Claims

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2026_09_18_menezes: An arXiv preprint of Menezes claims, for every $q=2^m$, an algebraic box-free tripartite $3$-graph with $q^4$ vertices in each part and $q^{11}$ edges, so that $\mathrm{ex}_3(n,K_3(2))=\Theta(n^{11/4})$. This answers the case $t=3$, $r=2$ yes; no other case with $t\ge3$ is touched.

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