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Claim. For independent uniform signs $\epsilon_k\in\{-1,1\}$ and $R_n$ the number of zeros of $P_n(z)=\sum_{k\le n}\epsilon_kz^k$ in the closed unit disk, counted with multiplicity,

$$R_n=\frac{n}{2}+O_\omega\bigl(n^{399/400}\bigr)$$

almost surely, so $R_n/(n/2)\to1$ almost surely, which answers Problem 522 in the affirmative. The first note, posted on the site's discussion thread on 2026-04-20 after Przemek Chojecki ran remarks of Kovač and Letwin through GPT-5.4 Pro, gave the exponent $149/150$; the second, A strong law for the roots of random Littlewood polynomials under Chojecki's name, produced with GPT-5.5 Pro and posted on 2026-04-27 with Letwin's permission as a streamlined note, gives $399/400$. Both notes count zeros through Jensen's formula and use the reciprocal polynomial for the upper bound. The first note, which says it follows the route proposed on the thread, compares logarithmic means at the radii $1$ and $1-n^{-1-\alpha}$, controls small values of $\lvert P_n\rvert$ with the log-integrability theorem of Nazarov, Nishry and Sodin, and gets almost-sure convergence of smoothed means from a smooth Berry–Esseen bound and a subsequence argument modeled on Angst and Poly. The revised note, which proves the stated $n^{399/400}$ bound, compares the means at the radii $1-n^{-401/400}$ and its reciprocal, quotes only the Nazarov–Nishry–Sodin theorem and proves its smooth central-limit estimate by a Lindeberg replacement. Nat Sothanaphan's AI check of the first note stopped halfway after finding several issues, the simplest an exponent in Proposition 7 that does not follow from the stated parameters, and the author revised. The author wrote that they were not able to formalize the argument.

Depends on. No page of this wiki.

Standing. Claimed. The thread's discussion of 2026-04-20 and 2026-04-21 concerned priority: Letwin had announced a more general paper that would imply the problem and mentioned a separate paper of Michelen and Yakir, neither of which has appeared; Chojecki wrote that they take no claim for the problem and offered the notes for anyone's use, a disclaimer of credit that this page does not read as a withdrawal of the result, and the thread records no check of the revised note. No proof claim was registered on the site's proof-claims tab and no refereed or arXiv version was found; the formal-conjectures statement of the problem cites the note as a proof posted in April 2026, and Kitamura's Lean repository credits it, with the Kwon–Zou note, as an informal proof of the $\{-1,1\}$ statement. The site's label records a Lean formalization of a later claim and no human acceptance (OPEN (LEAN); page last edited 06 December 2025). The other full claims are Kwon–Zou 2026, Snyder 2026, Kawada 2026 and Kitamura 2026.