Entire area-minimizing surfaces in $\mathbf{R}^n$ of density two are quadratic or planar

We classify any entire area-minimizing surface $M^2\subset\mathbb{R}^n$ with density $2$ at infinity as either planar, or the zero set of a quadratic holomorphic polynomial inside some affine copy of $\mathbb{C}^2$. We also prove algebraicity of $M^2$ when the tangent cone at infinity has multiplici