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Good thing: it *is* know that TV(Bin(n,1/2), Bin(n,1/2+ε)) ≍ ε√n in our regime* and so we're good! Again, we get our n = Ω(1/ε²) lower bound. 🥂 * See for instance (2.15) and (2.16) in this paper of Adell and Jodrá: https://t.co/1hgTk5BE2q 17/