3 problems

Support conjecture. The complement ${\mathbb R}^6\setminus|{\mathcal F}_{\mathbb Q}(T_0)|$ is the union of the relative interiors of all irrational rays in $P$.

Irrational-ray conjecture. The mutation fan ${\mathcal F}_B$ is the union of ${\mathcal F}_{\mathbb Q}(T_0)$ with the set of all irrational rays in $P$.

Nonnegative-orthant conjecture. The nonnegative orthant $(\mathbb R_{ge0})^n$ is a $B$-cone. This assertion is equivalent, for a given $B$, to the sign-coherence conjecture for pri…