Genus two G-function vanishing conjecture for ADE Frobenius manifolds

Let $M$ be a Frobenius manifold associated to an ADE singularity or to an extended affine Weyl group of ADE type. Its genus two free energy has a decomposition

$$\mathcal{F}_2=\sum_{p=1}^{16}c_pQ_p+G^{(2)}(u,u_x,u_{xx}),$$

where the $Q_p$ are contributions represented by genus zero correlation functions and $G^{(2)}(u,u_x,u_{xx})$ is the genus two $G$-function.

Genus two G-function vanishing conjecture. For every such $M$,

$$G^{(2)}(u,u_x,u_{xx})=0.$$

The conjecture concerns the vanishing of the non-explicit genus two contribution in the free energy for Frobenius manifolds arising from ADE singularities and extended affine Weyl groups of ADE type. The supplied text gives no resolution status.