The budget-threshold conjecture for constructing a copy of $K_5$

Let $n$ be the number of vertices, let $[M]$ denote the set of admissible times, let $t$ be a time parameter, and let $b$ be a budget parameter. A $(t,b)$-strategy is a strategy in the budget-constrained random graph process, and $B_t$ is the graph produced by time $t$. Write $f=o(g)$ when $f/g\to 0$ as $n\to\infty$, and say that an event holds a.a.s. when it holds with probability tending to $1$. The budget-threshold conjecture for $K_5$. For all $t\in[M]$, if

$$t=o\left(n^{3/2}\right)\qquad\text{or}\qquad b=o\left(\max\left\{\frac{n^{12}}{t^{7}},\left(\frac{n^{2}}{t}\right)^{5/3}\right\}\right),$$

then for any $(t,b)$-strategy, a.a.s. $B_t$ does not contain a copy of $K_5$. The authors explain that their methods give non-trivial bounds for $K_5$ but do not yet establish tight results for larger cliques; they believe the corresponding upper-bound behaviour should be correct, so the precise budget threshold remains open.