Mesh-Uniform Scott–Vogelius Stability on Three-Dimensional Freudenthal Meshes for Every Fixed k >= 4

We establish mesh-uniform Scott-Vogelius stability on three-dimensional Freudenthal meshes for every fixed polynomial degree k >= 4. The low-degree cases k = 4 and k = 5 are treated by explicit finite-dimensional constructions and bounded local repair mechanisms, while the k >= 6 regime is connected to the published Zhang framework. The resulting degree split yields a mesh-uniform right inverse of divergence, equivalently a Scott-Vogelius inf-sup constant bounded below independently of the mesh parameter h for every fixed k >= 4. A companion Lean 4 formalization artifact provides machine-checked verification of the new low-degree contribution and theorem-chain integration, conditional on the explicitly named published and standard interfaces documented in the artifact. External specialist review and peer review remain pending.