Nonnegative Laurent expansion conjecture for minors and chamber minors

Let $M$ be a generic square matrix, and let a double wiring diagram be arbitrary. The chamber-minor Laurent positivity conjecture. Every minor of $M$ can be written as a Laurent polynomial with nonnegative integer coefficients in the chamber minors of the diagram.

This refines the known result that every minor has a Laurent-polynomial expression with integer coefficients in the chamber minors. The conjecture strengthens that statement by requiring coefficientwise nonnegativity for every double wiring diagram.