Abstract
Phase Transport Geometry (PTG) requires a metric on the minimal phase manifold ()^6 that respects the closure hierarchy established in PTG-1 and the compact transport dynamics introduced in PTG-2. This paper constructs the closure-compatible metric, which projects out closure directions in the triplet and doublet sectors and retains only physically relevant phase differences. The resulting reduced metric defines the primitive curvature scale and provides the geometric backbone for curvature loading, excitation structure, sector organisation (PTG-4), mass scaling (PTG-5), and the physical interpretation developed in the PDT series. A formal uniqueness theorem is stated here and proved in the mathematical closure supplement PDT-MC-1.