The Lazard-ring computation conjecture for local Noetherian rings

Let $A$ be a local Noetherian ring. Write $d53f^*$ for the Lazard ring with cohomological grading. Lazard-ring computation conjecture. The natural map

$$\mathbb{L}^* \to \Omega'^*\big(\operatorname{Spec}(A)\big)$$

is an isomorphism. This conjectural computation extends the known result for fields of characteristic $0$, where it follows from work of Levine, and is a predicted description of the bivariant algebraic cobordism cohomology of the spectrum of a local Noetherian ring.