The distinct-factor branch of the genus-two wedge classification

For opposite non-gluing marks, general transmission itself recovers the two factor torsion orders, forces them equal, and identifies the asserted wedge period with that common order.

theorem Bananas.opposite_wedge_kGeneral_factor_orders (G H : CFGraph) (x u : G.V) (y v : H.V) (k : ℕ) (hG : Utilities.PointedGenusOneRigid G x) (hH : Utilities.PointedGenusOneRigid H y) (hu : u ≠ x) (hv : v ≠ y) (hCut : Utilities.TwoEdgeCutCondition (Utilities.vertexWedge G H x y)) (hK : KGeneralTransmission (mark (Utilities.vertexWedge G H x y) (Sum.inl u) (Utilities.wedgeRightVertex G H x y v)) k) : ∃ (a : ℕ), IsTorsionOrder (mark G u x) a ∧ IsTorsionOrder (mark H y v) a ∧ k = a