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Claim. The least number of edges of a $4$-uniform hypergraph that does not have property B, that is, that is not 2-colorable, is $23$: in the notation of Problem 901, $m(4)=23$. The paper's abstract records the earlier range $21\le m(4)\le23$ and determines the value by an exhaustive computer search for $4$-uniform hypergraphs with fewer than $23$ edges and no proper 2-coloring, which finds none.

Covers. The instance $n=4$ of the question, the exact value $m(4)=23$, which the site lists without a source. The values $m(2)=3$ and $m(3)=7$ are recorded in Erdős's 1963 paper. No value $m(n)$ with $n\ge5$ is known, and the order of $m(n)$ stays open.

Depends on. No page of this wiki.

Acceptance. P. R. J. Östergård, On the minimum size of 4-uniform hypergraphs without property B, Discrete Appl. Math. 163 (2014), part 2, 199--204, a refereed journal (refereed); the record dates the issue to January 2014 without a day, so the page is dated to the first day of that month. The site lists $m(4)=23$ in the problem's commentary without crediting a source, and labels the problem OPEN, so the commentary is not acceptance of this partial claim.