Exact Banzhaf realization of the two-level target distribution

For each $n\ge6$, define

$$\psi^n=\frac{1}{2n-1}(2,\dots,2,1).$$

A simple game is a monotone voting game on $n$ voters, and $\operatorname{Bz}(v)$ denotes its normalized Banzhaf power vector. Exact two-level Banzhaf conjecture. For every $n\ge6$, there exists a simple game $v$ such that

$$\operatorname{Bz}(v)=\psi^n.$$

The text notes exact simple-game realizations for $6\le n\le18$, while the assertion for all $n\ge6$ remains unresolved in the supplied material.