Conjecture on the optimality of the tree-strategy bound for the fourth weak Bruhat graph

Let $B_4$ be the fourth weak Bruhat graph, and let $\pi(B_4)$ denote its pebbling number. A tree strategy is a pebbling strategy represented by a tree, and a tree strategy weight function is a weight function arising from such a strategy.

Tree-strategy optimality conjecture for $B_4$. The bound

$$\pi(B_4)\leq 66$$

is best possible using tree strategy weight functions.

The paper has established the upper bound $\pi(B_4)\leq 66$ computationally; the conjecture asserts that this bound cannot be improved within the specified tree-strategy weight-function method.