The semi-elliptic Lindemann–Weierstrass conjecture

Let $\Omega$ be a lattice in $\mathbb{C}$ with algebraic invariants. Let $t_1,\dots,t_s$ be $\mathbb{Q}$-linearly independent algebraic numbers, and let $q_1,\dots,q_r,p_1,\dots,p_n$ be $k$-linearly independent algebraic numbers. Semi-elliptic Lindemann–Weierstrass conjecture. The $s+2(r+n)+rn$ numbers listed in the source, consisting of the exponentials, Weierstrass values, and Serre-function values, are algebraically independent over $\overline{\mathbb{Q}}$. This extends the Lindemann–Weierstrass paradigm to the semi-elliptic exponential function. The source records the cases $r=n=0$ and the stated special $\wp$-value case as known.