Morel's -invariance conjecture for -connected components

Let $k$ be a field, let $\mathcal{X}$ be a space, and write $\pi_0^{\mathbb{A}^1}(\mathcal{X})$ for its sheaf of $\mathbb{A}^1$-connected components. Morel's conjecture. The sheaf $\pi_0^{\mathbb{A}^1}(\mathcal{X})$ is $\mathbb{A}^1$-invariant for any space $\mathcal{X}$. This predicts that $\mathbb{A}^1$-connected components have the discreteness property expected of ordinary topological connected components. Other than the cases established in the surrounding discussion, the conjecture remains open.