Linear independence conjecture for regularized double zeta values with first argument 1

Let $J_{\mathfrak{D}}(1;{\rm odd},{\rm odd})$ denote the regularized double zeta values whose first argument is $1$ and whose remaining arguments are odd. Linear independence conjecture. There are no linear relations among $J_{\mathfrak{D}}(1;{\rm odd},{\rm odd})$'s. This concerns a case not covered by the paper's main theorems; its status is not resolved in the supplied text.