Global extension conjecture for semisimple Frobenius manifolds

Let $M$ be an $N$-dimensional semisimple Frobenius manifold such that it possesses a holomorphic genus one potential $\mathrm dG$. Global extension conjecture. There exists a convergent CohFT with underlying Frobenius manifold $M$. The local extension result does not settle global extension: restrictions on integration constants of the $R$-matrices may fail to fit together globally, so the existence of such a CohFT remains an open problem in the stated generality.