The site labels the problem OPEN (page last edited 01 April 2026; proof-claims tab accessed 2026-10-07). The tab carries one proof claim, submitted as full, by Qiyuan Gu (using GPT-6 Astra, GPT-5.6 Sol, Claude Opus 5, as the tab writes it), posted 2026-09-05 with a Zenodo write-up: it claims the almost-everywhere $\limsup$ bound as asked, and the first question with a constant that may depend on the point $x$, while a companion note by the same claimant states that for a non-nested triangular array no constant uniform in the array can serve; for a single sequence, as the Statement is posed, the uniform reading is not settled. A comment on the claim objects that only the weaker, point-dependent variant is answered, and the Statement does not fix the dependence of the $O(1)$ term, a point Tao [Ta26b] had already raised. In the reading of the Formulation the claim would settle only the second question. It is recorded, unadopted, as a partial claim on its claim page (Gu, 2026), and the derived standing in the frontmatter is open. Tao [Ta26b] proves, for every $\omega(n)\to\infty$, a dense set of $x$ with $L_n(x)\ge\frac2\pi\log n-\omega(n)$ for infinitely many $n$, short of the constant the question asks for.