WARNING LOTS OF LORE, if you are concerned about time please skip to what seems useful
para 0 - warning and contents
para 1 - why solving
para 2 - approach to solving min-rate
para 3 - layout description
para 4 - initial solve cost and first save
para 5 - arms and their functions
para 6 - later cost reductions
para 7 - attempts at further saves
para 8 - thoughts on the puzzle


Another day, another chance to learn, that's what I had thought to myself as I traversed the halls, intending to find a class to listen to. What I found instead was a couple of students huddled around a transmutation engine, creating some strange material. This turned out to be "palatable tissue", seemingly a challenge of some form between them to see who could make it the fastest (although I may note they did avoid rotations and pivots, presumably to maintain the palatability of the tissue). Of course this was another opportunity to practically test my skills so I got to work, borrowing some equipment from imperial to get started with.

Seeing as the students had been competing for speed, I too designed to do so, which first meant working out how to compose the tissue in the first place. Each monomer within the chain is comprised of two water atoms, an earth atom, an salt atom and two atoms that I had not come across in practice but knew to be vitae, themselves comprised of two salt atoms whilst producing an unhelpful mors.
Given that we have two inputs, one earth, one water and are aiming for an optimal rate, the first step is to find the most balanced taking of inputs, so as to waste as little as possible. Therefore we can divide the total of five salt's needed through the process into two of water and three of earth, so that each monomer requires pulling four water and four earth total. Since each input can only ever be pulled once every two cycles, this forces the rate to at least eight, since it is impossible for one to pull inputs fast enough to reach seven.

With this knowledge I set about creating my first layout, which posed many challenges, most notably how to get both the vitae and water to top and bottom sides of the chain. I settled on the current setup with three bonders used for creating the monomer, and a glyph of calcification above the earth input and higher of the two down-left to upper-right bonders. Should one find a way of creating this chain at the same rate using less parts, I imagine it would be via a better layout of these bonders, inputs and glyphs.

The original solution came to parts with relative value of six hundred gold, however that quickly dropped when removing an arm and track that pulled the chain into the correct place on the bonder, now delegated to the second water track.
Ah what am I saying, I have not explained the track layout.

Arms 1 2 and 3 both calcify a water input for the production of vitae, and remove the superfluous mors created in this process. Due to the length of this track these arms are pushed to their upper limit of capacity.
Arms 4 and 5 fill a similar role, calcifying the earth for the vitae, however without the need to remove the mors, they're left working only sixty-three percent of the time. 
Arms 6 and 7 are what I refer to as the second water track, as it takes the 2nd water for the monomer into the chain. However this track has a much more important role in constructing the correct joining bonds between water-salt-water layers and vitae-earth-vitae layers
Arms 8 and 9 despite being on the same track perform different roles. Arm 8 is the first water arm, bringing the first atom of each monomer into place. Arm 9 is the first vitae arm, slotting the upper vitae atom through the maze of other molecules and glyphs floating around the engine.
Arms 10 and 11 are the salt track, and like arms 6 and 7 are also vital for the fusion of layers. Of particular note is how they have to slot over the water-salt-water layer when returning to start.
Finally arms 12 and 13 are another split pair, arm 12 delivering the earth while arm 13 delivers the second vitae.

With that done, I return to the explanation of reduction of parts. The removal of that chain moving arm reduced it all the way to five hundred seventy gold, unfortunately this would be the last large reduction I would find. 
Back then disposal of mors was handled by a separate track made of 3 track, 2 arms and a bonder. By instead using a disposal I could replace the bonder with a 4th track, reducing by 5 gold.
Next I changed a movement on the lower vitae arm to be done by the 2nd water track, at this stage that vitae arm was separate and resided above the engine, roughly where arm 8 starts now moving 2 hexes to the right. Another 5 gold improvement through the removed track.
Of course anyone looking at the current solution knows I don't have a disposal, and this is when it happened. Putting the waste handling onto the water calcification track was much more efficient in instructions, even if disposal was no longer possible, due to any possible positioning increasing the track length too much. This only saved 5 gold since it saved an arm at the cost of an additional track and bonder.
The next save was more complex, it put both vitae arms on the same track which did nothing at first. However it allowed the salt track to loop underneath itself rather than over, which saved a track hex. This did come with complications, as threading the arms back to the start became a challenge, yet it did not render this impossible.
Finally the big shift to layout would come, vitae arms split up, one moved to the earth track, the other moved to the 1st water track. The earth and vitae had previously been towards the top left of the setup, and the 1st water being snuggled in the bottom right between the 2nd water track and the main engine.
Overall these 5 saves I cut further from 570g to 545g.

There are several things that I did try to reduce further however limits quickly imposed themselves, either from the layout itself or from forcing too much work upon given arms.
The most notable of these was an attempt to merge the earth calcification, water calcification and waste management. This on it's own doesn't make sense, since you need additional track and cannot remove any arms, thus one tried to ad the lower vitae responsibility as well. When doing this you have 4 atoms that need to be managed, water, earth, vitae and mors with 5 arms to deal with them. Since each atom needs to be pulled every 4th cycle (since there is another arm for earth and water and vitae/mors are only created on this cycle, you can consider how much arms can do in 4 cycles. Each atom needs to be picked and dropped with totals to 8 instructions, and each arm needs to move around the track such that a new arm replaces each old one, in this case the shortest track I could find was 13. Now we can consider the arms, each of them can do 4 instructions and we have 5 leading to 20 instructions handled. Those who can add will quickly see that we are asking the arms to do 21 instructions worth of work in 20 instructions space, which they won't go for without the alchemist agreeing to union demands.
Another series of attempts was made to improve the 2nd water track, as currently it has by far the most lazy arms, 5 cycles every 16 are wasted sitting in the same place (ignoring the bounce it performs). However when trying this I found that I needed to add additional regrabs to keep arms from straying to far - which in turn left too little time for other arms to reach important locations.
The last change is arguably the most drastic, trying to move the earth input in order to remove a glyph of calcification. There are two approaches to this, that both run into a similar issue, that the regular earth can no longer be placed into the chain at the required point. The first is to move the earth away from the engine, which adds one additional step to the path the earth must take, which leaves too little time to assemble the layer whilst starting the next monomer on time. The alternative was to swap the earth with the upper glyph of calcification, however this instead creates a tight angle between it and the upper vitae atom, which forces the earth to wait a cycle, creating much the same issue.

My belief is that this is a local minima for my layout, however with a better layout I strongly think that this can be improved upon. There is currently several arms with lazy inputs or long track movement which can assuredly be compacted in order to save track or even possibly more arms.
However I'm very pleased with this solve, it utterly trashed what I'd seen those students in the halls toy with, whilst still ensuring to keep the tissue palatable.

- I.F.S.

P.s. it tasted a little bit like beans, although given my palate, that might just be a poor sense of taste.