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This seems like such a good generalization that I almost can't believe it hasn't been discovered before. (Also nice to see an article where the author wants the material to be understandable instead of trying to impress us with unnecessary complexity)

It was indeed discovered before. My goal was, exactly as you said it, to make the material easily understandable.

I think this could also be used to calculate the mode?

lim n->0 argmin(x,sum(abs(x-s)^n))

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