The diameter-three t-pebbling conjecture

Let $G$ be a graph with $n$ vertices and diameter $3$, and let $t\geq 1$.

Diameter-three t-pebbling conjecture.

$$\pi_t(G) \leq 1.5n+8t-6.$$

This follows formally from the linear t-pebbling bound conjecture together with the stated diameter-three bound for ordinary pebbling. The source gives no resolution status.