The virtual Euler class conjecture for quasi-smooth derived schemes

Let $\boldsymbol{Y}$ be a quasi-smooth derived scheme, write $Y=t_0(\boldsymbol{Y})$, and let $\widetilde{Y}=t_0(\mathbf{T}^*[-1]\boldsymbol{Y})$. The class $e(\mathbf{T}^*[-1]\boldsymbol{Y})\in \mathrm{H}^{\mathrm{BM}}_{2\operatorname{vdim}\boldsymbol{Y}}(Y)$ is defined by the Thom isomorphism, and $[\boldsymbol{Y}]^{\mathrm{vir}}\in \mathrm{H}^{\mathrm{BM}}_{2\operatorname{vdim}\boldsymbol{Y}}(Y)$ denotes the virtual fundamental class constructed by Behrend--Fantechi. Virtual Euler class conjecture.

$$e(\mathbf{T}^*[-1] \boldsymbol{Y}) = (-1)^{\operatorname{vdim} \boldsymbol{Y} \cdot (\operatorname{vdim} \boldsymbol{Y} - 1) /2}[\boldsymbol{Y}]^{\mathrm{vir}}.$$

This predicts that the Euler class arising from the Thom isomorphism agrees with the virtual fundamental class up to the stated sign. The source gives no general resolution; it notes that the conjecture is known when the restriction of the cotangent complex to $Y$ is represented by a two-term complex of vector bundles, in particular when $Y$ is quasi-projective.