Out of all the metrics this week, sum was the one I felt least drawn to because of its ambiguous nature in optimization. Hardly any of my builds left their infancy before being deleted.

Fortunately, I did end up finding a start that I felt particularly compelling, and saw it through to what you see here. In hindsight, perhaps there is some analysis that could be done. Clearly the lower rank metals need to either be trashed or used, the latter of which was far too unwieldy. This meant I needed 12 reagents for one product, or 72 reagents total. I settled on 4 cycles per input, since I could either increase by one cycle and get rid of the extra 72 elsewhere, do a 3 cycle input pull and allow myself only an extra 72 cost + area, or do a 2 cycle input pull and trash a metal every cycle, none of which seemed too practical for me.

Ideally only 2 arms would be used for trashing, but I was unable to find a good layout for that and settled with three. Clearly different arms are needed to do the purification and projection, and it seemed like two arms were needed to assemble, so I convinced myself I'm within 2 arms of min arms, and due to the special arms, within 80g of min arm cost. Otherwise my solution feels pretty tight area-wise, so I anticipate that better sums will have a significantly lower cost through fewer bonders and debonders and/or special arms, or one that has higher rate. 