5 problems

Signed-column conjecture. For all $t\in\mathbb{T}_n$, the matrix $D_t^{B_0;t_0}$ has signed columns.

Sigma denominator-matrix conjecture.

Source-sink denominator recursion conjecture.

Property R conjecture. Property R holds when mutation at $k$ is a source-sink move.

Source-sink recursion conjecture. The initial-seed-mutation recursion holds in the case of source-sink moves in arbitrary cluster algebras.