Six closed genus-five constructions from the common positive proof #
The same canonical core weights are used on every face. Finite discrete specialization transports their rank from positive subdivisions to the contracted graph. No row-specific boundary construction is imported here.
theorem
AtanasovRanganathan.GenusFiveTwoPoleClosed.closedConstruction_of_fixed_positive_rank
{n p : ℕ}
(core : Utilities.Certificate.ExplicitPotential.Core n p)
(hNonempty : 0 < n)
(hConnected : core.Connected)
(hLoopless : ∀ (e : Fin p), core.tail e ≠ core.head e)
(weight : Fin n → ℤ)
(hWeight : ∀ (v : Fin n), 0 ≤ weight v)
(hDegree : ∑ v : Fin n, weight v = 4)
(hPositive :
∀ (s : Utilities.Certificate.SubdivisionGraph.Spec n p),
s.core = core → rank s.graph (Utilities.Subdivision.SubdivisionCoreSupport.coreDivisor s weight) ≥ 1)
:
Configurations.ClosedSubdivisionDharConstruction core hNonempty
A fixed nonnegative degree-four weight with positive-subdivision rank one gives a closed-orthant construction by discrete specialization.
Row 01 on its entire genus-preserving closed length orthant.
Row 02 on its entire genus-preserving closed length orthant.
Row 03 on its entire genus-preserving closed length orthant.
Row 04 on its entire genus-preserving closed length orthant.
Row 07 on its entire genus-preserving closed length orthant.
Row 13 on its entire genus-preserving closed length orthant.