Balanced blow-up conjecture for triangle densities

Let $G$ be a graph with triangle density $\gamma$, and let $f_B(\gamma)$ denote the minimum possible density of copies of $B$ among such graphs. For an integer $t\geq 2$, set

$$B=K_{t,t,t}.$$

Balanced blow-up conjecture. For every $t\geq 2$,

$$f_B(\gamma)=\gamma^{t^2}.$$

This asserts that the random-graph upper bound has the correct order for balanced blowups of $K_3$. The supplied text does not state a resolution; it notes that improvements to the corresponding lower bound would have applications in theoretical computer science.