---

Claim. Write $f^{(r)}(n;s,k)$ for the largest number of edges of an $r$-uniform hypergraph on $n$ vertices containing no $k$ edges on at most $s$ vertices, and $\pi(r,k)$ for the limit of $n^{-2}f^{(r)}(n;rk-2k+2,k)$, which exists for every $r\ge3$ and $k\ge2$ (Delcourt and Postle for $r=3$, Shangguan for $r\ge4$, as the paper recalls). Theorem 1.2 of Pikhurko and Sun states that $\pi(3,8)\ge3/16$. The $3$-graphs with no eight edges on at most ten vertices are exactly the $3$-graphs with no member of the site's $\mathcal F_{10}$, the family with $10$ vertices and $8$ edges, so $\mathrm{ex}_3(n,\mathcal{F}_{10})=f^{(3)}(n;10,8)$ and

$$\mathrm{ex}_3(n,\mathcal F_{10})\ge\Bigl(\frac3{16}-o(1)\Bigr)n^2, \qquad \frac3{16}=\frac9{48}>\frac8{48}=\frac16,$$

so $\mathrm{ex}_3(n,\mathcal F_{10})\sim n^2/6$ is false: the displayed asymptotic fails at $k=10$ with $\mathcal F_k$ the single family the site's wording defines, and the site's wording, an assertion about every $k\ge5$, is false. The lower bound comes from the paper's Theorem 3.1, a lower-bound criterion it quotes from Glock, Joos, Kim, Kühn, Lichev and Pikhurko, applied to an explicit $3$-graph built from copies of a five-vertex, three-edge configuration; the paper conjectures that $3/16$ is the exact value (Conjecture 1.3) and determines $\pi(r,8)=1/(r^2-r)$ for every $r\ge4$ (Theorem 1.1), which concerns higher uniformities and not this problem. The refutations at $k=5$, $6$, $7$, $8$ and $9$ are on Glock's page, the (6,4) page and the (7,5), (8,6) and (9,7) page.

Why it is rejected. The result is correct, but it answers the site's wording, the single family $\mathcal F_{10}$, not the corrected Statement of Problem 1076, whose family is cumulative: under the corrected Statement a $3$-graph avoiding $\mathcal F_4\cup\dots\cup\mathcal F_{10}$ is linear, so the bound says nothing against it, and the page does not count toward the problem's standing. The problem page's Notes credit the result.

Acceptance. Refereed: O. Pikhurko and S. Sun, On the quadratic 8-edge case of the Brown–Erdős–Sós problem, European J. Combin. 135 (2026), 104364, dated 4 March 2026 in the publisher's record, after the arXiv posting of 2 June 2025. The site does not cite the paper on this problem and its curator makes no statement about it; the proof is unreviewed, and no formalization is known.