6*9 = 54, which is *not* divisible by 4. this means that on the 14th (last) round of inputs, only one input needs to be pulled, which gives extra spare cycles to the other input.

the output’s asymmetry makes it easier to have L=2 (min latency) on the earth input than on the fire one. thus, we pull only earth on N=14. working backwards from that, N=13 needs to handle both inputs at L=4, and N=12 needs to handle the fire input at a leisurely L=6.

this naturally extends into a 4-cycle loop, that takes 1 spare atom + 2 of each input (in staggered sets) to make an output. this leaves unused only the first of each input plus the second earth input. because math works, that’s exactly enough for the 6 spare atoms that the loop will need.

that’s the general plan, the rest is just micro-optimization. strongest part of the solve is the hexarm handling the spare atoms. weakest parts of the solve are the piston that pistons only once, and the arm that acts only once.

i have 465/31/69 for CG, and 520/31/58 for CA, but they’re not distinct enough to warrant submitting as showcases.