4 problems

Three-solution conjecture. The zero conditions $$ have only the following three sets of solutions:

Twelve-solution conjecture. The zero conditions $$ have only the following twelve sets of solutions:

Nonexistence conjecture for conductor 5. None of the three combined $d$-numbers can satisfy both sets of conditions … .

Discreteness conjecture. This subset is not discrete in $\mathbb{R}$. The claim predicts accumulation among totally ordered algebraic integers satisfying the $d$-number condition;…