Kühn–Osthus lower-bound conjecture for complete-graph subdivisions

Let $d(t)$ be the smallest real number such that every graph with average degree more than $d(t)$ contains a subdivision of $K_t$. Kühn–Osthus lower-bound conjecture. As $t\to\infty$,

$$d(t)=\left(\frac{9}{64}+o(1)\right)t^2.$$

The source presents this as the conjectured correct asymptotic lower bound, while the exact implicit constant remains unresolved.