PTG-2: Compact Transport Geometry and Curvature Loading

Phase Transport Geometry (PTG) models coherent physical evolution using compact, periodic transport on the minimal phase manifold ($S^{1}$)^6 established in PTG-1. This paper introduces the compact transport potential T($\theta$) = K(1 − cos $\theta$), adopted as the minimal smooth periodic potential satisfying periodicity, symmetry, boundedness, and quadratic behaviour near equilibrium. The associated curvature operator distinguishes local spectral instability from global coherence loading. The separation between the spectral quantity $\lambda$max(K) and the aggregate quantity Tr(K) is a defining structural feature of PTG dynamics. This distinction provides the structural motivation for introducing finite coherence capacity in PDT-I and underlies the mass-scaling and collapse dynamics developed in PTG-5, PDT-II, and PDT-III.