The Oka-1 conjecture for rationally connected projective manifolds

Let $X$ be a projective manifold that is rationally connected, meaning that any two points of $X$ can be joined by a rational curve. Let Oka-1 denote the property that, for every open Riemann surface, compact Runge set, discrete interpolation sequence, and continuous map holomorphic near the relevant interpolation data, one can find a homotopic holomorphic map with the prescribed approximation and jet interpolation. The Oka-1 conjecture. Every rationally connected projective manifold is Oka-1. This is posed among open problems about weak Oka-1 manifolds; the source provides no resolution of the conjecture.