Feigin's cohomology conjecture for the Lie algebra of differential operators

Let $\mathrm{Dif}_1$ denote the Lie algebra of differential operators of order at most one on the circle, and let $\Psi_3,\widetilde\Psi_5,\widetilde\Psi_7,\widetilde\Psi_9,\dots$ be the odd cocycles constructed or proposed in the paper. Feigin's conjecture. The cohomology algebra is

$$H^*(\mathrm{Dif}_1,\mathbb C)=\wedge^*(\Psi_3,\Psi_5,\Psi_7,\dots)\otimes S^*(c_4,c_6,c_8,\dots),$$

where the subscript denotes the grading. The conjecture predicts the full structure of this cohomology, but the paper states that it has not been proved; representatives for $c_4,c_6,c_8,\dots$ were not known, and the nontriviality of the higher odd cocycles remained unresolved.