Morel's conjecture on rational points in the -homotopy category

Let $F$ be the base field, let $X$ be a smooth variety over $F$, and write

for the MorelVoevodsky homotopy category of schemes over $F$. The set $X(F)$ consists of the $F$-rational points of $X$, and $(,X)$ denotes the morphisms from

to $X$ in this category. Define an equivalence relation on $X(F)$ generated by elementary $^1$-homotopies, namely by pairs $x,y$ for which there exists a morphism $h:\mathbf{A}^1\to X$ with $h(0)=x$ and $h(1)=y$. Morel's conjecture. If $X$ is a smooth variety, the natural map

$$X(F)\to \operatorname{Hom}_{\mathcal{H}(F)}(\operatorname{Spec} F,X)$$

is surjective and identifies the right-hand side with the quotient of $X(F)$ by the equivalence relation generated by

$$(x\sim y)\iff \exists h:\mathbf{A}^1\to X\mid h(0)=x\text{ and }h(1)=y.$$

This conjecture describes morphisms from the point to the $^1$-homotopy category in terms of rational points modulo $^1$-homotopy. The supplied text gives no resolution status, so it remains open here.