Flat point conjecture for complete minimal surfaces in Euclidean three-space

Let $X$ be a nonflat complete minimal surface in $\mathbf{R}^3$, and let its Gauss map be the map assigning to each point the corresponding unit normal direction. A flat point is a point at which the Gaussian curvature vanishes.

Flat point conjecture. If $X$ has at least one flat point, then its Gauss map omits at most $3$ values.

This conjecture concerns the value-distribution theory of Gauss maps of complete minimal surfaces. The supplied text does not state whether it has been resolved.