Koszul-dual and intersection-theoretic formula for the non-linear D-Fredholm index

Let $X$ be a smooth scheme. Consider the non-linear $\mathcal{D}$-Fredholm index, its symbol complex, and the cycle defined by the associated graded symbol morphism in the total space of the cotangent stack. Non-linear $\mathcal{D}$-Fredholm index conjecture. The index can be expressed via Koszul duality by the right-hand side of the Grothendieck–Riemann–Roch formula on the loop stack of $X$. Moreover, the Euler characteristic of the derived global sections of its symbol complex may be expressed as a $K$-theoretic intersection number between $X$ and the cycle defined by the associated graded symbol morphism inside the total space of the cotangent stack. The source states that this conjecture is answered affirmatively in the paper, so its status is solved.