4 problems

Nuclear-rank conjecture. Every $2$-special group has nuclear rank $0$ or $2$, and its valid children are always $2$-special.

Wide realization conjecture. Every finite $2$-select $2$-group arises as the wide tower group of some cyclic cubic field.

Narrow realization conjecture. Every finite $2$-special $2$-group arises as the narrow tower group of some cyclic cubic field.

Fourth-layer compositum conjecture.