Odd-weight evaluation conjecture for multiple $t$-values

Let $t^{\sfrac{1\!}{2}}(2,\{1\}^{2n+1},2)$ denote the multiple $t$-value with the indicated indices, and let $t(k)$ denote the ordinary $t$-value of weight $k$. Odd-weight evaluation conjecture. For every nonnegative integer $n$,

$$t^{\sfrac{1\!}{2}}(2,\{1\}^{2n+1},2)=\frac{4+2n}{2^{3+2n}}t(5+2n).$$

This conjecture gives the odd-weight analogue of the preceding even-weight evaluation. The text notes that the usual symmetry theorem likely cannot establish it because $t(2n+1)$ is conjecturally irreducible, so a new technique is needed.