Well-definedness of Kronheimer–Mrowka's foam evaluation algorithm

Let $F$ be a closed pre-foam. Kronheimer–Mrowka's algorithm defines an element $J^\flat(F)\in \mathbf{k}$ by first resolving seam vertices using a chosen perfect matching when the seam graph is bipartite, and then applying the remaining reduction and evaluation rules.

Kronheimer–Mrowka's well-definedness conjecture. The quantity $J^\flat(F)$ is well-defined: it does not depend on the choices made in the seam-vertex cancellation step.

This asserts that the evaluation algorithm gives an invariant of the closed pre-foam despite the choice of perfect matching used to cancel seam vertices. The supplied text does not state whether this claim has been proved or disproved.