Waldschmidt's conjecture on algebraic independence of Weierstrass values

Let $\Lambda\subset\mathbb{C}$ be a lattice, let $\lambda\in\Lambda\setminus\{0\}$, and let $\omega\in\mathbb{C}\setminus(\mathbb{Q}\lambda\cup\Lambda)$. Waldschmidt's conjecture. Two among the five numbers

$$g_2,\quad g_3,\quad \wp(\omega),\quad \zeta(\omega)-\frac{\eta(\lambda)}{\lambda}\omega,\quad \frac{\eta(\lambda)}{\lambda}$$

are algebraically independent. This is described as a conjectural generalization of a theorem of Chudnovsky on algebraic independence of elliptic-function values. The source gives no resolution.