(Please only read these notes out if 100g is min cost)

Hi, Gooey here with my first tournament submission. The puzzle seems elegantly designed to make trackless cost a fun challenge. Access requirements imply that min primary is 100g, which allows you either three standard arms or one standard arm and a piston. More arms means more ability to multitask, so it seems obvious that three arms is the way to go. With such strict access requirements, the solution space is actually quite small, and can be pruned even further through some fairly simple reasoning based on lattice cosets.

All four hexes of the animismus glyph must be accessible, and a length 1 arm is the only mechanism capable of reaching two of those hexes at once, so the only possible length combinations are (1, x, y) for some x and y. (1, 2, 2), (1, 2, 3) and (1, 3, 3) are all problematic because no arrangement of the larger arms can preserve access while also allowing for handoff of single atoms between them, which must be done at some point during the solution if you want to be fast. (1, 1, 1) and (1, 1, 2) are the only remaining possibilities, with the third arm acting as a go-between allowing the other two disjoint arms to communicate.

Having more inputs than the minimum of two allows for crucial reductions in the tape length. I tried both the (1, 1, 1) and (1, 1, 2) arm configurations and the one with the longer arm won out, but only just. The best solutions of each type that I found had only 6 cycles difference between them. Just one cycle per period! Amazing! I've submitted the (1, 1, 1) as a showcase, because it is my favourite. In both cases, the arm which enables communication between the other two determines the fundamental period of the machine, and the other arms must do everything possible to allow it to work without any interruption. Arms 1 and 3 must perform some very tight dodges to get out of the way, all while shuffling material about and building the outputs.

I really enjoyed this puzzle. I am somewhat of a novice when it comes to optimisation, so I wouldn't be at all surprised if this gets beaten by quite a few people, but that's okay. I look forward to seeing what the professionals come up with!