A-stability conjecture for the third-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. A-stability conjecture. The scheme with $k=3$ is $A$-stable with respect to $\mu$ for $\lambda\in\mathcal{S}$. The claim is supported in the paper by stability analysis, numerical investigation, and the absence of detected negative values, but no proof is provided.