Rank one across a checked genus-three/genus-one core cut #
A two-regular genus-one side of a valid core articulation is a pointed rigid cycle after every positive subdivision. The public genus-three rigid-wedge theorem then supplies a degree-three rank-one divisor on the ambient graph.
theorem
Utilities.Certificate.CoreVertexCut.Data.bnExists_one_three_of_left_three_right_rigid
{n p : ℕ}
{spec : SubdivisionGraph.Spec n p}
(cutData : Data spec.core)
(hLeftGenus : cutData.leftGenus = 3)
(hRightRigid : cutData.RightRigidConditions)
:
A genus-three named side and rigid complementary genus-one side give a degree-three pencil on every positive subdivision.