A(alpha)-stability conjecture for the fourth-order biased IMEX scheme

Let the biased IMEX scheme be

$$\dot{y}_{\Delta t}^{[k]} = f(y^{n}) + \frac{1}{3}\bigl(2g(y^{n+1}) + g(y^{n-2})\bigr).$$

Here $\lambda$ is the explicit eigenvalue, $\mu$ is the implicit eigenvalue, and $\mathcal{S}$ is the explicit stability domain. The notation $A(\alpha)$-stable means that the implicit stability domain contains a wedge with half-angle $\alpha$. A($\alpha$)-stability conjecture. The scheme with $k=4$ is $A(\alpha)$-stable with respect to $\mu$ for $\lambda\in\mathcal{S}$, where the half-angle of the wedge of stability is

$$\alpha\approx 0.23\pi.$$

The statement is proposed as a stability result for the method; the supplied text gives no proof or resolution status.