The power-of-two interval conjecture for the Sprague–Grundy function

Let $x=(x_0,x_1,x_2)$ be a position with $x_1\leq x_2$, and let $u(x)=x_0+x_1+x_2$ denote the upper bound for its Sprague–Grundy value. The power-of-two interval conjecture. If $x_1<2^k\leq x_0+x_1$ for some $k\in\mathbb{Z}_{\geq}$, then $\mathcal{G}(x)=u(x)$. This is supported by computations and extends the cases where the first coordinate is at least the second; its general validity remains unproved.