PTG-4: Sector Structure, Chirality, and Structural Algebras

Phase Transport Geometry (PTG) organises the six phase degrees of freedom on the minimal phase manifold ($S^{1}$)^6 into triplet, doublet, and singlet closure sectors. These sectors support distinct classes of phase defects: collective closure defects in the triplet sector, orientation (chirality) defects in the doublet sector, and winding defects in the singlet sector. Each sector is canonically associated with a structural endomorphism algebra: End($C^{3}$), End($C^{2}$), and C respectively. These algebras classify the internal symmetry of the closure sectors and should not be interpreted as physical gauge groups. PTG-4 develops the geometric and algebraic structure of the closure sectors and states the Sector Algebra Theorem, proved in full in PDT-MC-1.