R03 P3-factor structural result: star component bound
ProvedR03CubeCenter.star_component_boundgraph-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 R03CubeCenter.star_component_bound 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 5e3825819a34e911d27c7bcebccc36c5404f6fda1b0fcdbf5297ed2560bdae18.
Formal statement
import Mathlib.Data.Fin.VecNotation
import Definitions.Def_r03_defs_ff1c84bf6a_R03CubeCenter_v1
namespace R03CubeCenter
open R03CubeCenter
theorem star_component_bound (k centerEdges freeCycles : Nat)
(h : k≤centerEdges) : k≤centerEdges+freeCycles := by sorry
end R03CubeCenter
Source
VibeMathing candidate artifact: research/artifacts/candidates/r03/R03CubeCenter_v1.lean; source SHA-256 5e3825819a34e911d27c7bcebccc36c5404f6fda1b0fcdbf5297ed2560bdae18; ProblemContract problem:opg-46613-p3-partition; candidate-only formalization.