The finite Euler sum quotient-space isomorphism conjecture

For $w\in\mathbb{N}$, let $\mathsf{FES}_{w}$ and $\mathsf{ES}_w$ be the $\mathbb{Q}$-vector spaces generated by finite Euler sums and Euler sums of weight $w$, respectively. Let $\zeta_\sharp^{\mathcal S}$ denote the $\sharp$-regularized symmetric Euler sum, where $\sharp=*$ or $\shuffle$. Finite Euler sum isomorphism conjecture. There is an isomorphism

$$f_{\mathsf{ES}}:\mathsf{FES}_{w}\longrightarrow \frac{\mathsf{ES}_w}{\zeta(2)\mathsf{ES}_{w-2}},\qquad \zeta_{\mathcal A}(\boldsymbol{s})\longmapsto \zeta_\sharp^{\mathcal S}(\boldsymbol{s}).$$

This extends the Kaneko–Zagier conjecture to Euler sums, identifying finite Euler sums with a quotient of ordinary Euler sums. Its status is not specified in the source.