In the beginning, I had a similar-looking pipeline, making a product every 8 cycles with the same latency as this solution. I had planned to make another pipeline to take it to one product per 4 cycles, with 4 cycles at the start to prepare the singular missing atoms in the product.

I tried for a few hours, trying to make the second pipeline. Then I realized I had the timing wrong and it wouldn't work. So I switched to making the single pipeline twice as fast. 

After a few hours, I concluded it was impossible to take consecutive inputs and turn them into the product (with one atom sourced from a buffer) with this latency. So I was back to making a two-pipeline solution. After many more hours, I gave up and uninstalled Opus Magnum because it was eating too much of my time.

But I couldn't sleep and I thought up a new way to approach this puzzle: A new single pipeline, still with the same rate and same latency from taking the core atoms. But now it would take the auxiliary atoms 6 cycles before the core ones. This means the auxiliary inputs would be grabbed on cycles 1, 5, 9, 13, 17, and 21 whilst the core ones on 7, 11, 15, 19, 23, and 27. 27 +  latency 5 = 32 cycles. 

However, now I can't take the inputs on cycles 1 and 3 as a buffer to fill the missing single atoms, I'll have to use cycles 3 and 25. The atoms from 25 would have only a few cycles to catch up to the product from cycles 21 and 27, but it would be possible if I delayed the output of product 5 just a bit.

The next day, armed with a new battle plan, I constructed this solution in only about 5 hours. Indeed, it was possible. A few tweaks were then done over the next day to reduce secondary. 

I feel like this plan for inputs is the only way to achieve 32 cycles, except for some special tactics at the start. It seems almost intentional. I am also excited to see how the others prove me wrong!