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Oct 4 at 13:32 comment added Brayden Ah. I see thank you.
Oct 4 at 11:31 comment added fedja @Brayden For $n=2$ there is either just one cap influencing the line, or a huge overlap, so we cannot create a situation where we have sufficiently many caps influencing the line to apply CLT while the overlaps still do not matter.
Oct 4 at 5:00 vote accept Brayden
Oct 4 at 5:00 comment added Brayden Very nice. I am reading your argument, where exactly does it fail for the case $n = 2$? Possibly my argument has a gap, but I can't see my error nor where your argument fails for $n = 2$.
Oct 4 at 3:46 history answered fedja CC BY-SA 4.0