Corrected Feigin cohomology conjecture for twisted differential operators

Let $\lambda\in\mathbb C$, let ${\mathfrak{gl}}(\lambda)$ be embedded in $\mathrm{Dif}_1$, and let

$$E_1^{p,q}=H^q\left({\mathfrak{gl}}(\lambda);\wedge^p\left(\mathrm{Dif}_1/{\mathfrak{gl}}(\lambda)\right)^*\right)$$

be the first page of the associated Feigin Serre–Hochschild spectral sequence. Corrected Feigin cohomology conjecture. For general $\lambda\in\mathbb C$,

$$H^\bullet({\mathfrak{gl}}(\lambda);\mathbb C)=\wedge^\bullet(\xi_1,\xi_3',\xi_3”,\xi_5',\xi_5”,\xi_7',\xi_7”,\dots),$$ $$E_1^{\bullet,\bullet}=\wedge^\bullet(\xi_1,\xi_3',\xi_3”,\xi_5',\xi_5”,\dots)\otimes S^\bullet(c_2,c_4,c_6,\dots),$$ $$d_2(\xi_1)=c_2,$$

and the spectral sequence degenerates at $E_2$, while

$$H^\bullet(\mathrm{Dif}_1;\mathbb C)=\wedge^\bullet(\xi_3',\xi_3”,\xi_5',\xi_5”,\xi_7',\xi_7”,\dots)\otimes S^\bullet(c_4,c_6,c_8,\dots).$$

The preceding version is contradicted by the paper's computation of $\dim H^3(\mathrm{Dif}_1;\mathbb C)=2$, so this corrected formulation is proposed as the replacement; the source gives no later resolution.