Orbifold Cartan conjecture for ramified holomorphic curves

Let $H_1,\dots,H_q$ be hypersurfaces of degrees $d_i$ in ${\mathbb P}^n$ in general position. Let $f:{\mathbb C}\to{\mathbb P}^n$ be a holomorphic curve that ramifies over $H_i$ with multiplicity divisible by $m_i$.

Orbifold Cartan conjecture. If

$$\sum_i\left(1-\frac{1}{m_i}\right)d_i>n+1,$$

then $f$ is algebraically degenerate, meaning that its image is contained in a proper algebraic hypersurface.

This is the hypersurface formulation of the orbifold Green–Griffiths–Lang conjecture and is presented as an unsolved problem in the paper.