  The article is to construct a graded ring isomorphism between
$H_0(ZF(\Delta^{\bullet}_k,\mathbb{G}_m^{\wedge *}))$ and the Milnor-Witt
K-theory ring $K^{MW}_{*\geqslant 0}(k)$, where $k$ is a field of
characteristic zero and $ZF_*(k)$ is the category of linear framed
correspondences of algebraic k-varieties, introduced by Garkusha and Panin. As
it was shown by Garkusha and Panin, this partially recovers the computation of
the motivic cohomotopy groups
${\pi}^{n,n}(\Sigma^{\infty}_{S^1}\Sigma^{\infty}_{\mathbb{G}_m}S^0)(k)$, which
is originally due to Morel.
