Decided to join once more just for HPC as the metric seems pretty interesting.

Congrats to whoever got P <= 3, I didn't find a way to set up the wands without everything crashing, given the H=4 constraint. 

The main idea behind the solve was to find a structure that can be slid while forming no unfixable bonds, this greatly reduces the number of operations to be made. The only structure that supports that is the 3x2 stick that results after forming the horizontal bonds and calcifying the fires in the right places because sliding the polymer over calcifyer/horizontal bonds results in errors that can't be fixed. 

The three main assemblies for the 3x2 sticks are directly joining two inputs sideways, making 1 elbow per input, and making 1 triangle with each input (maybe you can manip the input in other ways but that doesn't seem possible at P = 4)

I settled on two sticks as it requires the least manipulation on the input, which is preferred due to the height constraint. Then, I needed to find a way to push the 3x2 stick over the 2 horizontal bonders while calcifying in the right spots and then leaving it resting over the triplex bonder that joins the polymer together.

I tried different approaches, a length 3 arm going back and forth on a track couldn't slide everything far enough, so I used a combination of two arms to push the stick and leave it in the right place. This meant the input had to be horizontal so the track loop could return.

After a lot of tinkering, I managed to have a reliable way of making the polymer, there is a well-behaved looping solution that takes roughly 500 cycles to complete. However, that wasn't everything, now it needed to go FAST, which meant cheesing validation. 

By hardcoding each monomer, the time gets reduced from roughly 48 c per monomer to 39c but results in an awful programming experience. On top of that, the polymer can be yoinked from the right saving 2 monomers (80c). Also, the last monomers don't even need to be formed properly (7 is the min required) so I could form a long stick to push the polymer over all the glyphs at a much faster rate. All these techniques combined saved 200+ cycles and resulted in this abomination of a solution. I just hope someone found either 3P or a well-behaved faster solution as this one is painful to watch.