Diagonal Sprague–Grundy conjecture for E-Wythoff

Let $\mathcal{G}_{\mathcal{E}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in E-Wythoff. E-Wythoff diagonal conjecture. For integers $r\geq 0$ and $a\geq 2r$,

$$\mathcal{G}_{\mathcal{E}}(a,a+r)= \begin{cases} 3,&\text{if }a=2\text{ and }r=0,\\ 2a+r,&\text{otherwise}. \end{cases}$$

This conjecture describes Sprague–Grundy values on diagonals parallel to the main diagonal; the source gives no resolution and it remains open.