Existence and parametrization of structures over generically semisimple F-manifolds

Let $(M,t^0)$ be an irreducible germ of a generically semisimple F-manifold. A generically semisimple F-manifold structure conjecture. The existence and parametrization assertions in parts (a) and (b) hold: $(T)$-structures exist, and, when $T_{t^0}M$ is a Frobenius algebra, $(TP)$-structures exist; for a generically semisimple F-manifold with Euler field and sufficiently small representative $M$, $(TE)$-structures exist, have the same Stokes structure at points of $M-{\mathcal K}^{bif}$, are uniquely parametrized by maps from the components of the analytic spectrum $L_M$ to $\mathbb C$ via the regular singular exponent invariant, and in the Frobenius-algebra case the structure with all regular singular exponents equal to $m/2$ extends to a $(TEP)$-structure of weight $m$. These statements concern the existence and moduli of meromorphic connection structures associated with generically semisimple F-manifolds; the source presents them as a conjecture, but the supplied material gives no resolution evidence.