The split semi-elliptic Lindemann--Weierstrass conjecture

Let $\Omega$ be a lattice in $\mathbb{C}$ with algebraic invariants $g_2,g_3$. Let $s$ and $n$ be nonnegative integers. Let $t_1,\dots,t_s$ be $\mathbb{Q}$-linearly independent algebraic numbers, and let $p_1,\dots,p_n$ be $k$-linearly independent algebraic numbers. Split semi-elliptic Lindemann--Weierstrass conjecture. The $s+2n$ numbers

$$\mathrm{e}^{t_1},\dots,\mathrm{e}^{t_s},\wp(p_1),\dots,\wp(p_n),\zeta(p_1),\dots,\zeta(p_n)$$

are algebraically independent. This is a Lindemann--Weierstrass-type consequence of the split semi-elliptic conjecture; the source notes that the ordinary Lindemann--Weierstrass theorem and the Philippon--Wüstholz theorem establish special cases, but the full statement is open.