PTG-1: Closure Architecture and the Minimal Phase Manifold

Phase Transport Geometry (PTG) begins from a primitive structural axiom: the existence of an irreducibly collective triplet closure relation. This axiom generates the closure hierarchy (1,2,3) and determines the minimal compact phase manifold capable of supporting independent singlet, doublet, and triplet sectors. Under explicit structural assumptions, we show that this manifold is diffeomorphic to ($S^{1}$)^6 and prove its conditional minimality and uniqueness. PTG-1 provides the geometric foundation for compact transport (PTG-2), the closure-compatible metric (PTG-3), sector structure (PTG-4), defect mass scaling (PTG-5), and the physical interpretation developed in the PDT series.