Noguchi's extension conjecture for holomorphic maps across polar sets

Let $X$ be a Kobayashi hyperbolic compact manifold of dimension $n$. Let ${\mathbb B}$ be the unit ball in $\mathbb C^p$, and let $E$ be a closed polar subset of ${\mathbb B}$. Noguchi's extension conjecture. Every holomorphic map

$$f:{\mathbb B}\setminus E\to X$$

extends holomorphically across $E$. This is an extension problem for maps into compact Kobayashi-hyperbolic manifolds; the source presents it as a conjecture and gives no resolution.