E-Wythoff Sprague–Grundy values on a family of rows

Let $\mathcal{G}_{\mathcal{E}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in E-Wythoff. E-Wythoff row-value conjecture. For integers $a\geq 4$ and $2\leq r\leq a+1$,

$$\mathcal{G}_{\mathcal{E}}(a,3a+r)=4a+r-1.$$

This conjecture gives explicit Sprague–Grundy values for a family of positions and contributes to the proposed description of values on rows of E-Wythoff's game table; the source gives no resolution, so it remains open.