The ribbon-move equivalence conjecture

Fix a ribbon knot and consider ribbons spanning it. A ribbon 0-move, ribbon 1-move, finger move, and ribbon 3-move are the ribbon transformations described in the paper's figures; they induce, respectively, R0-, R1-, R2-reductions and an R3-transformation on the ribbon graph. Ribbon-move equivalence conjecture. Any two ribbons spanning the same ribbon knot are related up to isotopy by ribbon 0-moves, ribbon 1-moves, finger moves or ribbon 3-moves. If true, this would describe the relationship between all ribbons spanning a fixed ribbon knot and underpins the proposed reduction-based algorithm for computing its Conway-normalized Alexander polynomial.