Kaneko–Zagier isomorphism conjecture for finite multiple zeta values

Let $\FMZ_{w,1}$ be the $\Q$-vector space generated by finite multiple zeta values of weight $w$ and superbity one, and let $\MZV_w$ be the corresponding weight-$w$ space of multiple zeta values. For an index $\bfs=(s_1,\ldots,s_d)$, define the symmetrized shuffle value by

$$\zeta_\sha^\Sy(\bfs)=\sum_{i=0}^d(-1)^{s_1+\cdots+s_i}\zeta_\sha(s_i,\ldots,s_1)\zeta_\sha(s_{i+1},\ldots,s_d),$$

and analogously define $\zeta_*^\Sy(\bfs)$ using the stuffle-regularized values. Kaneko–Zagier conjecture. There is a $\Q$-algebra isomorphism

$$f_{\rm KZ}:\FMZ_{w,1}\longrightarrow \MZV_w/\zeta(2)\MZV_{w-2},\qquad \zeta_{\calA_1}(\bfs)\longmapsto\zeta_\sha^\Sy(\bfs).$$

This proposes a precise correspondence between finite multiple zeta values and symmetrized ordinary multiple zeta values modulo the ideal generated by $\zeta(2)$; the source presents it as an open conjecture.