Non-triviality of graded Satake diagrams

A graded Satake diagram is a decorated Dynkin diagram arising in the classification above, with the specified type I or type II $\mathbb{Z}_2$-graded Satake-diagram structure. Non-triviality conjecture. Graded Satake diagrams are non-trivial. This asserts that the classification contains no trivial graded Satake diagrams; the supplied text gives no further resolution or supporting context.