Explicit relative semi-abelian conjecture

Let $G$ be as in the relative semi-abelian conjecture, with notation $c_i$ and $t$ defined there. Explicit relative semi-abelian conjecture.

$$\operatorname{tr.deg}_{\overline{\mathbb{Q}}(\Omega_G)}\overline{\mathbb{Q}}(\Omega_G,R_1,\dots,R_n,\widetilde{\log}_G(R_1),\dots,\widetilde{\log}_G(R_n))\geq2\sum_{i=1}^m c_i g_i+t.$$

This is stated as a corollary of the relative semi-abelian conjecture, making the lower bound explicit in terms of the dimensions $c_i$ and $g_i$ and the torus dimension $t$.