SOX v1.3: Boundary Defense as a Logical Necessity

This release formalizes the first necessity theorem of the SOX framework using Lean 4. Building upon the axioms of solvency and extensivity, we identify the phase leader as the ontological subject of stability and prove that its persistence under volumetric noise requires boundary defense. Using an explicit incompatibility axiom, we demonstrate by contradiction that a solvent, extensive leader cannot coexist with unmitigated volumetric noise. Boundary defense therefore follows as a structural requirement rather than a phenomenological property. Historically associated with the Meissner effect, this exclusion principle is established here as a universal firewall for bulk coherent phases.