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Claim. Theorem 1.2 of Hao Huang, Jie Ma and Tianchi Yang, Extremal hypergraphs without generalized 4-cycles (arXiv:2609.37744v1), states: for every fixed $r\ge4$ and all sufficiently large $n$, $f_r(n)=\binom{n-1}{r-1}+\lfloor(n-1)/r\rfloor$, where $f_r(n)$ is the largest number of edges of an $n$-vertex $r$-uniform hypergraph with no generalized 4-cycle, four distinct edges $A,B,C,D$ with $A\cup B=C\cup D$ and $A\cap B=C\cap D=\emptyset$. The theorem also determines the extremal hypergraphs: each is isomorphic to the paper's construction (C1), the full star at one vertex together with a maximum matching of $r$-sets among the other $n-1$ vertices, or, when $r$ divides $n$, to (C2), the same hypergraph with one matching edge shifted by one vertex. The paper calls the statement the Erdős–Füredi conjecture (its Conjecture 1.1), after Füredi's 1984 conjecture that Füredi's lower bound is sharp for $r\ge4$, which the site records. The $f(n;t)$ of Problem 643 is the least edge count that forces such four edges, so $f(n;t)=f_t(n)+1$, and for fixed $t\ge3$ the identity $\binom{n-1}{t-1}=\frac{n-t+1}{n}\binom{n}{t-1}$ with $\lfloor(n-1)/t\rfloor=O(n)$ gives $f(n;t)=(1+o(1))\binom{n}{t-1}$ for every fixed $t\ge4$, the problem's question answered yes for those $t$, with the exact value for large $n$. The case $t=3$ is not covered: the paper's Section 7 says that several steps of the argument need $r\ge4$ and leaves the 3-uniform case of Conjecture 1.1 open.

Covers. The question for every fixed $t\ge4$, with the exact value of $f(n;t)$ for all sufficiently large $n$ and the extremal hypergraphs. The case $t=3$, where the conjectured bound is $f(n;3)\le\binom n2+1$ for large $n$ and the best upper bound is Pikhurko and Verstraëte's $\frac{13}{9}\binom n2$, is not covered.

Standing. The claimants are the three authors, who posted the preprint on arXiv on 2026-09-29; a comment in the site's discussion thread linked it on 2026-10-03. The authors state that AI tools were used only for proofreading and not in generating the mathematical ideas. The preprint is not refereed, the site's label is OPEN and its commentary does not credit the result, and nothing was built here, so the claim stays claimed.

Depends on. Nothing in this wiki; the claim rests on the cited preprint.