Conjecture on normals of complete minimal surfaces with planar ends

Let $X:\Sigma\setminus\{p_1,\ldots,p_m\}\to\mathbb{R}^3$ be a complete minimal surface with $m$ embedded planar ends $\{p_1,\ldots,p_m\}$. Let $n_X(p_i)$ denote the normal at the end $p_i$, and set $d=\dim\operatorname{span}\{n_X(p_i):i=1,\ldots,m\}$. Normals-at-the-ends conjecture. The normals at the ends span $\mathbb{R}^3$, that is, $d=3$. This conjecture would imply that the Morse index formula for unbranched Willmore spheres has the expected value for the associated minimal surfaces; the paper proves the assertion when there are four embedded planar ends, but its validity for arbitrary $m$ remains open.