4 problems

Binary-value conjecture. For every fixed positive integer $n$ and every fixed skew-symmetrizer $d_1,\dots,d_n$, the invariant $\delta$ takes only two possible values.

Odd-sign ordering conjecture. There exists a linear ordering $\prec$ such that every oriented chordless cycle $(i_1,\dots,i_d)$ in $B$ has an odd number of positive entries…

Seed dependence conjecture. The $L$-matrix depends, up to signs of its row vectors, only on the seed; equivalently, mutation sequences leading to the same seed yield the same $L$-m…

Skew-symmetrizable periodicity conjecture. The criterion that periodicity of tropical $y$-variables implies periodicity of seeds is also true for skew-symmetrizable $B$.