The discovery of the solution is inspiring and interesting, but the time to verify the solution is extremely long.

@emlun I figured out a method that just sets up for up to 5 extra atoms up top. The fact that they are air atoms makes no difference, I just make it deal with the potential 5 atoms, then discard what is left.

Full throughput: 620/2577/473 [imgur.com]

Very cool puzzle! I might take some inspiration from this to make something similar...

My first (successful) attempt clocks in at 480G / 4292C / 1895A but cheats a bit by discarding the reagents into an infinite chain after reading them.

@garr890354839 Think about if there's something you can do that behaves differently depending on whether there's an atom present or not.

How do you not hard-code something like this?

I got the general case down to 555/4561/424 https://i.imgur.com/r6T1emq.gifv
Then I improved it to make a tighter gif 570/4553/418 https://i.imgur.com/cU61fwL.gifv
Then I figured I could save money by ditching the obliterator and going with an infinite tail.
I saved 40g but paid for it with a huge increase in area (and huge decrease in frame rate)
530/4553/1309

@armin.rigo yeah, I found an alternative editor on github, that worked.

@FractalusRex: in general, using the "ompuzzle" web editor. In this case, it's a custom Python script that produces the puzzle file directly: https://gist.github.com/arigo/cc4c014d473e4621293094801ce67f8c

Looks interesting.

One question though, how do you get the product requirement and the reagent to be that large? The editor only allows up to a width of 9, right?

I got it 430/9628/539 for arbitrary inputs, and 175/1504/59 by cheating and hard-coding it, I love this puzzle!
Genuine. [cdn.discordapp.com]
Cheating [cdn.discordapp.com]

This was a very interesting puzzle. It took me a while and looking at other people solutions to understand what was asked since I did not think it was possible to do this.
I think this helped me really undestand what a Turing-Complete mechanism is.

I made it.
https://i.imgur.com/Vh0EHYh.gif

By cheating (not using the input) my minimum are 1408 cycle. (Made it since my last comment. :P)

I re-made my single thread solution as a REAL single thread (single piston), then cost optimized it.
Those would work with any random sequence, with a stipulation: The last info-block can't be a zero.
https://i.imgur.com/3IOjvvR.png

oh wow, now I feel sort of stupid I hadn't thought of that, thanks

It's certainly possibe. One way is to drag everything (both the current and possibly the next chain) a single step forward at the same time, e.g. using two arms. They will usually grab and move a single chain, except during the transition. You don't have to do any backward move.

for a bit more detail:

I'm having problems with the transition between 2 chains of input because the next chain loads when I'm still working on the previous so it can't go back into that space, but I haven't been able to device a way to split of 1 digit from the chain without it either going back (which during transition would cause it to collide with the newly loaded chain), or it depending on dragging the chain from 1 digit further along the chain (which during the transition drags the new chain and cause it to collide with the end of the previous chain).

I've found solutions to just automatically "read" the data and have it be translated into the right metal, however, I've been unable to find a solution which would work for any sequence (i.e. if the length were different and/or order was different), all solutions I've come up with so far depend at least on either a fixed length or at least one digit of the chain fulfilling a certain condition (e.g. the last 2 not both being lead). Essentially I want it to work whether the chain is length 1 or length 1 million, and whether it's all lead, all gold, or anything in between.

I'm curious whether others have found a solution which would satisfy these constraints I've given myself, or if perhaps I've set a goal which is too ambitious and perhaps even impossible

The opposite puzzle is to build the chain with Air atoms from the metal chain. I couldn't upload it as a regular workshop item (getting Unknown Error 2). If you're interested, download it directly from https://baroquesoftware.com/nan-industry/c156905570481439.puzzle and put it manually into your game directory (on Windows, Documents\my games\Opus Magnum\<some string of numbers>\custom\).

I got 2537 cycles for arbitrary input. Did anyone actualy implement the complex logics needed to get <2520?

12,1k cycles with a "single threaded" design. :D

？？？？？？？？？？？？？？？？？？？？？？？？

"could be in theory re-encoded in the instructions" Yeah I did that. Although now that I think about it I do have ideas for how to read the information... Really, what would have made this easier is "the number of times the lead must NOT be transmuted"...