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Claim. Every $m$ counted by $F(A,B)$ is a product of two integers at most $N$, so $F(A,B)\le M(N)$, the number of distinct entries of the $N\times N$ multiplication table. Ford's theorem on the multiplication table (Corollary 3 of the paper, with $x=N^2$) gives

$$M(N)\asymp\frac{N^2}{(\log N)^{\delta}(\log\log N)^{3/2}},\qquad \delta=1-\frac{1+\log\log2}{\log2}\approx0.086,$$

so $\max_{A,B}F(A,B)\ll N^2/((\log N)^{\delta}(\log\log N)^{3/2})$. The paper itself does not mention the problem. The one-line comparison was first posted in the site's thread on 23 November 2025 by Wouter van Doorn, and the site's commentary credited it to him until its edit of 2 May 2026. Chojecki's post announcing the 2026 manuscript and the curator's post of 2 May 2026 both attribute the upper bound to that comment. The claim value is proved, since the result is a proved inequality, the upper half of the estimate that the full claim records as answered.

Covers. The upper bound only. It settles the exponent of $\log N$ from above and leaves the lower bound, which the 2026 claim supplies.

Acceptance. Refereed: Kevin Ford, The distribution of integers with a divisor in a given interval, Annals of Mathematics (2) 168 (2008), no. 2, 367--433, DOI 10.4007/annals.2008.168.367 (issue dated September 2008, by its Crossref record); the library card is ford_2008_distribution_integers_divisor_given_interval. Reviewed: the site's curator, Thomas Bloom, rests the upper bound on this theorem in the commentary (last edited 2 May 2026). Nothing is independently reviewed by this project.

Date. The page is named by the arXiv posting of 18 January 2004, the result's first public appearance.