Nimber construction conjecture for digraph placement games

For a game value $X$, let $f(X)$ be the minimum number of vertices in a digraph placement game having value $X$. For an integer $n\geq1$, let ${\ast n}$ denote the nimber of order $n$. Nimber construction conjecture. For every integer $n\geq1$,

$$f({\ast n})=2n.$$

Every nimber ${\ast n}$ is known to be constructible with $2n$ vertices using ordinal sums, so the conjecture concerns the matching lower bound. The claim remains open in the supplied text.