A1-contractibility conjecture for topologically contractible surfaces

Let $X$ be a smooth topologically contractible surface. Surface contractibility conjecture. The variety $X$ is ${\mathbb A}^1$-contractible if and only if it is isomorphic to ${\mathbb A}^2$. This conjecture proposes that, among smooth topologically contractible surfaces, only the affine plane is ${\mathbb A}^1$-contractible; it would answer the low-dimensional question raised in the survey, and remains open.