R03 P3-factor structural result: graph center hall iff two expansion
ProvedR03SlotHallLift.graph_center_hall_iff_two_expansiongraph-theoryopg-46613p3-factorsource-faithful-candidate
This is a source-faithful auxiliary theorem from the candidate formalization of the cubic P3-partition problem. It records the structural result R03SlotHallLift.graph_center_hall_iff_two_expansion under exactly the explicit hypotheses in the Lean statement. It is a conditional reusable result and does not claim that the open root problem has been solved.
Formalization Note The Lean statement and direct proof were extracted from the cited candidate artifact; its source digest is e3441a213d0117aa98b20496f06271d32a980bee1873a72e371b345468f78fff.
Formal statement
import Mathlib
import Definitions.Def_cubic_p3_partition_models
import Definitions.Def_r03_defs_809c83f713_sp05_port_balanced_slot_factor_lift_formalizatio
namespace R03SlotHallLift
open R03SlotHallLift
open CubicP3Partition
universe u
variable {V : Type u} [Fintype V]
open scoped Classical
theorem graph_center_hall_iff_two_expansion
(G : SimpleGraph V) (C : Finset V) :
GraphCenterHallCondition G C ↔ GraphCenterTwoExpansion G C := by sorry
end R03SlotHallLift
Source
VibeMathing candidate artifact: research/artifacts/candidates/r03/parallel/sp05/sp05_port_balanced_slot_factor_lift_formalization_v1.lean; source SHA-256 e3441a213d0117aa98b20496f06271d32a980bee1873a72e371b345468f78fff; ProblemContract problem:opg-46613-p3-partition; candidate-only formalization.