Geometric Confinement from Torsion Flux Tubes: An Algebraic Unification of QCD and Gravity

We present a mathematically rigorous geometric unification where gauge fields emerge as componentsof an extended Cartan connection. The key innovation is the introduction of dynamicalcontraction operators Cn[Θn] that selectively couple spacetime torsion to specific gauge sectors. Thisframework naturally explains confinement in QCD as a geometric phenomenon arising from torsion flux tubes, while electroweak sectors remain non-confining due to symmetry breaking. Startingfrom a unified variational principle with exact dimensional consistency, we derive all fundamentalequations – Einstein–Cartan, Yang–Mills, Dirac, and Higgs. The model predicts the Nambu–Gotostring action emerges from transverse integration of localized torsion, exhibits Z3 flux quantization,and matches all lattice QCD predictions with mathematical precision. All gauge sectors are cleanlyseparated through an extended algebraic structure without ad hoc assumptions. The framework employs dimensionless variables to ensure exact dimensional consistency, with all physical predictionsexpressed as dimensionless ratios of natural scales.