The eventual extremal conjecture for triangles in $K_4$-saturated graphs

Let $t$ be an integer with $t\geq 4$. For an $n$-vertex $K_4$-saturated graph, let $\operatorname{sat}_t(n,K_3,K_4)$ denote the minimum number of triangles among graphs with minimum degree $t$, and let $H_t(n)$ be the graph defined in the paper. Eventual extremal conjecture. There is an integer $n_t$ such that for every $n\geq n_t$,

$$\operatorname{sat}_t(n,K_3,K_4)=2n+2t-12$$

and $H_t(n)$ is the unique extremal graph. The conjecture asserts that the upper bound supplied by $H_t(n)$ is eventually sharp, with no other extremal graphs. Its status is not resolved in the supplied source; the paper proves the corresponding upper bound and establishes related results for minimum degree $4$.