The positivity conjecture for skein partition functions

Let $M$ be a closed, oriented $3$-manifold, and write its skein partition function as an Euler expansion with integer exponents $c_k$. Positivity conjecture for skein partition functions. The skein partition function of any closed oriented $3$-manifold admits an Euler expansion with non-negative exponents $c_k$. This is motivated by a conjectural correspondence between skein modules and cohomological Donaldson–Thomas invariants, whose partition functions have positivity and an intrinsic BPS-cohomological interpretation. The conjecture remains open in the source.