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Claim. $\mathrm{ex}(n;K_{2,2})\gg n^{3/2}$, the statement of Problem 714 for $r=2$, in the sharp form $\mathrm{ex}(n;C_4)=(\tfrac12+o(1))n^{3/2}$, since $K_{2,2}=C_4$. This is Corollary 2 (printed p. 219) of P. Erdős, A. Rényi and V. T. Sós, On a problem of graph theory, Studia Sci. Math. Hungar. 1 (1966), 215--235 (received 1 February 1966; the volume carries the year only, so this page's name uses the receipt date as a placeholder); library source card. With $\mu(n)$ the largest number of edges of a graph on $n$ vertices with no cycle of length four, the corollary states $\lim\mu(n)/n^{3/2}=\tfrac12$. The lower bound comes from Theorem 1, which is not new here: the paper reproduces it with its proof from Erdős and Rényi, Publ. Math. Inst. Hung. Acad. Sci. 7/A (1962), 623--641, to be self-contained (printed p. 217), and its own result for this problem is Corollary 2. The construction is the polarity graph of the projective plane over $GF(P)$: the $P^2+P+1$ points are the vertices, two distinct points joined when their coordinate triples have zero dot product; two lines meet in one point, so two vertices have at most one common neighbor and the graph has no four-cycle, and it has at least $\tfrac12(n^{3/2}-n)$ edges by display (1.6). Monotonicity of $\mu$ and a prime in a short interval below $\sqrt n$ (the paper's (1.15)) carry the bound to every large $n$; the upper limit is Reiman's count of common neighbors. The footnote on p. 219 records Brown's independent proof of the same asymptotic by the same construction, recorded on Brown's claim page.

Covers. The instance $r=2$ of the statement for every $r\ge2$, and nothing else: the paper says nothing about $K_{r,r}$ for $r\ge3$. The case $r=3$ is Brown's, on his claim page; the site's commentary credits Erdős, Rényi and Sós with $r=3$, which their paper does not contain.

Depends on. Nothing in this wiki: the construction, the prime-distribution input and the counting are the paper's.

Acceptance. Refereed: Studia Scientiarum Mathematicarum Hungarica, a refereed journal. No reviewed evidence is listed: the site labels the problem OPEN, and commentary on an open problem is not an acceptance. This corpus supplies no independent proof review: the statements of Theorem 1 and Corollary 2 are checked against the print, and the prime-distribution input and the proofs are not.