Depth-four classification conjecture for unramified multiple mixed values

Let $M(\bs;\varepsilon)$ denote a multiple mixed value of depth $4$, let $T(\bs)$ denote a multiple t-value, and classify indices as wide, slender, or narrow by whether their largest component is at least $4$, equal to $3$, or at most $2$. Depth-four MMV classification conjecture. In depth $4$, the following list should exhaust all wide or slender unramified MMVs that are neither MZVs nor MtVs:

$$\begin{gathered} M(1,2,4,2;-1,1,1,1),\ M(4,1,2,2;1,-1,1,1),\ M(3,1,1,3;-1,1,1,-1),\\ M(1,4,1,2;1,1,-1,1),\ M(3,2,1,2;1,1,-1,1),\ M(2,2,1,4;-1,-1,1,-1),\\ M(2,3,1,2;1,1,-1,1),\ M(1,2,1,4;1,1,-1,1),\ M(4,1,2,2;-1,1,-1,-1),\\ M(4,2,1,2;1,1,-1,1),\ M(3,3,1,2;1,1,-1,1),\ M(2,4,1,2;1,1,-1,1),\\ M(2,2,1,4;1,1,-1,1),\ M(3,1,2,2;1,-1,1,1),\ T(3,1,1,2),\ T(1,1,3,2). \end{gathered}$$

Moreover, $T(1,1,1,2)$ and $M(1,2,1,2;1,1,-1,1)$ are the only narrow unramified non-MZV and non-MtV elements of depth $4$ besides the three unramified families covered by the cited theorems. The conjecture gives a numerical classification of exceptional depth-four unramified MMVs.