Modular Schanuel conjecture without derivatives

Let $z_1,\ldots,z_n\in\mathbb{H}^{+}$, write $\mathbf{z}=(z_1,\ldots,z_n)$, and let $j$ be the modular function. Let $\Sigma$ be the set of special points, and let $\dim_{G(\mathbb{Q})}(\mathbf{z}\mid\Sigma)$ denote the corresponding $G(\mathbb{Q})$-dimension relative to $\Sigma$. Modular Schanuel conjecture.

$$\mathrm{tr.deg.}_{\mathbb{Q}}\mathbb{Q}\left(\mathbf{z},j(\mathbf{z})\right)\geq \dim_{G(\mathbb{Q})}(\mathbf{z}\mid\Sigma).$$

The source states that this derivative-free version follows from Modular Schanuel with derivative, so it is a consequence rather than an independent conjectural assumption. Its status is therefore the same unresolved status as the stronger conjecture.