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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. The manuscript's Theorem 1 (p. 2) states

$$f(N)\le\Bigl(\frac{667}{806}+o(1)\Bigr)N\approx0.8275\,N ,$$

a smaller constant than the $25/28\approx0.8929$ of the site's elementary argument (van Doorn's claim page). The method is that argument carried further: for a finite set $D$ of positive integers and a dilation factor $m$ with $mD\subseteq[1,N]$, a relation-free $A$ meets $mD$ in at most the independence number of the unit-fraction hypergraph on $D$; the manuscript takes $D$ to be the $29$ nontrivial divisors of $720$, computes that independence number by an exact-arithmetic certificate (its Appendix A), and sums over a disjoint family of dilates.

Covers. An upper bound for the estimate of $f(N)$. 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 $667/806$ without determining the constant.

Standing. Claimed. The manuscript is dated 27 May 2026 on its title page and posted on ResearchGate; it has no arXiv version, no journal record and no independent review, and the site does not cite it. A comment of 4 July 2026 in the site's discussion thread reports the manuscript and its constant, and another comment of the same day says that it is AI-generated and carries no statement to that effect; the file itself says nothing about how it was written, and this page records the thread's description as the thread's. The manuscript was read whole, statement and proof, in the version its source card describes; the certificate was not rerun here and nothing was checked. Smaller constants have since been asserted: a computational constant of $319/390\approx0.818$ in a thread comment of 4 July 2026 without a written proof, which has no page, and an upper bound of $15437/19344\approx0.798$ announced in Della Pietra's repository, which has its own claim page.