Lara Rodríguez and Thakur's conjecture on zeta-like multizeta values

For a multizeta value $\zeta_{A}(s_{1},\ldots,s_{r})$ of weight $w:=\sum_{i=1}^{r}s_i$, call it zeta-like if the ratio $\zeta_{A}(s_{1},\ldots,s_{r})/\zeta_{A}(w)$ is algebraic over $k$. A multizeta value is Eulerian when its ratio to the corresponding power of the Carlitz period is in $k$. Lara Rodríguez and Thakur's conjecture. If $\zeta_{A}(s_{1},\ldots,s_{r})$ is zeta-like, then

$$\zeta_{A}(s_{2},\ldots,s_{r})$$

is Eulerian. This conjecture concerns the inheritance of Eulerian properties by the tail of a zeta-like multizeta value. The paper applies its main criterion to confirm this conjecture, so the assertion is solved.