General Faltings height formula for arithmetic divisors and CM cycles

Let $f\in H_{1-n/2, \bar{\rho}_L}$, let $c^+(0,0)$ be its constant term, let $\hat{\mathcal{Z}}(f)$ be the associated arithmetic divisor, and let $\kappa(0,0)$ be the constant coefficient of $\mathcal{E}_N$. Let $\mathcal{Z}(U)$ be the CM cycle and $K_T$ the associated compact open subgroup. General Faltings height conjecture. One has

$$\left\langle \hat{\mathcal{Z}}(f),\mathcal{Z}(U)\right\rangle_{Fal}=\frac{2}{\operatorname{vol}(K_T)}\left(c^+(0,0)\kappa(0,0)+L'(\xi(f),U,0)\right).$$

This extends the zero-constant-term formula by including the constant-term contribution. It is presented as a consequence of the finite intersection conjecture and the Archimedean height formula, but the supplied text gives no resolution status.