Proved, in the site's label, PROVED (page last edited 18 November 2025). The answer is yes. Yokota (1988), in the paper the site cites as the solution, proved $D(N)/N\le(\log N)^{1+\delta(N)}$ with $\delta(N)\to0$ (the zbMATH review, Zbl 0652.10015), which Liu and Sawhney restate as $D(b)\ll b(\log b)(\log\log b)^4(\log\log\log b)^2$; Liu and Sawhney (2024; published 2026) improved this to $D(b)\ll b(\log b)(\log\log b)^3(\log\log\log b)^{O(1)}$. Either bound implies $b(\log b)^{1+o(1)}$. Yokota's paper is refereed but paywalled, so its statement is recorded from the zbMATH review. Liu and Sawhney's Theorem 1.5 is refereed (International Mathematics Research Notices, published online 14 January 2026); the library records it from arXiv v1 as a statement with a proof sketch. Two accepted full claims carry the standing: Yokota's 1988 theorem, the site's citation, and Liu and Sawhney's Theorem 1.5. Two accepted partial claims record Bleicher and Erdős's bounds: their J. Number Theory paper ($D(P)\ge P\lceil\log_2P\rceil$ for primes and $D(N)\le KN(\ln N)^3$) and their Illinois paper ($D(N)\le\lambda^3(N)N(\ln N)^2$ and a sharper prime lower bound). The lower bound $D(p)\gg p\log p$ for primes shows that the exponent $1$ of $\log b$ cannot be lowered. The site's discussion and proof-claim pages carry no further claim.