Unified Brauer–Siegel conjecture for elliptic curves over function fields

Let $\{E_i/K_i\}$ be an asymptotically very exact family of elliptic curves over function fields. Let $c_{E_i/K_i}$ be the leading coefficient of the $L$-function at $s=1$, let $d_i=n_{E_i}+4g_{K_i}-4$ be the degree of $L_{E_i/K_i}(s)$, and let $L_{\{E_i/K_i\}}(s)$ be the associated limiting $L$-function. Unified Brauer–Siegel conjecture. One has

$$\lim_{i\to\infty}\frac{\log |c_{E_i/K_i}|}{d_i}=\log L_{\{E_i/K_i\}}(1).$$

This statement is presented as a unification of the preceding fixed-field and base-change conjectures, expressing the normalized asymptotic leading coefficient through the limiting $L$-function at the central point. Its status is conjectural in the source.