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Claim. The preprint Towards the Erdős matching conjecture for 4-uniform hypergraphs: stability and applications by Peter Frankl, Hongliang Lu, Jie Ma and Yuze Wu, arXiv:2602.19230 (posted 2026-02-22, revised 2026-06-10), states that the maximum number of edges of an $n$-vertex $4$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom n4-\binom{n-s}{4},\binom{4s+3}{4}\}$ whenever $n\ge5s$ and $n$ is sufficiently large. In the notation of Problem 1020, with $k=s+1$,

$$f(n;4,k)=\max\left(\binom{4k-1}{4},\binom n4-\binom{n-k+1}{4}\right) \qquad(n\ge5(k-1),\ n\ge n_0).$$

The abstract describes a stability result of independent interest, applied to minimum-degree thresholds for matchings in $5$- and $6$-uniform hypergraphs. A reader posted the preprint on the site's discussion thread on 2026-02-24.

Covers. The case $r=4$ for $n\ge5(k-1)$ with $n$ large. The rest of the case $r=4$ is the subject of the later claims on Hou, Hu and Liu 2026, for $k\ge6005$ and $n\ge4k$, and Babanskyy 2026, for every $k\ge2$ and $n\ge4k$.

Depends on. No page of this wiki.

Standing. Claimed. The preprint is not refereed, no proof claim was registered on the site's proof-claims tab, and the site's label and commentary, last edited on 28 December 2025, do not mention it. The proof is not verified by this corpus.