Tangent–cotangent equivalence conjecture for derived $\Gamma$-schemes

Let $X$ be a $\Gamma$-scheme, let $\mathbb T_X^\Gamma$ denote its $\Gamma$-tangent $\infty$-category, and let $\mathbb L_X^\Gamma$ denote its cotangent complex. Tangent–cotangent equivalence conjecture. There exists a natural equivalence

$$\mathbb T_X^\Gamma\simeq\mathbf{R}\!\operatorname{Hom}_\Gamma(\mathbb L_X^\Gamma,\mathcal O_X).$$

This would identify the $\Gamma$-tangent object with the derived Hom from the cotangent complex, but the source gives no evidence of resolution.