Field-independent minimum rank for extended cube graphs

Let $t$ be an integer satisfying $t\equiv 0,1,2\pmod{6}$, and let $r$ be an integer with $r>\lfloor t/6\rfloor$. The extended cube graphs are denoted by $\operatorname{ECG}(t,6r-t-4)$. Extended-cube conjecture. These graphs have field-independent minimum rank, and their adjacency matrices are universally optimal. This conjecture is proposed as a possible characterization of the extended cube graphs for which maximum nullity equals the zero forcing number over an arbitrary field; equality does not hold for all extended cube graphs, and the conjectured field-independence and universal optimality remain unresolved in the supplied text.