Givental's conjecture on the R-matrix action for semisimple CohFTs

Let $V$ be the state space of a cohomological field theory with metric $\eta$, and let $R=1+O(z)$ be an endomorphism-valued power series satisfying $\eta(R(z)v,R(-z)w)=\eta(v,w)$. The symplectic loop group acts on CohFTs by the stated graph-sum construction, using $R^{-1}(\psi)$ at markings, the corresponding bivector at edges, and $T(\psi)=\psi(1-R^{-1}(\psi))\mathbf 1$ at additional vertex markings. Givental's conjecture. The $R$-matrix action is free and transitive on the space of semisimple CohFTs based on a given Frobenius algebra. This is a classification claim for semisimple CohFTs via the symplectic loop-group action; the supplied text gives no resolution status.