The modified Cartan conjecture

In 1928 H. Cartan stated a conjecture about holomorphic curves in $\mathbb{P}^n$ parametrized by the unit disc, omitting $n+2$ hyperplanes in general position. He proved it for $n=2$. In 1996 the first-named author constructed counterexamples for all $n\geq 3$, and proposed a modified form of Cartan