The cell-zeta motivic isomorphism conjecture

Let ${\cal FC}$ be the algebra of formal cell-zeta numbers, let $\zeta_2$ be the element whose period is $\zeta(2)$, and let $\widehat{\mathcal{M}}(\mathbb Z)$ denote the completed algebra of framed mixed Tate motives unramified over $\mathbb Z$. The motivic map $m$ sends formal cell-zeta numbers to framed mixed Tate motives. Cell-zeta motivic isomorphism conjecture. ${\cal FC}$ is a free $\mathbb Q[\zeta_2]$-module, and the induced map

$$m:{\cal FC}/\zeta_2{\cal FC}\longrightarrow \widehat{\mathcal{M}}(\mathbb Z)$$

is an isomorphism. This would identify formal cell-zeta values modulo the weight-two relation with the completed algebra of unramified mixed Tate motives over $\mathbb Z$, giving a motivic description of all cell-zeta relations.