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Claim. Let $f(N)$ be the extremal function of Problem 301: the largest size of a set $A\subseteq\{1,\ldots,N\}$ with no relation $1/a=1/b_1+\cdots+1/b_k$ among distinct elements, $k\ge2$. The site's commentary credits Wouter van Doorn with an elementary argument proving

$$f(N)\le\Bigl(\frac{25}{28}+o(1)\Bigr)N\approx0.8929\,N .$$

The argument as the commentary gives it: as $a$ runs over the integers $8^b9^cd$ with $(d,6)=1$, the sets $S_a=\{2a,3a,4a,6a,12a\}\cap[1,N]$ are pairwise disjoint; a relation-free $A$ must omit at least two elements of $S_a$ when $a\le N/12$ and at least one when $N/12<a\le N/6$; a short count finishes the proof. The problem page checks the two counting facts: within $D=\{2,3,4,6,12\}$ every four-element subset contains one of the relations $\frac12=\frac13+\frac16$, $\frac13=\frac14+\frac1{12}$, $\frac14=\frac16+\frac1{12}$ and $\frac12=\frac14+\frac16+\frac1{12}$, and the integers $a$ of that form have density $3/7$, so at least $3N/28-o(N)$ elements are omitted.

Covers. The upper bound $f(N)\le(25/28+o(1))N$ only. It does not bear on the particular question, whether $f(N)=(1/2+o(1))N$, and it bounds $\limsup f(N)/N$ above by $25/28$ without determining the constant.

Standing. Claimed. The result exists only as the site's commentary: no written source by the author states it, and it has no arXiv version, no journal record, no formalization and no independent review. The commentary credits it to van Doorn, but the site labels the problem OPEN (page last edited 16 January 2026;) and lists no parts, so the credit is not an acceptance and no reviewed evidence is listed. The claim is dated by the earliest archived copy of the site's page that carries the remark, that of 16 September 2025 (the second link); the archived copy of 4 October 2024 carries the site's earlier formulation of the problem without it, and no copy between the two is archived. Wang's manuscript of 27 May 2026 and Della Pietra's repository of 30 July 2026 both cite the bound as the one the site records; the smaller constants they claim are on Wang's claim page and Della Pietra's upper-bound claim page.