I know this seems like a strange place to post this but I can't really find anything on it anywhere, that is conclusive. I would like to propose a theorem which is...
For any given n-space arbitrary ordered polynomial, all of the coefficients for a particular order averaged together and reconstructed into the same functional polynomial, will yield the same values as the individual polynomials results when those are averaged together (via an arithmetic mean).
I don't have a proof for it, but it seems correct for every example I can come up with. I don't have the mathematical skill to prove it rigorously.
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