The conjecture that every algebraic cobordism module is logarithmic

Let $S\in\mathrm{Rg}$ be a base ring, let $\mathrm{MS}_{\mathrm{Nis}}(S)$ denote the Nisnevich motivic stable category over $S$, and let $\mathbf{MGL}$ be the algebraic cobordism spectrum. An object is logarithmic when it satisfies the logarithmic extension property defined in the paper. Algebraic cobordism module logarithmicity conjecture. Every $\mathbf{MGL}$-module in $\mathrm{MS}_{\mathrm{Nis}}(S)$ is logarithmic. The paper presents this as a consequence that would become reachable if the preceding conjecture on $\mathbf{MGL}$ were proved; no proof or resolution is supplied.