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The original was posted on /r/factorio by /u/Unkwn_43 on 2023-08-11 17:10:51.
After spending several hours (and a few sheets of scratch paper), I've really only thought of two possible/practical arcosphere balancing setups for SE:
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The basic way: using chained folding recipes to have a reusable "catalyst" of spheres to convert any arcosphere into any arcosphere. The downside being you need to figure out the 56 chains to produce every sphere from any possible input. The positive being arguably simplicity.
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The linear algebra way: using linear regression to return the outlier arcosphere amounts to the average amount. Positives is there is no chaining, the system will self balance to a certain amount of each type of sphere. Downside is that this is hard(er) to implement.
I only came to the idea of using the second method because I had taken a linear algebra class last semester, I have no idea how someone without a math background could come up with that method. That leaves the "catalyst" solution as the only remotely practical one, I'm curious as to what other people used for their solutions and what Earendel 'intended' when he created the mod. I know there is a circular nature to the arcosphere problem (if you look carefully at the sprites there is a highlighted section on an eighth on the outside edge of each type of arcosphere) but I don't see how this particularly helps with figuring out chaining.