Claims

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2026_07_29_korsky: A forum claim submitted by Samuel Korsky asserts that Rademacher random multiplicative sums are almost surely O(root N (log log N)^(1/4+epsilon)), so the limit superior in Problem 520 is 0 and the answer is no; pending.

2026_07_31_durkan_pearce_crump: An arXiv preprint proves that Steinhaus and Rademacher random multiplicative sums are almost surely O(root x (log log x)^(1/4+epsilon)); in the Rademacher case the limit superior in Problem 520 is 0, so the answer is no; pending.

2026_08_04_hoystad: A self-contained Lean development by Høystad: almost surely the Rademacher sums divided by sqrt(N log log N) tend to 0, so no positive constant is the limit superior and Problem 520's answer is no; accepted on Lean built here.

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