The formal cell-zeta algebra and framed-motive algebra isomorphism conjecture

Let $\mathcal{FC}$ be the algebra of formal cell-zeta numbers, and let $\mathcal{M}(\mathbb{Z})$ be the commutative graded Hopf algebra of equivalence classes of framed mixed Tate motives unramified over $\mathbb{Z}$. For a convergent cohomology class $\omega$, the associated framed motive is $m(\omega)$, and these assignments define a map

$$m:\mathcal{FC}\longrightarrow\mathcal{M}(\mathbb{Z}).$$

The formal cell-zeta isomorphism conjecture. The map $m$ is an isomorphism. This would identify formal cell-zeta values, modulo their motivic relations, with the framed mixed Tate motive algebra; the supplied text gives no resolution.