 surplus silver, at any previous cycle you are short with at least one metal

of course this requires getting the gold as template in time, and output the template metal at last

for pipelining, i begin by building the period 4 triplex pipeline, which would use the last 12 quick silver from cycle 11

then i made the prolif prototype, which uses quick silver at cycle 1, 3 and 7 for reject, templating and purif

second silver for purif uses the template, creating a 1 cycle delay in purif which is acceptable

I stuck at a bad layout for dex pipeline, but things goes smooth after i find a way to smuggle the quick silver at cycle 5 and 9 above the prolif glyph

felt this is very cost efficient, and exciting to see any better solve than this