Faltings-height formula conjecture for arithmetic special cycles

Let $d$ be the dimension parameter used in the paper, let $f\in H_{1-d,\bar\rho_L}$, and let $\hat{\mathcal{Z}}(f)$ and $\mathcal{Z}(W)$ be the associated arithmetic divisor and cycle. Let $c^+(0,0)$ be the indicated Fourier coefficient, let $\kappa(0,0)$ be the constant term of $\mathcal{E}(\tau,L)$, and let $\mathcal{L}'(0,\xi(f),L)$ denote the derivative appearing in the paper. Faltings-height formula conjecture. For every $f\in H_{1-d,\bar\rho_L}$,

$$\left\langle \hat{\mathcal{Z}}(f),\mathcal{Z}(W)\right\rangle_{\mathrm{Fal}}=\frac{1}{2}C(W,K)\left(c^+(0,0)\kappa(0,0)-\mathcal{L}'(0,\xi(f),L)\right).$$

Here $\kappa(0,0)$ is the constant term of $\mathcal{E}(\tau,L)$. This is the second conjecture described as equivalent to the finite-intersection formulation, and the supplied text gives no evidence that it has been resolved.