PTG-5: Defect Mass Scaling and Return-Closure Invariants

Phase Transport Geometry (PTG) interprets mass as the coherence burden required to sustain a stable compact defect on the phase manifold ($S^{1}$)^6. Earlier papers established the closure hierarchy (PTG-1), compact transport and curvature loading (PTG-2), the closure-compatible metric (PTG-3), and the sector structure and structural algebras (PTG-4). PTG-5 introduces the structural mass functional implied by these geometric and algebraic ingredients. Each factor in the mass expression is motivated by the preceding PTG papers, and the multiplicative structure reflects the independent contributions of closure, winding, loading, excitation mode, sector symmetry, and return-closure invariants.