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Jun 7, 2019 at 4:23 comment added Clement C. My bad, I had missing the (crucial) "I'm solely looking for a reference for who to cite"... I don't know of a reference for it, but it may just be either folklore, or "not explicitly known/stated as such but an easy fact."
Jun 7, 2019 at 4:15 comment added Mark Schultz-Wu I have a similar proof, my issue is that I completely expect this to be in the literature somewhere already, and I'd like to cite it properly (and potentially see if anyone has generalizations, as even for distributions not specified via fixed point numbers there seems to be some connection by how well the probabilities can be approximated by dyadic rationals and the entropy usage, at least for "approximately sampling", meaning sampling from a distribution within $1/2^p$ from the true one in SD).
Jun 7, 2019 at 0:17 history answered Clement C. CC BY-SA 4.0