Welcome to my first ever calculation solve. I don't know what I'm doing. Maybe this is good, maybe it sucks. who knows. I'm just gonna talk about my thoughts.

My original design pain-stakingly figured out exactly which element the template was. After a lot of building things, I had a cost of nearly 2000, a 40 instruction loop, nearly 400 area, and a non-functional metals section. I promptly decided to try again from the start. My first breakthrough was realizing that I didn't need a bunch of quintessence and a tri-bonder to individually test for each of the 4 basic elements, but instead could simply use a duplicator, calcifier, and anime glyph to test for all of them at once, and from there a single circuit could solve all of them, plus a disposal path in case of metals. For metals, instead of projecting en-route to the output, which would require 6 distinct routes, I could simply project at the start and use a hexarm to vary the timing of the pickup (and thus how much projection happens). Unfortunately, the metals setup requires a 5-instruction loop, which as far as I can tell locks the best rate we can have for metals at 30. The basic elements could be done in rate 4, but this would require a much longer tape loop, and therefore would take far more instruction than the rate change would be worth.

I haven't found any better method for solving the puzzle since, but I've managed to optimize my method. What once took 800G and 160 area now takes only 650G and 80 area, and a couple less instructions, for over 200 sum reduction. At this point, I think the best course of action is to optimize the rate for metals, but that seems to require a large change to my setup, so it may take a while for me to find any improvements with that.

Also, I ended up with one hex near the center of the build that isn't used for area, so a perfect Critelli location